基于Boltzmann输运方程的SPECT系统解析建模方法

Analytical System Modeling Method for SPECT Based on the Boltzmann Transport Equation

在单光子发射断层成像(SPECT)中,为了校正劣化因素的影响,提高图像质量,需要对SPECT成像的物理过程进行准确建模．本文提出了基于Boltzmann输运方程及其Neumann级数解理论的SPECT系统解析建模方法,并采用数论高维数值积分算法对解析建模公式进行数值求解．分别对点源、均匀圆柱体模型和NCAT模型进行SPECT投影过程计算,将其结果与传统的Monte Carlo建模方法进行比较．结果表明解析建模方法的计算速度和精度综合性能优于Monte Carlo建模方法,且具有不受统计噪声影响的优点,因而更适于进行SPECT成像过程的建模．

In single photon emission computed tomography （SPECT）, accurately modeling of the physics of SPECT imaging process is essential to degrading factor compensation and image quality enhancement. In this paper, an analytical SPECT modeling method is proposed based on the theory of the Boltzmann transport equation and its Neumann series solution. The analytical model was numerically evaluated using high dimensional integration algorithm based on number theory. SPECT projection images for both uniform cylinder phantom with point source and NCAT phantom were calculated and compared with those which were generated by conventional Monte-Carlo modeling methods. Results show that the analytical modeling method demonstrates improved performance in computation accuracy and speed relative to the Monte-Carlo method, as well as the advantage that the computational results of the analytical method are free from statistical noise. Therefore, we conclude that the analytical method is more appropriate for modeling the SPECT imaging process than Monte-Carlo modeling methods.