Imaging system and method

Field of the invention

The present invention relates to systems and methods for the imaging of single photon emissions. The preferred embodiment will be described in connection with single photon emission imaging from small animal models. However, the invention should not be considered as being limited to this exemplary field of use.

Background of the invention

Single-photon emission imaging devices are typically based on either mechanical or electronic collimation. Mechanical collimators using pinholes are typically composed of high _, atomic number materials that modulate the photon flux incident on a detector. These systems allow a high resolution estimate of the radio-tracer distribution to be obtained. However, since the pinhole(s) of the collimators will only allow a small fraction of the incoming rays to be received at the detector, this leads to low received photon counts or data events and therefore low sensitivity. Moreover, in many cases the field of view of the imager is greatly constrained by the pinhole geometries and locations used.

On the other hand, electronic collimation which uses the Compton scattering mechanism to ^■ bypass the need for mechanical collimators, results in high count rates. Electronic collimation (Compton collimation) requires no physical modulation of the incident flux. However, . the resolution of the image estimate is limited by the detector position and energy resolutions and Doppler broadening. Following a Compton scattered event, an additional tracking or interaction ordering step is performed to determine the first and second interactions that define a cone of response (CoR). The subsequent back-projection of CoRs from many such events yields a high sensitivity, but low resolution, estimate of the radioisotope distribution in the subject. Accordingly, there is a need for improved imaging systems and methods which address or ameliorate at least one of the aforementioned disadvantages of the prior art, or provid a useful alternative to them.

Reference to any prior art in the specification is not, and should not be taken as, an acknowledgment or any form of suggestion that this prior art forms part of the common general knowledge in Australia or any other jurisdiction or that this prior art could reasonably be expected to be ascertained, understood and regarded as relevant by a person skilled in the art.

Summary of the invention

In a first aspect the present invention provides a photon detection system including: a collimator comprising, a mask that is substantially opaque to photons to be detected by said detector, said mask including one or more first transmission zones and one or more second transmission zones through which said photons can be transmitted; a detector for receiving photons from a source via transmission through the transmission zones of the collimator, wherein, said detector and collimator are arranged such that a respective source projection of the first transmission zones and second transmission zones are at least partly non-overlapping within at least a part of the detector.

Most preferably a respective source projection of the first transmission zones and second transmission zones are entirely non-overlapping. Preferably the field of view of the detector through the first and second transmission zones is at least partially overlapping.

Preferably the one or more first transmission zones are pinholes. It is also preferable that the one or more second transmission zones are larger transmission zones, for example, but not limited to, slits, holes, voids and other larger apertures. In this specification the term "pinhole" is used to describe a small transmission zone in a mask (collimator) through which photons may pass. Pinholes permit image reconstruction using linear back projection through them. Typically a pinhole will have a double cone shape in cross section and sub-millimetre inner radius. In the preferred embodiments the inner radius of the pinholes is 0.15 mm. Conversely an "aperture" or "larger aperture" is used to describe a transmission zone in a mask, through which photons may pass, which is larger than a pinhole. Such apertures are larger than pinholes and do not lend themselves to image reconstruction using linear back projection.

The detector can be configured to detect photons using at least two detection mechanisms, for example, Compton scattering detection and photoelectric absorption detection. A preferred form of the invention described herein is designed to operate with incident photons in the energy range from 5 keV to 600 keV. The thickness of the interchangeable collimator portions should be increased with energy to minimize the transparency of the solid parts of the transmission zones at the desired energy of operation. As an example, the thickness of a material such as Tungsten for 140 keV photons would typically be 6 mm.

Preferably the detector and collimator are arranged such that photons arriving at the detector within the source projection of the second transmission zone(s) are detected by Compton scattering. Advantageously, this aids image reconstruction by allowing the cone of response (CoR) of a detected photon to be modulated by the second transmission zone. In a preferred form, where the first transmission zone(s) are small, (e.g. pinholes) the detector and collimator are arranged such that photons received at the detector, within the source projection of the first transmission zone(s), but not within the source projection of the second transmission zone(s), can be detected by any useful detection mechanism. This is possible because image reconstruction is modulated by the very small first transmission zone(s). The second transmission zone or zones can define a pattern of transmission zones of any desired shape, but, most preferably they form a pattern that, during image reconstruction will substantially isotropically modulate the back projection of photons into the imaging volume.

The first transmission zone(s) are preferably surrounded by the second transmission zones. Preferably the second transmission zones comprise one or more slits surrounding a region including a plurality of first transmission zones. Most preferably each second transmission zone comprises at least part of a circular slit. The slits preferably together, or alone, form at least one ring surrounding the first transmission zones.

In a preferred form the photon detection system includes: a collimator comprising, a mask that is substantially opaque to photons to be detected, said mask including a one or more pinholes and one or more larger apertures through which photons can pass; a detector for receiving photons from a source via the pinhole(s) and aperture(s) of the collimator; said detector and collimator being arranged such that: a projection of the source of photons through the apertures and pinholes onto the detector result in portion of the pinhole projection on the detector which is not overlapped by the aperture projection to provide a high resolution detection region in the detector.

