Positron range reduction in positron emission tomography imaging
AssigneeParto Negar Persia Co.
InventorsHojjat Mahani, Mustafa Abbasi, Mohammad Reza Ay, Saeed Sarkar, Mohammad Hossein Farahani
Life of this patent
Estimating the term…
Abstract
Methods and systems are disclosed, including a method for confining an annihilation range of a positron, from a plurality of positrons emitted from an object being imaged in a positron emission tomography (PET) imaging system. Confining the annihilation includes applying a stochastic multidimensional time varying magnetic field on the positron. Optionally, the stochastic multidimensional time varying magnetic field includes components in each of three dimensions.
Claims17
A method for confining an annihilation range of a positron from a plurality of positrons emitted from an object being imaged in a positron emission tomography (PET) imaging system, the method comprising applying a stochastic time-varying multidimensional magnetic field on the positron, wherein the stochastic time-varying multidimensional magnetic field is according to the following:
- B
- i
-
- (
- t
- )
- =
- B
- 0
-
- ∑
- n
- =
- 0
- ∞
-
- sgn
-
- (
- N
- i
-
- (
- nT
- )
- )
-
- rect
-
- (
- t
- -
- nT
- T
- 1
- )
- ,
- where i=1, 2, 3 is a spatial component of the stochastic time-varying multidimensional magnetic field;
- t is a time instant;
- B0 is an amplitude of the stochastic time-varying multidimensional magnetic field in the spatial component;
- sgn is a sign function;
- Ni(t) is a stochastic process with a uniform distribution with a range of [−½,½] in the spatial component i;
- rect is a rectangular function;
- T=2π/ω is a time period of the stochastic time-varying multidimensional magnetic field, where co is an angular frequency of the stochastic time-varying multidimensional magnetic field;
- and
- T1=T/2 is a width of the rectangular function, wherein the angular frequency and the amplitude of the stochastic time-varying multidimensional magnetic field are configured such that the following conditions are satisfied:
- ω>>2πλ and ω>>2π/τthermalization and ω>>>ωc and
- ω
- c
- ω
-
- R
- L
- ⪡
- L
- T
-
-
- and
-
-
- v
- initial
-
- 2
-
- π
- ω
- ⪡
- L
- T
- ,
- where λ is an annihilation rate of the positron;
- τthermalization is a thermalization time of the positron;
- LT is a transport length of the positron;
- νinitial is an initial velocity of the positron;
- and
- RL is a relativistic positron gyro radius defined by the following:
- R
- L
- =
- 1
- ω
- c
-
- (
- 1
- -
- m
- positron
- 2
-
- C
- 4
- (
- E
- +
- m
- positron
-
- C
- 2
- )
- 2
- )
- 1
- /
- 2
-
- C
- ,
- where mpositron is mass of the positron;
- C is the speed of light;
- E is the kinetic energy of the plurality of positrons;
- and
- ωc is a relativistic gyro frequency according to the following:
- ω
- c
- =
- eB
- 0
- γ
-
-
- m
- positron
- ,
- where e is the elementary charge and γ is the Lorentz factor.
A method for confining an annihilation range of a positron from a plurality of positrons emitted from an object being imaged in a positron emission tomography (PET) imaging system, the method comprising applying a stochastic magnetic field on the positron,
- wherein applying the stochastic-magnetic field includes applying a time-varying magnetic field.
A system for confining an annihilation range of a positron from a plurality of positrons emitted from an object being imaged by positron emission tomography (PET) imaging, the system comprising a magnetic field supplier configured to apply a stochastic time-varying multidimensional magnetic field on the positron.
A method for confining an annihilation range of a positron from a plurality of positrons emitted from an object being imaged in a positron emission tomography (PET) imaging system, the method comprising:
- creating, at a time t, the positron at a position within the object;
- and
- over a time period extending from t, confining the annihilation range along each of three mutually orthogonal reference axes that extend from the position, wherein the controllable confining includes:
- applying, for each of the three mutually orthogonal reference axes a stochastic time-varying multidimensional magnetic field, over the time period, the field having a spatial component along each of the three mutually orthogonal reference axes, each spatial component having an amplitude, wherein:
- each amplitude, at t, is based at least in part on a running sum of n products, n ranging from 0 to infinity,
- the elements of each of the products include a sgn of a stochastic process at a time nT, corresponding to the reference axis,
- the elements of each of the products further include a rectangle function of an argument that includes t and nT,
- T is a duration that is based, at least in part, on an angular frequency of the time-varying stochastic magnetic field,
- the angular frequency is greater than an annihilation rate of the positron, scaled by a constant, and is greater than an inverse of a thermalization time of the positron scaled by the constant
- the angular frequency is much greater than a relativistic gyro frequency of the positron,
- a ratio of the angular frequency to the relativistic gyro frequency of the positron is greater than a ratio of a relativistic gyro radius of the positron to a transport length of the positron, and
- the relativistic gyro radius of the positron is based, at least in part on a combination that includes, concurrently, all among a mass of the positron, the speed of light, a relativistic gyro frequency of the positron, and a kinetic energy of the positron.
Dependencies are inferred from the claim text.