An application of the fast combinatorial non-negative least squares (FC-NNLS) method in parametric image generation of dynamic PET study

Objectives Voxel-based parametric image generation in dynamic PET data analysis has been based on linearizing the kinetic models, usually applying basis function method. However, in the estimation of parameters in non-constrained linear system, negative values occur very often leading to noisy parametric images. Since all physiological parameters are non-negative, nonnegative least squares (NNLS) method is proposed. Furthermore, voxel-based dynamic PET needs fast procedures to reduce the computing burden. In this study, we validated a novel-developed fast non-negative-constrained least squares method (FC-NNLS, van Benthem 2004) in a dynamic PET study.

Methods When linearizing a conventional 1-tissue compartment model, a linear system can be set up as AX=B, where A is a matrix of model coefficients, X is a matrix of model parameters and B is a matrix of voxel radioactivity. This is a typical multi-RHS (right-hand-side) system with large number of observation vectors. FC-NNLS algorithm reduces substantially the computational burden for large-scale data by calculating the pseudoinverse matrix of main matrix A only once. Data from ten healthy and unhealthy subjects from 15O-labelled water perfusion studies are used in this study. Dynamic data were analyzed in two ways: 1) conventional ROI-basedand 2) parametric image generation using FC-NNLS method.

Results The cardiac blood flow is highly correlated (r=0.93) between the ROI-based analysis and the FC-NNLS method. Computational time for generating parametric image with FC-NNLC on current typical PC (dual CPU, 16MB RAM, windows XP/7) is less than one minute for a typical dynamic PET study data set (128*128*64 with 24 frames). It meets the requirement in practice.

Conclusions The novel algorithm of non-negative-constrained least squares method, named FC-NNLS is validated in cardiac PET perfusion study for parametric image generation.This algorithm will be applied to 2-tissue compartment model in the future