The region in the detector defined by the aperture projection can additionally provide a high sensitivity detection region in the detector.

Both the high resolution detection region and high sensitivity detection region of the detector can be used to detect photons simultaneously.

In a further aspect, the present invention provides a collimator for a photon detector comprising: a mask that is substantially opaque to photons to be detected by said detector, said mask including one or more first transmission zones and one or more second transmission zones through which said photons can be transmitted; said first and second transmission zone(s) being arranged with respect to each other and the detector, in use, such that the respective source projection through the first transmission zones and second transmission zones are substantially non-overlapping within at least a part of the detector.

The respective source projection of the first transmission zones and second transmission zones are preferably entirely non-overlapping.

Preferably the field of view of the detector through the first and second transmission zones is at least partially overlapping. Preferably the one or more first transmission zones are pinholes. It is also preferable that the one or more second transmission zones are larger transmission zones, for example, but not limited to, slits, holes, voids and other larger apertures.

The second transmission zone or zones can define a pattern of transmission zones of any desired shape, but, most preferably they form a pattern that, during image reconstruction will substantially isotropically modulate the back projection of photons into the imaging volume.

The first transmission zone(s) can be surrounded by the second transmission zones. Preferably the second transmission zones comprise one or more slits surrounding a region including a plurality of first transmission zones. Most preferably each second transmission zone comprises at least part of a circular slit. The slits preferably together, or alone, form at least one ring surrounding the first transmission zones.

In a further aspect, the present invention provides a method of forming an image of a source of photons including: receiving a first group of photons from a source via at least one first transmission zone of a collimator; receiving a second group of photons from a source via at least one second transmission zone of a collimator; processing data representing the first and second groups of photons to form at least one image of the source.

Preferably the first and second groups of photons are received using a common detector. Most preferably the first and second group of photons are initially detected in substantially non overlapping portions of the common detector. The non overlapping portions of the common detector can be defined by non-overlapping portions of the respective source projections of the first and second transmission zones on the detector.

Preferably the step of processing data representing the first and second groups of photons to form an image of the source, includes: processing data representing the first group of photons using at least one first technique; and processing data representing the second group of photons using a second technique.

In the case that the first transmission zone(s) in the collimator are pinhole(s) the step of processing data representing the first group of photons can include back projecting a line of response to the source through at least one pinhole for each photon.

In the. case that the second transmission zone(s) in the collimator are larger apertures, the step of processing data representing ^" the second group of photons can include, for each photon, back-projecting a cone of response from a point in the detector to the source, said portion of the ^' cone of response being modulated by the second transmission zone(s). In a further aspect, the present invention provides an image generated using a system or method described in relation to any one of the aspects or examples contained herein.

In one example the image contains a combination of pinhole derived data and data a derived from photons passing through one or more larger apertures. Preferably the data is gathered substantially simultaneously. Most preferably it is gathered with a common detector.

As used herein, except where the context requires otherwise, the term "comprise" and variations of the term, such as "comprising", "comprises" and "comprised", are not intended to exclude further additives, components, integers or steps.

Brief description of the drawings / figures Illustrative embodiments of the present invention will be described, by way of non-limiting example only, in connection with the following figures, in which:

Figure 1 illustrates an exemplary detector set-up made in accordance with an embodiment of the present invention;

Figure 2 is a schematic representation of a collimator and detector system made in accordance with an embodiment of the present invention;

Figures 3 and 4 illustrate a first exemplary collimator design in accordance with the present invention;

Figures 5 and 6 are ray-tracing diagrams illustrating a method of optimising the large area apertures (or slits) of the collimator design of figure 3; Figures 7 and 8 illustrate a second exemplary collimator design in accordance with the present invention;

Figure 9 Illustrates a ray tracing for 500 photons emitted from location y = 0 passing through the collimator of figure 7;

Figure 10 illustrates plots of the effective transmission and system effective sensitivity for the collimators of figures 3 and 7;

Figures 1 1A and 1 1 B illustrate the square and circular collimators and associated image voxels where the transmission p, = 1 ; Figures 12 illustrates a triple intensity p anar phantom source distributions used in tests of embodiments of the present invention;

Figure 13A illustrates a plot showing the number of events as a function of the number of interactions in the event for the two collimator configurations of figures 11 A and 11 B Figure 13B illustrates a 2D histogram in log-scale showing of the photon emission positions at the source plane, for events that passed through the cylindrical collimator and interacted in the detector-stack;

Figures 14A and 14B are histograms of the positions at which the photon emission ^■ vectors intersect the collimator plane for all detected Compton scattered events for the square and the cylindrical geometries, respectively;

Figures 15A and 15B are histograms of the event data from a slice at y = 0.0 in Fig. 14B showing the intersections of the emission vectors with the collimator plane and equivalent histograms showing the data from all slices in along the y axis; and

Figures 16A to 16F illustrate image estimates at the volume slice where the source was located. Figures 16A to 16D were generated with data from a square collimator, whereas Figures 1.6E and 16F are generated with data from a cylindrical collimator.

