Method for determining parameters of a reaction of a gamma quantum within a scintillator of a PET scanner

Abstract

A method for determining parameters of a reaction of a gamma quantum within a scintillator of a PET scanner, comprising transforming a signal measured in the scintillator using at least one converter into an electric measurement signal, wherein the method comprises the steps of: obtaining access to a reference parameters memory (10) comprising reference signals represented in a time-voltage (Wt-v) coordinate system and in a time-amplitude fraction (Wt-f) coordinate system and having associated reaction parameters; sampling the electric measurement signal (S) measured in the time-voltage (PT-V) coordinate system and in the time-amplitude fraction (Pt-f) coordinate system; comparing results of the sampling (PT-V, PM) of the electric measurement signal (S) with the reference signals (Wt-V, Wt-f) and selecting reference shape parameters so that the reference (W) is best fitted to the results of the sampling (PT-V, PM) of the electric measurement signal (S); and determining the parameters of the reaction of the gamma quantum within the scintillator (1) for the electric measurement signal (S) based on pre-calibrated functions that determine the values of parameters of signal shape depending on the parameters of the reaction of gamma quantum within the scintillator.

Claims

1. A method for determining parameters of a reaction of a gamma quantum within a scintillator of a Positron Emission Tomography (PET) scanner, comprising transforming a signal measured in the scintillator using at least one converter into an electric measurement signal, wherein the method comprises the steps of: obtaining access to a reference parameters memory comprising reference signals represented in a time-voltage (W.sub.t-v) coordinate system and in a time-amplitude fraction (W.sub.t-f) coordinate system and having associated reaction parameters; sampling the electric measurement signal (S) measured in the time-voltage (P.sub.t-v) coordinate system by means of a multithreshold leading edge discriminator and sampling the electric measurement signal (S) measured in the time-amplitude fraction (P.sub.t-f) coordinate system by means of multithreshold constant fraction discriminator; comparing results of the sampling of the electric measurement signal (S) measured in the time-voltage (P.sub.t-v) coordinate system with the reference signals represented in the time-voltage (W.sub.t-v) coordinate system; comparing results of the sampling of the electric measurement signal (S) measured in the time-amplitude fraction (P.sub.t-f) coordinate system with the reference signals represented in the time-amplitude fraction (W.sub.t-f) coordinate system; selecting reference shape parameters so that the reference (W) is best fitted to the results of the sampling of the electric measurement signal (S) in the time-voltage (P.sub.t-v) coordinate system and in the time-amplitude fraction (P.sub.t-f) coordinate system; and determining the parameters of the reaction of the gamma quantum within the scintillator for the electric measurement signal (S) based on pre-calibrated functions that determine the values of parameters of signal shape depending on the parameters of the reaction of gamma quantum within the scintillator; wherein the parameters of the reaction of the gamma quantum include energy deposited within the scintillator and a position and a time of the reaction.

2. The method according to claim 1 wherein the fit quality is determined from the minimum chi-square value (χ.sup.2.sub.min).

3. A system for determining parameters of a reaction of a gamma quantum within a scintillator of a Positron Emission Tomography (PET) scanner wherein the signal measured in the scintillator is transformed using at least one converter into an electric measurement signal (S), the system comprising a reference parameters memory comprising reference signals in a time-voltage (W.sub.t-v) coordinate system and in a time-amplitude fraction (W.sub.t-f) coordinate system along with reaction parameters assigned to the reference signals; a multithreshold leading edge discriminator configured to sample the electric measurement signal (S) in the time-voltage (P.sub.t-v) coordinate system; a multithreshold constant fraction discriminator designed to sample the electric measurement signal (S) in the time-amplitude fraction (P.sub.t-f) coordinate system; a comparator configured to: compare the results of the sampling of the electric measurement signal (S) measured in the time-voltage (P.sub.t-v), coordinate system with the reference signals represented in the time-voltage (W.sub.t-v) coordinate system; compare the results of the sampling of the electric measurement signal (S) measured in the time-amplitude fraction (P.sub.t-f) coordinate system with the reference signals represented in the time-amplitude fraction (W.sub.t-f) coordinate system; select the parameters determining the shape of the reference (W) that are best fitted to the results of the sampling of the electric signal (S) in the time-voltage (P.sub.t-v) coordinate system and in the time-amplitude fraction (P.sub.t-f) coordinate system; and determine the parameters of the reaction of the gamma quantum within the scintillator from pre-calibrated functions that determine the values of parameters of signal shape depending on the parameters of the reaction of the gamma quantum within the scintillator, wherein the parameters of the reaction of the gamma quantum include energy deposited within the scintillator and a position and a time of the reaction.

