Stochastic dynamic model for estimation of rate constants and their variances from noisy and heterogeneous PET measurements

A method for comparing intra-tumoural radioactivity uptake heterogeneity in preclinical positron emission tomography studies

Background

Non-uniformity influences the interpretation of nuclear medicine based images and consequently their use in treatment planning and monitoring. However, no standardised method for evaluating and ranking heterogeneity exists. Here, we have developed a general algorithm that provides a ranking and a visualisation of the heterogeneity in small animal positron emission tomography (PET) images.

Methods

The code of the algorithm was written using the Matrix Laboratory software (MATLAB). Parameters known to influence the heterogeneity (distances between deviating peaks, gradients and size compensations) were incorporated into the algorithm. All data matrices were mathematically constructed in the same format with the aim of maintaining overview and control. Histograms visualising the spread and frequency of contributions to the heterogeneity were also generated. The construction of the algorithm was tested using mathematically generated matrices and by varying post-processing parameters. It was subsequently applied in comparisons of radiotracer uptake in preclinical images in human head and neck carcinoma and endothelial and ovarian carcinoma xenografts.

Results

Using the developed algorithm, entire tissue volumes could be assessed and gradients could be handled in an indirect manner. Similar-sized volumes could be compared without modifying the algorithm. Analyses of the distribution of different tracers gave results that were generally in accordance with single plane preclinical images, indicating that it could appropriately handle comparisons of targeting vs. non-targeting tracers and also for different target levels. Altering the reconstruction algorithm, pixel size, tumour ROI volumes and lower cut-off limits affected the calculated heterogeneity factors in expected directions but did not reverse conclusions about which tumour was more or less heterogeneous.

Conclusions

The algorithm constructed is an objective and potentially user-friendly tool for one-to-one comparisons of heterogeneity in whole similar-sized tumour volumes in PET imaging.

Regional compensation for statistical maximum likelihood reconstruction error of PET image pixels

In positron emission tomography (PET), there is an increasing interest in studying not only the regional mean tracer concentration, but its variation arising from local differences in physiology, the tissue heterogeneity. However, in reconstructed images this physiological variation is shadowed by a large reconstruction error, which is caused by noisy data and the inversion of tomographic problem. We present a new procedure which can quantify the error variation in regional reconstructed values for given PET measurement, and reveal the remaining tissue heterogeneity. The error quantification is made by creating and reconstructing the noise realizations of virtual sinograms, which are statistically similar with the measured sinogram. Tests with physical phantom data show that the characterization of error variation and the true heterogeneity are possible, despite the existing model error when real measurement is considered.

Error-corrected estimation of regional kinetic parameter histograms directly from pet projections

Positron emission tomography (PET) is a unique method to investigate physiology in the living body. Kinetic models with kinetic rate constants describe the dynamic radioactive tracer uptake in living tissue. If the variation of the kinetic parameter values within a specific tissue region could be determined accurately, it would give valuable quantitative information about the tissue heterogeneity. In this study we developed a unique method to estimate the variation from the regional kinetic parameter histograms. To determine the kinetic parameter values, we chose non-penalized maximum likelihood (ML) estimation due to the specific statistical error properties of the ML estimates. The parameter values were estimated directly from the time series of PET projections. The choice of the estimation method enabled us to utilize the ML theory in error correction. We developed a Monte Carlo approach to determine the regional error distributions. The true variation of the kinetic parameters could then be revealed by correcting the regional ML estimate histograms with the estimated error distributions. The method was tested with simulated data. In simulations both the average and the deviation of the kinetic parameters were determined from the error-corrected histograms with good numerical accuracy for the selected region of interest.