Detailed description of the embodiments

In a preferred embodiment there is provided a detector including a combination of mechanical and electronic (hybrid) collimation. The general principle behind the design of the preferred embodiment is to overlap the fields of view of the first transmission zones (which are pinholes) and second transmission zones (which are slits), but to separate their respective source projections on the detector to thereby preserve the high resolution pinhole data. The intended energy range for operation of this exemplary embodiment is from 30 to 511 keV.

The arrangement of both pinholes and larger apertures in the collimator serves to increase the number of photons which impinge on. the detector stack without polluting the high resolution pinhole projection data. The structure of the preferred embodiment will enable image reconstruction using both lines of response (LoRs) from well-defined pinholes in the collimator and modulated comes of response (CoRs) from larger apertures in the collimator. In preferred forms the larger apertures are arranged on the collimator relative to the pinholes, such that: • The larger apertures focus incident photons at pre-determined regions of the detector stack.

• The photons passing through the larger apertures are preferably directed in a manner which maximizes the probability of a Compton scatter being the primary interaction mechanism.

• The pinhole field of view (pFoV) and aperture field of view (aFoV) can be allowed to at least partly (and possibly fully) overlap in order that the resulting images can be combined and/or quantitatively compared.

Figure 1 is a schematic illustration of an imaging system implementing one embodiment of the present invention. The imaging system 100 generally includes an interchangeable aperture array positioned in front of a detection system and is configured to image a source of photons, for example a small animal that has had certain tissues treated with a radioactive tracer.

The system 100 includes a cooled insulated housing 102. Cooling is provided by cooling pipes 104 through which cooling fluid is circulated. The housing supports a set of guide rods 106 on which is carried a collimator arrangement 108. The detector(s) 1 2 can also be mounted on the rods to enable their relative positions to be adjusted. The system is preferably operated over a broad energy range, and therefore it is not practical to utilize a single geometry over this range as the level of scatter and penetration into the collimator increases with energy. To address this issue, an interchangeable collimator mounting structure is provided which is able to support a maximum thickness of 1.50 cm of Tungsten collimator inserts, sufficient to limit the transmission at 511 keV to < 3% (3 σ ). Up to nine aperture arrays, consisting of pinholes, slats or open spaces, can be mounted as inserts in the volume.

Inside the housing 102 there is located a radio frequency (RF) shielding box 1 10. Inside the RF shielding box 1 0 and, aligned with the collimator 108, is positioned a detection system 112. On the other side of the collimator 108 to the detection system 1 12 there is placed the source 1 14 which is to be imaged.

As illustrated best in figure 2, the detection system 1 12 includes of a stack of Silicon double- sided strip-detectors (Si-DSSDs) 120 and a Cadmium Telluhde (CdTe) hybrid-pixel detector (HPD) 122. Each of the 5 Si strip detectors of the stack has an active volume of 0.8 x 31.9 x 31.9mm ³ , which is segmented into 64 orthogonal strips on each side. The strips each have a width of 400pm and gap of 100pm. The detectors are bonded to GM-IDEAS VA64TA Application Specific Integrated Circuits (ASICs) and are operated in a DC coupled configuration. ^• The HPD includes 51.2 x 51.2 x 2.00mm ³ CdTe crystal with a 256 x 256 pixelated anode. The crystal is bump-bonded to the 0.2mm pitch custom-designed read out ASIC. The multiplexed outputs from both the VA64TA1 and HPD ASICs is read out and controlled through a Data AcQuisition (GDAQ) system.

The. predominant interaction mechanism through which gamma rays interact in the detectors varies significantly with the source energy. For incident photons where e ₀ < 100 keV, the primary interaction mechanism is photo-electric absorption. When e ₀ ≤ 50 keV photoelectric absorption occurs primarily in the Si-DSSDs. For e ₀ < 50 keV, the photoelectric absorptions are primarily in the HPD. Therefore, the experimental configuration is optimal when operated as a multi-resolution Single Photon Emission Imaging (SPEI) device.

Table 1 lists the geometry of one exemplary system, setting out the size, pixel size, thickness, and location of the source, collimator 108, strip detectors 120, and back plane detector 122. Each element (1 14, 108, 120, 122) is aligned along a common axis (x-axis).

Size (y-z) Pixel size (y-z) Thickness Location

[mm]

[mm] (x) [mm] (x) [mm]

Source 30.0 (dia) N/A 0.0 -60.0

Collimator 60.0 (dia) N/A 5.0 0.0

Si-DSSDs 31.9 31.9 0.2 x 0.2 0.8 9, 11 , 13, 15,17

HPD 20.7 20.7 0.5 x 0.5 2.0 23.0 Table 1 : The geometry of an exemplary system

Figures 3 and 4 illustrate a first example of a collimator, in perspective view and cross section respectively. The collimator 108 includes a first portion 300 in hich first transmission zones, namely pinholes 302,304,306 are arranged. A second portion 308 which, in this case, surrounds the first portion 300 includes one or more second transmission zones in the form of large CQllimating apertures 310.