Description

BRIEF DESCRIPTION OF FIGURES

(1) Example embodiments are presented on a drawing wherein:

(2) FIG. 1 presents the outline of an example detection system;

(3) FIGS. 2A and 2B present the sampling in voltage and amplitude fraction domains;

(4) FIG. 3A-3D compare the effects of sampling in voltage and amplitude fraction domains;

(5) FIG. 4 presents the effect of the distance between the place of the reaction and the converter on the signal profile;

(6) FIG. 5 presents an example strip detector;

(7) FIG. 6 presents example detector responses for three different places of reactions of a gamma quantum within the scintillator.

DETAILED DESCRIPTION

(8) FIG. 1 presents the outline of the detection system. The system comprises scintillator 1 and converter 2 that converts the light signals from the scintillator into electric signals S. The electric signals S are delivered to multifractional constant fraction discriminator 3 and a multithreshold leading edge discriminator 4. Discrimination of signals is carried out with respect to a triggering signal generated by the triggering system 5. In addition, the system consists of a TDC converter 6, an ADC converter 7 and a computer 12 comprising a threshold setting and data readout system 8 used to define thresholds at discriminators 3, 4 and to read the data delivered from the TDC converter 6 and the ADC converter 7. In addition, computer 12 comprises a comparator 9 that collects and compares information from the threshold setting and data readout system 8 and the reference parameters memory 10, allowing to determine the similarity of data and thus to obtain the parameters 20. The entire process is described in more detail below.

(9) FIG. 2A presents the sampling of the signal in the voltage domain using a multithreshold (n-threshold) leading edge discriminator 4, while FIG. 2B presents the sampling of the signal in the amplitude fraction domain using a multifractional (m-fractional) constant-fraction discriminator 3. Simultaneous sampling of the signal in both domains facilitates precise determination of the position and the time of the interaction between the gamma quantum and the scintillator strip as well as determination of the energy deposited by the gamma quantum within the scintillator. The reconstruction method transforms the defect consisting in a variation in signal shape and amplitude dependent on the distance between the place of ionization and the photomultiplier (cf. FIG. 4) to an advantage facilitating reconstruction of said place on the basis of said variation. The method for reconstructing the ionization place was developed on the basis of the following findings: (a) the shape of the light signal (number of photons as a function of time) at the ionization place does not depend on the place of reaction of the gamma quantum; (b) the signal amplitude increases monotonously with the energy deposited by the gamma quantum; (c) the shape of the light pulse reaching the photomultiplier depends on the distance between the ionization place and the photomultiplier; (d) the image of the signal sampled within the amplitude fraction domain does not depend on the shape of that signal; (e) the image of the signal sampled within the voltage domain depends on both the amplitude and the shape of the signal (FIG. 3).

(10) Characteristics (a) and (b) are commonly known and require no explanation.

(11) Characteristic (c) is derived from observation that photons diverge at different angles from the place of pulse generation and therefore the distances (and thus times) traveled by individual photons from the ionization place to the photomultiplier depend on the angle of photon emission.

(12) Characteristics (d) and (e) were concluded from the fact that the output of the leading edge discriminator preset with the reference voltage of V.sub.0 is time “t” being the solution of the equation V(t)=V.sub.0, where V(t) is the voltage vs. time relationship (signal shape—solid line in FIG. 2). At the same time, a constant-fraction discriminator provides a value of variable “t” that “solves” the equation V(t)=f.Math.A where A is the signal amplitude and f is the fraction set at the discriminator. For a particular pulse shape, e.g. g(t), the function of amplitude may be expressed as: V(t)=A.Math.g(t). This means that given a particular signal shape and a preset fraction f, the constant fraction discriminator operating on signal V(t) should give the value of time t that provides the solution for equation g(t)=f that depends only on the preset fraction f and not on the signal amplitude A. This has been visually illustrated on the right side of FIG. 3.

(13) FIGS. 3A-3D present a scheme that illustrates qualitative differences between discretization of signals within the voltage-time space as shown in FIGS. 3A and 3C and within the amplitude fraction-time space as shown in FIGS. 3B and 3D. An example of sampling of signals of the same shape but amplitude differing by a factor of 2 is presented. The graph illustrates the fact that the trace of the signal discretized in the amplitude fraction domain does not depend on the amplitude itself. At the same time, the shape of the signal discretized within the voltage domain depends on the amplitude.

