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Mathematical Models for Nuclear Medicine


Development and Application of Mathematical Modeling for Nuclear Medicine Dynamic Studies

Tech Area / Field

  • INF-SOF/Software/Information and Communications

3 Approved without Funding

Registration date

Leading Institute
NIIIT (Pulse Techniques), Russia, Moscow

Supporting institutes

  • VNIIEF, Russia, N. Novgorod reg., Sarov\nCancer Research Center, Russia, Moscow


  • Siemens AG / Medical Engineering Group, Germany, Erlangen\nLawrence Livermore National Laboratory / University of California, USA, CA, Livermore

Project summary

Nuclear medicine is one of the most important parts of clinical medicine. The main point of this method consists in an administration of radiopharmaceuticals into a patient's organism with the following registration of 2D or 3D radiotracer distribution in time by gamma-radiation position sensitive detector. Obtained static images of a studied organ give information of existence and size of pathological domain with abnormal radiopharmaceuticals accumulation. Dynamic studies can also give information on target organ functional status, because the observed set of gamma-chronogramms reflects the process of radioactivity changes in time for selected regions of interest.

As a rule, empirical and subjective techniques for gamma-chronogramms processing are widely used in practical medicine. But traditional approaches are ungrounded, so they lead to significant errors in diagnostic parameter estimation. This problem could be solved with the help of a priori information on the radiopharmaceutical transport in a patient's organism. This information is formalized as a mathematical model reflected radiotracer kinetics. The unknown parameter identification problem consists in estimation of the parameter vector, which yields the best fit between the model outputs, and the measured curves. Estimated physiological-based parameters describe functional status of a studied organ or system.

A new approach to nuclear medicine diagnostics on the basis of mathematical modeling of radiopharmaceutical kinetics is the main objective of the proposed project.

The project's actuality is dictated by the nonuniform advancement of different stages in the field of nuclear medicine technology. On the one hand, development of equipment for measurement and data registration methods has received primary emphasis, especially in the work of the leading foreign firms implementing nuclear medicine equipment. On the other hand, a very important for diagnostics stage of measured data mathematical processing is characterized by low scientific level. So it is the main reason of low accuracy and significant errors of diagnostics. This problem becomes more complex in the case when the diagnostic technique with inadequate processing is used in a large number of clinics for a lot of patents.

The project's scientific novelty consists in:

- development of the mathematical models with optimal structure for liver and bone nuclear medicine studies, as well as for organic and tissue hemodynamics studies;
- development of software package for new physiologically based parameter identification, that makes it possible to obtain unique diagnostic information;
- application of methods of differential equations with partial derivatives that were not used for these purposes previously, this approach helps to closely approximate formalized description of radiotracers transport to real processes, as well as to obtain unique information on the physiological parameters changes in space.
- development of algorithms and software for functional images generation in the terms of different diagnostic parameters;
- design of a universal dynamic phantom for testing of created mathematical models adequacy and validity based on physical modeling of radiopharmaceuticals transport.
- development of mathematical models for nuclear medicine dynamic studies of main organs and physiological systems (liver, bone and tissue hemodynamics);
- development of practical recommendations on the base of the unique calculations using with the help of created programs;
- verification of theoretical results by the dynamic phantom.

As a result Technical Proposals (TP) for commercial software version development will be made, that makes the created models implementation in wide clinical practice possible.

It is important that the project allows to solver a set of real clinical problems, in particular, in the field of clinical oncology, where the project's results can solve such problems as:

1) revealing of hemiliepatoectomy indications and contraindications for tumor or liver metastasis patients according to nuclear medicine studies of liver functional condition;
2) proper correction of radiation therapy or chemotherapy assessed course for tumor metastasis patients (various localization of tumors) according to series of nuclear medicine studies;
3) optimization of plan for precision treatment on cell level in post-operation period after hemihepatoectomy according to nuclear medicine studies of different liver structural components functional condition;
4) exact determination of amputation borders for osteogenic sarcoma of inferior limb patients according to nuclear medicine bone functional studies (metabolic parameters of sarcoma's biological activity) whereas traditional diagnostic methods allow to reveal more narrow zone of structural bone destruction, so proposed approach gives possibilities to prevent metastasis and relapses appearance after operation;
5) the possibility determination for amputation of inferior limb with osteogenic sarcoma to be refused after neoadjuvant chemotherapy, depending on its efficiency, according to nuclear medicine bone studies;
6) estimation of biological activity for primary bone tumors to predict the pathological process course according to nuclear medicine bone studies;
7) determination of suitableness of skin flap for reconstructive mammaplasty (bioprosthetics) after mastectomy according to nuclear medicine studies of microcirculation in flap;
8) planning of optimal post-operation treatment and rehabilitation for osteogenic sarcoma patients according to nuclear medicine studies of microcirculation in stump.

Potential role of foreign collaborators:

Foreign collaborators support the main ideas of the proposed project, which gives greater opportunities for nuclear medicine, and confirm actuality and practical implementation of the project. They are interested in the application of the expected results in software packages for standard nuclear medicine equipment and clinical patients’ studies especially oncological ones. Foreign collaborators participate in the discussion of theoretical and technical problem solution proposed by the authors of the project.


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