The three pinholes 302,304,306 in this example are arranged at the corners of an equilateral triangle with a side length of 6mm. Figures 5 and 6 show a ray tracing diagram showing a cross-section through the example collimator of Figs. 3 and 4 to illustrate the cross-sectional shape of the large slit shaped apertures in a preferred embodiment. As can be seen, the geometry of the aperture 310 is defined by locations A, B, C, D, E and F. Figure 6 is an enlarged view of the geometry of the slit shaped aperture 310 and the ray tracing to form the slit 310.

Collimator thickness, Pinhole definition and backplane detector dimensions

In 2D, the pinhole dimensions were calculated from the projection onto the y-axis. This configuration then allows the source projections to be determined. The source was a uniform circular distribution on the y-z plane. In 2D, this distribution was a projection onto the y-axis. As will be appreciated by those skilled in the art, a typical source will be spherical or cylindrical, and the method to described to design the geometry of the slit(s) or other large apertures, can be readily adapted to deal with such 3D sources.

The y-z dimensions of the back plane detector 122 were fixed to be the same as the size of the source projection, through the pinholes, at the x-location of the detector. To maintain the directionality of the collimator, a minimum thickness of Tungsten (Lw) through which any ray-traced photon trajectory must pass can be defined. For this example, L _w was fixed at 1.02 mm for which 95% (or 2 σ ) of 140 keV incident photons are stopped in the collimator.

Upper limit of FoV of the large aperture In the- illustrated embodiment, the large area apertures 310 are sized and positioned with respect to the pinholes 302, 304, 306 such that photons emitted from the source 1 14 which pass through the aperture(s) 3 0 are unlikely to (or cannot) arrive at the backplane detector 122 directly (i.e. without undergoing Compton scattering in the strip detectors, 120). Such photons require more complex processing to reconstruct images, and thus can be viewed as contaminating the pinhole projection data.

To implement this concept a line from location H at the top edge of the HPD 122 is chosen to connect to the upper edge of the FoV (source). The line intersects the collimator walls at A and B. Locations A and B mark the limits of the upper and lower sides of the slit through which gamma rays can pass without impinging on the HPD. This location is chosen as photons that pass through the large-area slits and are incident on the HPD are likely to undergo photoelectric absorption. Such photons result in an unresolved event-type and contaminate the pinhole projection. Locations C and D lying on the vector AB are then selected at a distance from A and B equal to L _w as AC and BD become the edges of the slit.

It can also be seen in this embodiment the line H-A can also be seen as notionally dividing the detector stack 120 into a first region within the source projection of the first transmission zone of the collimator (e.g. the pinholes), and a second region within the source projection of a second transmission zone of the collimator (e.g. the larger apertures.) In this example, any photons that first interact with the detector 120 in the first region (either by a photoelectric absorption or as the first scattering event in Compton scattering detection), can be determined to have come through the first transmission zone. Similarly, any photons that first interact with the detector 120 in the second region (either by a photoelectric absorption or as the first scattering event in Compton scattering detection) can be determined to have come through the second transmission zone. Preferably photons that first interact with the detector 120 in the second region are detected via Compton scattering.

As will be apparent, in other embodiments, where a backplane detector that is larger than the field of view of the pinholes, the point H can lie . inward from the edge of the detector. In this case, the point H lies at the division between the source projection of the pinholes and source projection of the larger area apertures on the backplane detector.

Lower limit of FoVof the large aperture

Location G is the position of the top edge of the first of the Si-DSSD 120. Two vectors are defined that connect G to C and D and intersect with the collimator walls at E and F. The cross- sectional geometry of the slit 310 is now defined by locations A, B, C, D, E and F. This slit is the primary large-area aperture that maximizes the ratio of resolved to unresolved event types without polluting the pinhole projection data. The FoV of the aperture is defined by the vectors HA and GE. As will be appreciated the locations of A or B of the slits can be adjusted for the desired final FoV of the source. The locations can be chosen by considering the slit-to-slit and slit-to-pinhole distances and selecting the set that produces the greatest transmission within the FoV of the source. More slits can be added to the remaining section of the collimator by starting new lines from location H. The addition of subsequent slits should not violate the condition that the minimum thickness of any ray traced from the source is greater than L _w . Figures 7 and 8 show such an extension of the design to a collimator 700 with 3 slits on each of the upper and lower sides. The collimator 700 is generally similar to the collimator 300 from figure 3 , and includes a set of pinholes 702 in a first region and a series of three slits 704, 706, 708 surrounding the pinholes 702. The limiting cases of the ray tracing are shown on the upper part of the collimator 700. At each slit, two vectors that define the range of the FoV are defined between locations G and H and the upper and lower edges of the slit. As can be seen from these examples, the fields of view of the pinholes and slits overlap (as seen at the "source side" of figures 5 and 7), but their respective source projections, (illustrated on the detector side of figures 5 and 7) are substantially non-overlapping. This arrangement preserves the high resolution pinhole data received in the non-overlapped portion of the source projection of -the pinholes, and enables high count images and high resolution images to be captured simultaneously on the one detector.

