Adaptation of the modified Bouc-Wen model to compensate for hysteresis in respiratory motion for the list-mode binning of cardiac SPECT and PET acquisitions: testing using MRI

Purpose: Binning list-mode acquisitions as a function of a surrogate signal related to respiration has been employed to reduce the impact of respiratory motion on image quality in cardiac emission tomography (SPECT and PET). Inherent in amplitude binning is the assumption that there is a monotonic relationship between the amplitude of the surrogate signal and respiratory motion of the heart. This assumption is not valid in the presence of hysteresis when heart motion exhibits a different relationship with the surrogate during inspiration and expiration. The purpose of this study was to investigate the novel approach of using the Bouc–Wen (BW) model to provide a signal accounting for hysteresis when binning list-mode data with the goal of thereby improving motion correction. The study is based on the authors’ previous observations that hysteresis between chest and abdomen markers was indicative of hysteresis between abdomen markers and the internal motion of the heart. Methods: In 19 healthy volunteers, they determined the internal motion of the heart and diaphragm in the superior–inferior direction during free breathing using MRI navigators. A visual tracking system (VTS) synchronized with MRI acquisition tracked the anterior–posterior motions of external markers placed on the chest and abdomen. These data were employed to develop and test the Bouc–Wen model by inputting the VTS derived chest and abdomen motions into it and using the resulting output signals as surrogates for cardiac motion. The data of the volunteers were divided into training and testing sets. The training set was used to obtain initial values for the model parameters for all of the volunteers in the set, and for set members based on whether they were or were not classified as exhibiting hysteresis using a metric derived from the markers. These initial parameters were then employed with the testing set to estimate output signals. Pearson’s linear correlation coefficient between the abdomen, chest, average of chest and abdomen markers, and Bouc–Wen derived signals versus the true internal motion of the heart from MRI was used to judge the signals match to the heart motion. Results: The results show that the Bouc–Wen model generated signals demonstrated strong correlation with the heart motion. This correlation was slightly larger on average than that of the external surrogate signals derived from the abdomen marker, and average of the abdomen and chest markers, but was not statistically significantly different from them. Conclusions: The results suggest that the proposed model has the potential to be a unified framework for modeling hysteresis in respiratory motion in cardiac perfusion studies and beyond.