Probabilistic analysis of PET images using informed prior models and machine learning

Introduction: A recent method proposed for probabilistic and quantitative analysis of reconstructed PET images, which uses informed prior information, has the potential as a foundation for quantitative clinical assessments of PET images. This method allows for the assessment of characteristics of the in-vivo activity concentration, such as the probability of finding in-vivo high activity and high contrast. However, the methodology is based on a computationally demanding sampling method, which is not feasible to apply to 3D PET volumes in practice. Therefore, we propose using a novel machine learning method to accurately and quickly compute features of the in-vivo activity distribution.

Methods: A reconstructed PET image can be considered as the result of a convolution of the in-vivo activity concentration of an injected tracer with a point spread function (PSF) and some spatially correlated noise. Information about the in-vivo activity concentration, given a PET image, can be inferred using a probabilistic framework from the a posteriori probability distribution (pd), which is given by the product of a pd representing prior information and a likelihood describing the expected noise using a specific PSF. Unless a very simple prior is used, there is no analytical description of the pd. In such cases, sampling methods can be used to generate a sample of the posterior distribution, which represents a collection of noise-free, sharp images that are all consistent with the prior pd, the forward model, and the noise model. From such a sample, several descriptive features can be computed, such as the probability of the activity level being above a specific threshold and the mean activity concentration.

As an alternative to sampling the posterior pd, which can be computationally intractable in 3D, we suggest using a neural network specifically designed to directly estimate any descriptive feature of the posterior pd without needing to sample the posterior pd. This is achieved by:

• construction of a training dataset consisting of sets of realizations of the prior distribution and a corresponding simulation of a possible reconstructed PET image (using a specific PSF and noise model);

• construction, and training, of a neural network with a specific output layer that ensures that the output of the neural network can describe any continuous or discrete feature.

If the training dataset is large enough and the neural network is general enough, then this type of neural network will produce results that are similar to using a sampling approach, but it will be much faster by many orders of magnitude.

Results: We demonstrate the method for analyzing reconstructed PET images obtained from patients potentially with breast cancer. First, the PSF and noise model are estimated by scanning a known object, a phantom. We then compute the resolution limit achieved with a specific choice of noise model, PSF, and optimal prior model. Then, a realistic prior model is constructed to represent in-vivo high-activity regions indicative of cancer, enabling computation of the probability of locating high activity and high contrast. It is demonstrated how analysis and visualization of the estimated features of the posterior pd, provide the clinical expert with an improved quantitative basis on which the clinical assessment is made.

Conclusions: This study suggests that the use of probabilistic analysis of reconstructed PET images, using informed prior models, can provide a quantitative basis for clinical assessment and potentially allow clinical experts to identify small lesions of high activity tracer concentration that would otherwise be difficult or impossible to assess. By using the proposed machine learning-based method, the probabilistic approach can be applied to 3D PET images with minimal computational effort.