The effective transmission ET _W as a function of emission location y and angle a (angle of photon emission from the source plane) of the optimized large-area slits, can be calculated from,

ETwi i) = exp (ΐ1· α}] . ( 1 ) where Lw(y,a) is the total depth of Tungsten that the ray intersects with the collimator, and μ—

W

is the total linear attenuation coefficient for Tungsten at the source energy. For 140 keV photons, μ-^ = 30.2 cm ^'1 . In the following discussions, μ will always refer to the linear attenuation coefficient. The effective transmission outside the bounds of the collimator is neglected. The mean effective transmission from each emission location in y is given by,

After traversing the collimator, the modulated photon flux impinges on the Si-DSSD stack 120. The effective attenuation of the stack 120 is given by,

EAsiiy. o) = 1 - exp - (3) where Ls, (y,a) is the total depth of Si and μ— is the total linear attenuation coefficient of Si.

Si

For 140 keV, u— = 0.32 cm ^'1 . The effective sensitivity of the system is proportional to the

Si

product of the collimator transmission and the attenuation in the Si-DSSD stack, given by.

< ES _eys > (y) = ET _w {i a)EA _Si {y, a)da, (4)

If the sampled emission angles are binned (discretized), Equations 2 and 4 become,

1 ^lV

< ETw > (IJ) = ∑ ETw (y , <¾)Δα, (5)

< ES _eyi > (y) ETw {Ji r Oi)EAsi{y, , )Δα·, (6)

Where Δ α = π Ι , is the number of angular bins and a, = - n il + ί Δ α.

Figures 9 and 10 together illustrate the advantage that the preferred embodiment presents over the use of a collimator containing pinholes alone, in terms of the numbers of photons received.

Figure 9 illustrates an example of the rays emitted from a point at the centre of the source distribution (y = 0). The limits of the ray vectors show the range in a of the trajectories that are used to calculate the effective transmission at this location. All the rays with ET _W below 5% are shown to be stopped in the collimator. Figure 10 shows the distributions Of < ET _W > and < ESsys > as the number of slits included is increased. The effective transmission < ET _W > is illustrated in the upper plot and system effective sensitivity < ESsys > is illustrated in the lower plot. Solid and dashed lines represent the distributions for the collimators with one and three slits, respectively. The distributions were calculated in 1.0 mm increments along the y-axis. At each location, 5000 photons were uniformly emitted within an angular range of 2 π . When there are no slits in the collimator, <ET _W > and < ES _sys > are negligible. When changing from one slit to three slits, < ET _W > and < ESsys > are significantly increased as expected. The FoV is also significantly increased with the extension to three slits.

Numerical validation

To test the inventor's proposed detection system, a collimator as described above, was extended to 3D. and modelled in Geant4. The collimator was constructed, from two parts, an inner section reserved for pinholes and an outer part containing slits. The slits in the outer sections were formed using the G4BREPSolidPolyhedra class objects. The extension from square to cylindrical configurations was performed by increasing in the number of sides of each polyhedron. A first test collimator design 1 100 illustrated in figure 1 1A was composed of three concentric square slits 1 102 that were matched to the geometry of the detector stack 1104. The second was a cylindrical geometry illustrated in figure 1 1 B. In this case the collimator 1 1 10 is identical to that illustrated in figure 8, and includes a set of three concentric circular slits 1 1 12 matched to the dimensions of the detector stack 1 1 14. .Simulations were run for both collimator configurations with e ₀ = 140 keV. For each of the two simulations 5.0 x 10 ⁸ events were generated from the distributed source shown in Fig. 12. The source distribution was a triple intensity planar phantom consisting of three circular distributions 11 , I2 and I3. The outer circle (II) had a radius of 15.0 mm and the two inner circles had radii of 6.0 mm and 4.0 mm. The three distributions had relative intensities of 1 : 10:50 mm ^"2 . In figures 1 1A and 1 1 B the dots 1 108, 1 1 18 in front of the collimator 1 100, 1 110 represent the image voxels where the transmission pt = 1. The shades of the dots 108, 1 1 18 represent the values of CoR at the voxels. The transparent squares 1 104, 1 1 14 represent the detector layers. The short straight line 1 106, 1 1 16 shows the recoil photon trajectory connecting the first and second interactions forming the CoR. The data generated from each simulation were then processed and reconstructed according to the algorithm described below.

