Reconstructing time-varying position of individual radioactive cells directly from positron emission tomography (PET) measurements
View Patent ↗A method of reconstructing time-varying position of individual radioactive point sources directly from Positron Emission Tomography (PET) measurements is provided that includes using a PET scanner to acquire list-mode coincidence events of a moving radioactive point source, using an appropriately programmed computer to model a trajectory of the moving radioactive point source as a 3D function of a temporal variable, then apply an optimization procedure to find the trajectory that minimizes a distance between the trajectory and the recorded list-mode coincidence events, and using the PET scanner to output a real time position of the radioactive point source.
1. A method of reconstructing time-varying positions of an individual radioactive cell, comprising:
a. transplanting to a human or animal host a radioactive cell;
b. acquiring a positron emission tomography (PET) scan, using a PET scanner, of said human or said animal host to obtain a list of coincidence events containing lines and corresponding timestamps;
c. using a computer to:
i. model a time-varying position of said radioactive cell as a 3D function of a temporal variable;
ii. determining an average distance for different parameters of said 3D function, wherein said average distance is determined by computing a geometrical distance between one said line in said list of coincidence events and a 3D position given by said 3D function for said timestamp corresponding to said one line, wherein an average of all said computed geometrical distances is computed;
iii. iteratively repeating said modeling step i) and said average distance determination of step ii) until said average distance converges to a minimum distance; and
d. reconstructing a time-varying position of said radioactive transplanted cell, using said PET scanner, by outputting said 3D function of said temporal variable of said reconstructed time-varying position of said transplanted radioactive cell, wherein said reconstructed time-varying position provides an estimate of individual cell migration in real time inside said human or animal host.
2. The method of claim 1 , wherein said 3D function comprises a B-spline function of said temporal variable.
3. The method according to claim 1 , wherein a regularization term is added to said geometrical distance to favor desirable trajectories over undesirable trajectories, wherein if no said list of coincidence events are detected over a pre-defined time interval, a shortest trajectory is selected from available said list of coincidence events.
4. The method of claim 1 , wherein said geometrical distance comprises a mean-square distance.
5. The method according to claim 1 , wherein said computing a geometrical distance comprises assigning a constant value to events that have a geometrical distance greater than a predefined distance d max .