Patent ID: 11899144
Assignee: CZECH TECHNICAL UNIVERSITY IN PRAGUE, INSTITUTE OF EXPERIMENTAL AND APPLIED PHYSICS
Field: Medical technology (Instruments)
Classification: CPC G  A | IPC A  G

Claim 1:
2. The method of improving the positron source position determination in an object investigated by the positron emission tomography according to claim 1 wherein the reconstruction of positions of the source of positrons in the object is performed using the kinematics of positron in flight annihilation with electrons on the basis of the measured energies of the individual pairs of concurrently occurring annihilation photons and of the coordinates of the positions of their registration in the affected detection elements (D1jk) and (D2jk) in the three-dimensional coordinate system according to the relativistic relations resulting from the energy and momentum conservation laws,

cos θ=mc2[(E1+E2)/E1E2]−1, where E1E2=(¼)[(E1+E2)2−(E1−E2)2],

cos ϕ=(E1−E2 cos θ)/[(E1+E2)(E1+E2−2mc2)]1/2,

T+=E1+E2−2mc2,

where E1 and E2 are the measured energies of photons resulting from annihilation of the positron with kinetic energy T+ with an electron that was at rest or in thermal motion,
that are influenced by the Doppler shift, where E1 pertains to the photon with the Doppler shift towards higher energy, E2 towards lower energy, the mc g gives the rest energy of the positron or electron, p+ represents the momentum vector of the annihilating positron, p1 and p2 represent the momentum vectors of each annihilation photon from the pair, θ indicates the angle expressing the non-collinearity of those photons, ϕ the angle between the directions of vectors p1 and p+, while the position of positron annihilation in such an event is determined from the coordinates of the affected detection elements (D1jk) and (D2jk), which in coincidence measure E1 and E2 of the relevant annihilation photons, and the calculated values of T+ and the angles θ and ϕ.