Compton Reconstruction for large area apertures

Estimates of the source distributions were formed utilizing Compton-cone reconstruction with consideration of the transmission properties of the collimator. For an incident gamma ray emitted from location r ₀ , with energy e ₀ . the Compton scatter angle 9 _C at the first interaction is related to the energy deposited Ei by, where e. _\ = e ₀ - E^ is the energy carried by the recoil photon after the interaction. For an ideal system, the scattering angle 9 _C defines a CoR on which the photon emission location originated. For a finite imaging volume in a realistic system the intersection of the CoR with the imaging volume gives a probability distribution of the likelihood that the photon was emitted from each voxel in the volume. The probability density function Φ of the CoR can be generally expressed as:

1

(ν _ν ) =— p _t (r _v ) - pvi · Ρ6' · ρ(ι-νΐ , Λ|ι9ο·, £'ι) · ρΐ2 ' Ρ* > (8) where r _v is the location of an arbitrary voxel inside the imaging volume, r _v1 is the vector from r _v to the cone apex r^ p _f (r _v ) is the collimator transmission function, p _v i is the probability that the gamma ray from r _v reaches the interaction location n given it traverses the collimator, p _c is the probability that a Compton scatter occurs at p ₁₂ is the probability that the photon reaches the second interaction location r ₂ , p, is the probability of an interaction at r ₂ and p(r _v1 , A|0 _C . £i) is the probability of the emission at r _v Compton scattering ^' at an angle 9 _C resulting in a measured energy E _v The last of these probabilities is a double differential cross section, which can be approximated by, where θ _ν is the angle between r _v1 and the vector of the cone axis r ₁₂ , p(6 _c ) is the scattering function and ρ _Λ (θ _ν | 9 _C ) is the angular uncertainty. Below are detailed descriptions of all the terms in equations 8 and 9.

Collimator transmission function: The slits on the collimator limit the cone back-projections as only certain gamma ray trajectories have a significant probability of traversing the Tungsten. The collimator transmission is given by, p. (r _vl ) = exp -/ - Lr )] · ( 10) where L _w (r _v i) is the length that r _v1 intersects with the collimator material. The collimator transmission function has values 0 < p _f (r _v i) < 1 , depending on the thickness of Tungsten traversed. To obtain L _w (r _v ), a 3D ray-tracing algorithm was implemented. Currently, to simplify the calculation, p ₍ (r _u1 ) was set to zero for V Lw{r _v ) > 0. Effect of the aperture transmission function on image reconstruction: The effect of the collimator transmission function is also demonstrated in Figs. 1 1a and 11 b. The transmission function of the collimator truncates the CoR cone surface and therefore reduces the number of possible locations from which the source emission may have occurred. It was also found to improve the accuracy of the gamma-ray tracking algorithms as the majority of the false interaction orderings cannot be traced back through the collimator.

Detector interaction probabilities: The probability that a Compton scatter occurs in a detector can be represented as: f- ^l Sii ^e Oi Z) r * r

__ «p [-^ (r

where μ— (e _0> Z) is the incoherent scattering linear attenuation coefficient and μ— (e ₀ , Z) is

Si Si the total attenuation coefficient. For a stack geometry the probability that the photon traversed all other detectors between the source and n can also be included. This probability is given by,

Following the initial scatter, the photon must then escape the primary interaction detector and traverse all other material intersected along r ₂ . This probability is given by, Finally the photon must undergo a second interaction at r ₂ , with probability, p, = 1 - exp [^SiMPD ^L SiMPD ( ^r t3)] , C W) t hit

where μ „. _{rTri r} and L are the linear attenuation and depth of intersection of the

Su HPD Si, HPD

detector, either Si or HPD, at the second. interaction. Scattering distribution function: Given a Compton scatter is recorded, the angular probability for unpolarised incident photons is governed by p(8 _c ), the scattering corrected Klein-Nishina cross section [5], [12], given by,

•sin - . , Z), (15)

9c

! ⁷¹

where K is a normalization factor so that J p(9)d9 = 1 , S(x, Z) is incoherent scattering

o

function with x = sin θ/λ(Α) and λ(Α) = 12.39852/e0(keV). S(x,Z) is material dependent and its

daKN

functional dependence can be found in [8], I is Klein-Nishina cross section at 9 _C given

dQ 9c

by, where r _e = e ² /(^e ₀ m _e c ² ) = 2.818 x 10 ^"15 m is the classical electron radius.

Angular uncertainty function: For an arbitrary gamma ray, r ₀ i has a magnitude r _a1 . Similarly, the first and second interaction positions r ₁ and r ₂ define a vector r ₁₂ with magnitude r ₁₂ . The angular uncertainty due to detector spatial resolution can be described as, Θ _Γ =— Ί + Q' ² (1 4- IP) - 2a cos 9 _C . ^' ( 17) where a = , β = , ΔΓι and Ar ₂ are the spatial resolutions of the detectors in which the first and second interactions occurred.

The angular uncertainty due to energy resolution can be obtained from the derivative of equation 7 with respect to the energy of the scattered photon ei . The uncertainty is expressed as, άθ _Ε = . ΔΕ. ( I S)

t ^' l Sm Hc where ΔΕ is the energy uncertainty caused by Doppler Broadening and detector energy resolution. The energy uncertainty due to Doppler Broadening can be approximated according to, ^' where Δ p ₂ /m _e c is the dimensionless FWHM of the Compton profile. Δ p _z /m _e c for Si and CdTe are equal to 0.95 x 10 ^"2 and 2.03 x 10 ^"2 , respectively.