(14) The signal discretized using an n-threshold leading edge discriminator consist of a set of points (V.sub.i,t.sub.i) where i=1, 2 . . . , n—this signal corresponds to results of sampling within the P.sub.t-v representation system. Discretization using an m-fraction constant fraction discriminator provides a set of points (f.sub.j,t.sub.j) where j=1, 2 . . . , m, wherein this set corresponds to results of sampling within the P.sub.t-f representation system. The change in the shape may be measured for example by deviation from a predefined reference W. The reference W may consist in the shape of the signal generated by an infinitesimally small scintillator and expressed within the time-voltage representation system (referred to as reference W.sub.t-v) and the time-amplitude fraction representation system (W.sub.t-f); in general, however, the reference may be of any shape, for example that of a straight line approximating the shape of the rising edge:
V.sub.std(t)=a.sub.sp.sub.—std.Math.t+b.sub.sp
and
f.sub.std(t)=a.sub.sf.sub._.sub.std.Math.t+b.sub.sf

(15) In the above example of a straight line, the shape V(t) is given by a linear function with slope a and intercept b. The reference slope in fraction vs. time representation system may differ from this in the voltage vs. time representation system. The shape is determined by slope a.

(16) The consistency of the signal with the reference is measured by the minimum chi-square value (χ.sup.2.sub.min) obtained from the fitting of the reference shape to the discretized signal when b is the only variable parameter. Chi-square is the standard measure of consistency between the function being fitted and the results of the measurement, used for example in the least square fitting method.

(17) Therefore, the distance between the ionization place x and the photomultiplier (FIG. 4) may be determined from discretization of the signal within the amplitude fraction domain from the relationship χ.sub.sf.sup.2.sub.min(x) obtained after previous calibration, for example using a collimated beam of annihilation quanta. Calibration consists in determination of the function χ.sub.sf.sup.2.sub.min(x); given a collimated beam, one may perform measurements for different x values and determine χ.sub.sf.sup.2.sub.min of the recorded signals for every x.
χ.sub.sp.sup.2.sub.min is the minimum value of function
χ.sub.sf.sup.2(a.sub.sf.sub._.sub.std,b.sub.sf)=Σ(t.sub.j.sub._.sub.fit(a.sub.sf.sub._.sub.std,b.sub.sf)−t.sub.j).sup.2
with b.sub.sf as the free fit parameter. In the above definition, t.sub.j stands for the signal time measured for the j-th amplitude fraction and t.sub.i.sub._.sub.fit(a.sub.sf.sub._.sub.std, b.sub.sf) stands for the time of the j-th amplitude fraction calculated from the fitted curve f.sub.std(t). The place of ionization x may also be determined from the relationship a.sub.sf(x) obtained from previous calibration. In this case, the f.sub.fit(t)=a.sub.sf.Math.t+b.sub.sf function is being fit with both a.sub.sf and b.sub.sf as free parameters.

(18) Next, following determination of the ionization place, the signal amplitude is determined on the basis of the signal discretized within the voltage domain from the relationship a.sub.sp(A,x) or χ.sub.sp.sup.2.sub.min(A,x) obtained after previous calibration, for example using a collimated beam of annihilation quanta. χ.sub.sp.sup.2.sub.min is the minimum value of function
χ.sub.sp.sup.2(a.sub.sp.sub._.sub.std,b.sub.sp)≡Σ(t.sub.j.sub._.sub.fit(a.sub.sp.sub._.sub.std,b.sub.sp)−t.sub.j).sup.2
with both a.sub.sp and b.sub.sp as free parameters. The signal amplitude may also be determined as the highest reference voltage at which a logical pulse has been generated by the discriminator.

(19) With the knowledge of the signal amplitude and the distance between the ionization place and the photomultiplier, the energy deposited within the scintillator is determined from previously prepared calibration curves. To this end, one should establish independent calibration references E(x,A)—for each position x, the relationship E(A), where E is the deposited energy and A is the signal amplitude, should be determined.

(20) Next, the photomultiplier signal onset time (t.sub.0) can be determined from functions V.sub.fit(t) and f.sub.fit(t), for instance as a weighted average with weights consisting of the uncertainties of fitting, using the following equations: V.sub.fit(t.sub.0)=0 and f.sub.fit(t.sub.0)=0.

