Reconstruction of positron emission tomography images using adaptive sliced remeshing strategy.

Purpose: The reconstruction of positron emission tomography images is a computationally intensive task which benefits from the use of increasingly complex physical models. Aiming to reduce the computational burden by means of a reduced system matrix, we present a list mode reconstruction approach based on maximum likelihood-expectation maximization and a sliced mesh support. Approach: The reconstruction strategy uses a fully 3D projection along series of 2D meshes arranged in the axial plane of the scanner. These series of meshes describe the continuous volumetric activity using a piece-wise linear function interpolated from the mesh elements. The mesh support is automatically adapted to the underlying structure of the activity by means of a remeshing process. This process finds a high-quality compact mesh representation constrained to a controlled interpolation error. Results: The method is tested using a Monte Carlo simulation of a Hoffman brain phantom and a National Electrical Manufacturers Association image quality phantom acquisition, using different sets of statistics. The reconstructions are compared against a voxelized reconstruction under different conditions, achieving similar or superior results. The number of parameters needed to reconstruct the image in voxel and mesh support is also compared, and the mesh reconstruction permits to reduce the number of nodes used to represent a complex image. Conclusions: The proposed reconstruction strategy reduces the number of parameters needed to describe the activity distribution by more than one order of magnitude for similar voxel size and with similar accuracy than state-of-the-art methods.

Phototransduction early steps model based on Beer-Lambert optical law.

The amount of available rhodopsin on the photoreceptor outer segment and its change over time is not considered in classic models of phototransduction. Thus, those models do not take into account the absorptance variation of the outer segment under different brightness conditions. The relationship between the light absorbed by a medium and its absorptance is well described by the Beer-Lambert law. This newly proposed model implements the absorptance variation phenomenon in a set of equations that admit photons per second as input and results in active rhodopsins per second as output. This study compares the classic model of phototransduction developed by Forti et al. (1989) to this new model by using different light stimuli to measure active rhodopsin and photocurrent. The results show a linear relationship between light stimulus and active rhodopsin in the Forti model and an exponential saturation in the new model. Further, photocurrent values have shown that the new model behaves equivalently to the experimental and theoretical data as published by Forti in dark-adapted rods, but fits significantly better under light-adapted conditions. The new model successfully introduced a physics optical law to the standard model of phototransduction adding a new processing layer that had not been mathematically implemented before. In addition, it describes the physiological concept of saturation and delivers outputs in concordance to input magnitudes.