The FWHM of the detector energy resolution is energy dependent and of the form y = ax+b, where x is the deposited energy in keV, and a and b are material-dependent parameters. In this example, the values of a and b are chosen to be 0.01 and 2.0 for the Si detectors, and 0.015 and 4.0 for the CdTe detector. These values were approximated from the distributions expected from such detectors. The total energy uncertainty becomes,

AE = FWHM ² + ΑΕΪ (20) and the total angular uncertainty is:

ΑΘ = Δ/?2 + Δ(¾ (21)

Finally, the normalised CoR PDF can be approximated by, where σ is chosen to be Δ Θ/2.35, and C is a normalisation factor,

1

(23)

0.9\/2πσ ² + 0.1ν ^Λ 2 (3 ) ^{2 "}

It should be noted that equation 22 is an approximation, both in the shape and the width of the function. This approximation is reasonable as long as Doppler broadening is the dominant factor in ΔΘ. Results

The data from the simulations were filtered to remove the- histories for Rayleigh scatters and interactions that occurred in the collimator or housing as no a-priori knowledge of this information can be recorded ^' experimentally. To provide realistic measurement data, uncertainties due to the nominal spatial and energy resolutions of the experimental detectors were added to the ideal data. The Compton interaction sequences were then randomized and re-ordered using a version of Bayesian reconstruction where the source location was assumed to be at negative infinity on the x-axis.

Fig. 13A shows the statistics for Compton events as a function of event fold (the number of interaction in an event) for the square and cylindrical geometries. The cylindrical collimator yielded increases of 14.9% and 19.0% in the numbers of total and successfully ordered events, respectively, in comparison with the square collimator. An increase was achieved even though the open-fraction of the square collimator is greater. The percentage of successfully tracked events for the cylindrical geometry was 66.0%, compared to 63.7% for the square geometry. The majority of the unsuccessfully ordered events were not included in the image estimate as they were attenuated in transmission correction.

For the result shown in Fig. 13A, the realistic resolved / unresolved ratios are 0.143 and 0.161 for squared-and cylindrical collimators, respectively; From a comparable simulation, where the outer region of the collimator was completely open, the mean resolved / unresolved ratio was calculated to be 0.190. The lower resolved / unresolved ratios can be attributed to multiple scatter events being clustered into single pixels and the inclusion of housing interactions in the collimator data set but not jn the comparable simulation one. Fig. 13B shows the 2D event histogram of the photon emission positions, at the source plane, for events that passed through the cylindrical collimator and interacted in the detector-stack. The distribution closely resembles the phantom shown in Fig. 12, and shows that the FoV of the slits covers the entire distributed planar phantom.

Figs. 14A and 4B show 2D histograms of the positions at which the photon emission vectors intersect the collimator plane for all detected Compton scattered events for the square and cylindrical geometries, respectively. The narrow distributions closely reproduce the precise outlines of the collimator apertures. This agreement demonstrates the effectiveness of the exemplary design at minimizing the number of unresolved events, i.e. events for which the primary scatter occurs in the collimator, that compose the data set. The variation in intensity shown in Figs. 14A and 14B is due to the combination of the change in the number of emitted photons that intersect the apertures as a function of distance from the centre of the FoV and the asymmetric source distribution. From these distributions, the cylindrical collimator has been shown to outperform the square collimator.

Figs. 15A and 15 B show the profiles of the event data presented in Fig 14B. In Fig. 15A, histograms of the event data from a slice at y = 0.0 show the intersections of the emission vectors with the collimator plane for all events in the top plot, and for resolved Compton scatter events in the bottom plot. Equivalent histograms are shown in Fig. 15B for all slices in y projected onto the z-axis. The well resolved lines in Fig. 15A illustrate the ability of the exemplary collimator design to eliminate virtually all scatter from the collimator being present the event data. Analysis of data from the square collimator produced very similar trends and as such is not illustrated.

Image Reconstruction Results

The event data described above were reconstructed utilizing the technique described herein. The intersection of each back-projected CoR with each voxel in the imaging volume was calculated and summed. To reduce the computation time, p _v , p ₁₂ and p, were set to 1.0 as these terms were deemed to have a minimal effect on the final distribution. The reconstructions were performed both with and without the inclusion of experimental factors to investigate the change in performance. The effects of the collimator on the image reconstruction were also ^■ investigated by performing back-projections with and without the collimator transmission function. It should be noted that while the simulated data was blurred with the expected levels of experimental position and energy resolutions and Bayesian interaction ordering; time uncertainty that would result in pile-up and random coincidence were not considered.

Figs. 16A and 16B show the image estimates, at the depth where the source was located (x = -60 mm), for data collected with the square collimator (fig 11 A) and without inclusion of the. collimator transmission function (i.e. cone-surface back-projection). The back-projection results from ideal data are shown in fig 16A, while those using realistic experimental factors are shown in figure 16B. s can be seen the source appears as a single unresolved distribution in both cases and the size of this distribution is shown to increase significantly with the application of the experimental factors. Under these conditions, the data from the cylindrical collimator (fig 1 1 B) also resulted in similar distributions and so is not illustrated.