(21) The photomultiplier signal onset time can be determined after parameters of functions V.sub.fit(t) and f.sub.fit(t) are established. The functions are fitted to the measurement results. In the example embodiment described herein, the function is a straight line approximated to the rising edge of signal, but it may also be another function that would better reflect the shape of the signal onset. Regardless of the shape of the function, the effective signal onset may be calculated, for example as a solution of the equation V.sub.fit(t)=0. Thus, in case of a straight line, solution of the equation would involve identification of a parameter t at which the line intercepts the x axis.

(22) Preferably, the shapes of the fitting functions V.sub.fit(t,x) and f.sub.fit(t,x) are independently tabulated for every detection module after being calibrated using appropriate radiation type, for example annihilation radiation in case of detectors used in positron emission tomography. Preferably, the light signal from the scintillator is converted into an electric impulse in more than one place.

(23) FIG. 4 presents changes in the shapes of light pulses resulting from propagation of the pulse from the reaction place to the converter.

(24) FIG. 5 presents an example of a strip detector with an electronic readout system that facilitates signal sampling in voltage and amplitude fraction domains as well as determining signal charges. The chart presents a schematic discretization of signals for four voltage thresholds and four amplitude fractions. Signals measured at the right end are marked as squares while signals measured at the left end are marked as circles. Based on the method disclosed herein, sampling in the voltage and amplitude fraction domains facilitates determination of the place and the time of the reaction of the gamma quantum as well as of the energy deposited within scintillator 1 on the basis of the signal from the left photomultiplier 21 and independently on the basis of the signal from the right photomultiplier 22. Signals from converters 21, 22 are sent to two sampling systems 111, 112 and to respective ADC converters 71, 72 (as shown in FIG. 1). The sampling systems 111, 112 generate points presented in the graphs. The ADC converters 71, 72 are used to measure the charge of signals from the converters. Determination of the place of the reaction of a gamma quantum may also be made on the basis of the difference in times being determined on the left and on the right side of the strip and application of the procedure disclosed in a PCT application WO2011/008119, with photomultiplier signal onset time being determined using the above-described method of the disclosed solution. The use of two converters 21, 22 on the opposite sides of the strip 1 significantly enhances the sensitivity of the method for determining the place of ionization as it permits the method being disclosed in this application to be used for determining the place of ionization in several independent manners, including: (a) from the result of sampling within the amplitude fraction domain and application of the above-described method independently for the left photomultiplier 21 and the right photomultiplier 22. (b) from the ratio of slope factors a.sub.sp.sub._.sub.left/a.sub.sp.sub._.sub.right (x) (based on discretization in the voltage domain) (b) from the ratio of slope factors a.sub.sf.sub._.sub.left/a.sub.sf.sub.—right (x) (based on discretization in the amplitude fraction domain) (d) from the relationship between the differences in the times of flight Δt(f,x)≡t.sub.L−t.sub.R (f,x) and fraction f and the gamma quantum reaction place x (e) from the ratio of charges measured by ADC converters: Q.sub.L/Q.sub.R (x)

(25) FIG. 6 presents examples of detector responses for three different places of the reaction of a gamma quantum within scintillator 1: closer to the left converter (0L), at the center (0), and closer to the right converter (0R). The right side of the figure presents schematic graphs of the time differences between the left and the right pulses (Δt≡t.sub.L−t.sub.P) depending on the amplitude fraction and place of the reaction of the gamma quantum for these three cases. As illustrated in FIG. 6, not only the absolute value of the difference between the times of signals from the left and the right converter (Δt≡t.sub.L−t.sub.P) as measured for a particular amplitude fraction or a reference voltage allows determination of the place of reaction of the gamma quantum, but also the shape of the function f(Δt) as determined by multi-threshold constant-fraction discriminator changes depending on the place of the reaction of the gamma quantum x, thus facilitating independent determination of x.

(26) While the technical solutions presented herein have been depicted, described, and defined with reference to particular preferred embodiment(s), such references and examples of implementation in the foregoing specification do not imply any limitation on the invention. Various modifications and changes may be made thereto without departing from the scope of the technical solutions presented. The presented embodiments are given as example only, and are not exhaustive of the scope of the technical solutions presented herein. Accordingly, the scope of protection is not limited to the preferred embodiments described in the specification, but is only limited by the claims that follow.