An improved optimization algorithm of the three-compartment model with spillover and partial volume corrections for dynamic FDG PET images of small animal heartsin vivo

Abstract

The 3- Compartment model with spill-over (SP) and partial volume corrections (PV) has been widely used for noninvasive kinetic parameters study for dynamic FDG PET images of small animal heart in vivo. However, the approach still suffers from the estimation uncertainty or slow convergence caused by the commonly used optimization algorithms. The aim of the study was to develop an improved optimization algorithm with better estimation performance. Femoral artery blood samples, image derived input functions (IDIFs) from heart ventricles and myocardial time-activity curves (TACs) were derived from sixteen C57BL/6 mice data obtained from the UCLA Mouse Quantitation Program. Parametric equations of the average myocardium and the blood pool TACs with SP and PV corrections in a 3-compartment tracer kinetic model were formulated. A hybrid method integrating Artificial Immune System (AIS) and Interior-Reflective Newton (IRN) method were developed to solve the equations. Two penalty functions and one late time point tail vein blood sample were used to constrain the objective function. The estimation accuracy of the method was validated by comparing results with experimental values using the errors in the areas under the curves (AUC) of model corrected input function (MCIF) and the 18F-FDG influx constant Ki. Moreover, the elapsed time was used to measure the convergence speed. The overall AUC error of MCIF for 16 mice averaged -1.4±8.2%, with correlation coefficients of 0.9706. Similar result can be seen in overall Ki error percentage, which was 0.4±5.8% with correlation coefficient of 0.9912. The t-test P value for both showed no significant difference. The mean and standard deviation of MCIF AUC and Ki percentage errors have lower values compared to the previously published methods. The computation time of the hybrid method is also several fold lower than using just stochastic algorithm. The proposed method significantly improved the model estimation performance in terms of the accuracy of the MCIF and Ki, as well as the convergence speed.

Low-Dose Imaging in a New Preclinical Total-Body PET/CT Scanner

“…Using the formalism developed in Zhong et al (33), Zhong and Kundu, (34), Li et al (35), and Li and Kundu. (36), a 3-compartment kinetic model that can simultaneously correct for SP and PV effects for both the blood pool and myocardium, generate a model corrected blood input function (MCIF) and compute kinetic rate parameters (K1-k3), was used to compute rate of myocardial FDG uptake, Ki (35). The above analysis was performed using the MATLAB_r2018a (Mathworks Inc., Natick MA) computing environment.…”

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Enhanced Extraction of Blood and Tissue Time-Activity Curves in Cardiac Mouse FDG PET Imaging by Means of Constrained Nonnegative Matrix Factorization

“…This model, while satisfactorily describing the spillover issues, tries to estimate 15 parameters simultaneously by minimizing a constrained objective function and, as such, may lead to uncertainty in parameter estimation. Li and Kundu have developed a hybrid optimization method based on the artificial immune system algorithm to reduce the uncertainty caused by guess values in simultaneous estimation models [ 16 ]. Locke et al [ 17 ] applied the ordered subset expectation maximization—maximum a posteriori algorithm and “froze” the heart around the diastolic phase to reduce the cross-contamination between LVC and myocardium and then boosted the obtained TACs by a predetermined RC.…”