Figs. 16C and 16D show image estimates from the same data as is presented in Figs. 16A and 16B , however, the collimator transfer function has been included in each back-projection. The resulting reconstructions have a significant reduction in the level of overall blur and the high intensity source distribution is now just visible above the background. However, there are significant artefacts in the horizontal and vertical directions, resulting from the modulation of allowed incident photon trajectories. Such artefacts makes the highest intensity distribution, distribution 13, difficult to resolve. In Figs. 16E and 16F, equivalent representations to those in Figs. 16C and 16D are shown for data collected with the cylindrical collimator. The addition of event data from an increased range of incident angles results in a large improvement in image quality. The high intensity profile is now clearly visible and the intermediate intensity distribution can also be observed in the ideal data. In order to quantify the quality of different image estimates the contrast and noise properties for the three features and the background were measured by overlaying the exact phantom. As an example of the calculation, the contrast between regions I3 and II was obtained by dividing the difference of the mean intensities of regions 13 and II by the sum of the mean intensities, or Zl l— i !iL Table II shows the contrast for each of the regions of the images reconstructed

< 13 > + < I\ >

from data collected using the square collimator, with and without the inclusion of the collimator transmission function, and the cylindrical collimator with the inclusion of the transmission correction. In the table, B denotes the mean background level. For the square collimator both the ideal and realistic data, the contrast between the intermediate intensity circle (12) and the low intensity circle (II) is completely dominated by the criss-cross artefacts. However, the contrast of 13:11 and II :B increase significantly with the inclusion of the transmission function. When the cylindrical collimator is used, the contrast further increases in all cases for both, the ideal and realistic data.

< IN >

Table III shows the signal-to-noise-ratio (SNR). The SNR was calculated as for each

< B > distribution. For both collimator geometries, the SNR increases significantly with the inclusion of the transmission correction. The improvement in the SNR for the square collimator with the transmission function was between 60% and 150%. By moving from the square geometry to a cylindrical geometry, a further increase of between 10% and 30% was obtained.

A further study was also carried out to investigate the performance of this cylindrical collimator with 364 keV incident photons. From the reconstructed images, the source distribution could be resolved, however the SNR values were poor compared to those of the cylindrical collimator shown in Table III. The image quality could be improved by redesigning the collimator with ^• increased thickness.

TABLE II: Image contrast for the square and cylindrical collimators

Square Cylindrical Phantom w/o trans. w/ trans. w/ trans.

13:11 0.117 0.332 0.361 0.916

Ideal 12:11 -0.006 -0:013 0.070 0.818

I1 :B 0.302 0.498 0.530 1.000

Realistic 13:11 0.003 0.168 0.196 0.916

12:11 0.005 -0.008 0.056 0.818

I1 :B 0.079 0.347 0.398 1.000

TABLE III : SNR for the square and cylindrical collimators

Square Cylindrical

w/o trans. w/ trans. w/ trans.

I3:B 2.359 5.951 6.951

Ideal I2:B 1.843 2.908 3.750

11. B 1.866 2.982 3.260

Realistic I3:B 1.180 2.891 3.454

I2:B 1.184 2.031 2.601

11 :B 1.172 2.061 2.324

As can be seen from the ^' foregoing, a hybrid collimator including pinhole and larger apertures such as slits or open areas when used in conjunction with a detector of the type illustrated can provide a combination of high-resolution low-sensitivity pinhole data with low-resolution high- sensitivity Compton information to form an combined image. Using a design in accordance with the preferred embodiment the large-area apertures are able to sample the primary FoV.

For both embodiments described the collimator transfer function modulated the back-projection of the CoRs into the imaging volume and significantly improved the image quality quantified by contrast and SNR. It can also be seen that a cylindrical geometry collimator outperformed a square geometry collimator. The isotropic modulation of the cone surfaces resulted in less artefacts and more highly resolved image estimates. Also, the cylindrical geometry provided increased sampling of the FoV due to more optimal positioning of the slits. Combination of pinhole derived data and data a derived from photon passing through the larger apertures can be performed in several ways, including, but not limited to:

1. In the regions where aFoV and pFoV overlap, the combination will result in an increase in SNR as the event statistics will be significantly increased. The resolution of the pinhole data should not be significantly degraded as the CoRs are modulated so heavily.

2. In the regions where aFoV extends beyond pFoV, the combination will result in the capability of being able to perform region of interest selection.

Advantageously the high-sensitivity image (or image portion) produced through slits helps quickly locate the source location so that the higher-resolution but lower sensitivity image of the source can be captured. For example, if a radiotracer has been selected to image the heart of a mouse, the geometry can be configured to obtain a high resolution image of the heart located in a lower resolution full body image. This allows the clinician to assess the uptake accurately, compared to the surrounding regions. An additional advantage is that fast collection through the large-aperture data can be utilized to tell the clinician quickly that the configuration should be adjusted, as for different sized animals, the organs are in different regions.

It will be understood that the invention disclosed and defined in this specification extends to all alternative combinations of two or more of the individual features mentioned or evident from the text or drawings. All of these different combinations constitute various alternative aspects of the invention.

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