The paper proposes a new algorithm for constructing the velocity field, which is based on the study of the integral functional on the ensemble of trajectories. The resulting analytical representation of the variation of the integral functional gives us the gradient of the investigated functional. It allows to find the desired parameters using gradient methods, which determine the velocity field. This approach allows both optical flow and non-optical flow construction. The proposed algorithm can be used in the analysis of various images, in particular in radionuclide image processing.

The paper considers the problem of gated myocardial perfusion single photon emission computed tomography (SPECT) data processing. An approach to the quantitative analysis of gated myocardial perfusion SPECT data used in software developed in the SPbSU is presented. The article presents and formalizes the complete data processing workflow. All the main tasks of the data processing are considered. Mathematical representation of problem domain objects is presented. A detailed algorithm of the data processing is given. The algorithmis implemented as component of the data processing software suite.

The designed software makes it possible to capture and process data in static, dynamics,tomography and synchronization modes. The data processing allows qualitatively and quantitatively estimate the results of radionuclide studies.Nuclear medicine is a branch of medical science involving the application of radioactive substances in the diagnosis and treatment of disease. The data processing in nuclear medicine is very important for the estimation of the functional status of the various organs and body systems [1-3]. Single-photon emission computed tomography (SPECT) data processing was considered in this work [4]. The main stages of data processing were studied. The purpose of this study was to develop and apply mathematical methods for SPECT data processing.Data processing has been involved the following main stages: data correction [5], tomography reconstruction [6], mathematical modeling of dynamic processes [1-2], calculation of diagnostic parameters, functional images construction [7-9], and three-dimensional visualization.Motion correction in single photon emission computed tomography (SPECT) and dynamic scintigraphy is one of the most important steps of the processing of radionuclide studies. It is impossible to avoid the position changing of the patient or its target organs during data acquisition. Detection and correction of patient motion during the acquisition of diagnostic data were considered. The algorithms of motion correction based on the method of cross-correlation function and optical flow were developed [5][6].A parallel implementation of MLEM using an OpenCL programming language was used for SPECT image reconstruction [10]. This technology allows the program to run on any modern GPU from major manufacturers as nVidia, AMD and Intel.Mathematical models of dynamic processes were suggested that allow determining the velocity field according to given distribution density of radiopharmaceuticals [1,6].Mathematical modeling of static, dynamic and gated processes was considered for quantitative analysis of studies in nephrology, osteology, endocrinology and cardiology.

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