Apparatus for determining energy of hadron particles

Abstract

Groups of particles of hadron radiation (e.g. protons) are transmitted in a system, such as a Computed Tomography (CT) imaging system. A method of determining residual energy of a particle of hadron radiation comprises determining trajectory data for individual particles in each of a plurality of the groups of particles, for example using proximal and distal beam trackers with position sensitive detectors. The method determines total residual energy data for each of the plurality of the groups of particles, for example using a RERD range telescope or calorimeter. The method determines residual energy of the individual particles using set of equations such as matrix equations. They may be solved by minimising a loss function or using interpolation, with binning of trajectories of similar residual energy. Particles having the same, or a similar, trajectory are determined to have the same residual energy. This may be used in proton beam therapy (PBT).

Description

BACKGROUND There are three main recognised treatment methods for cancer: surgery, chemotherapy, and radiotherapy. The most common form of radiotherapy involves the use of external beams of high-energy x-rays. A more recent form of radiotherapy utilises very high-energy beams of charged particles, notably protons. This is called Proton Beam Therapy (PBT). The chief advantages of using protons, or other charged particles, is that they travel a finite distance into tissue. This distance is controllable by modifying the initial energy of the protons. Figure 1 shows how PBT can deliver a greater fraction of the dose to a target location, such as a tumour site, and significantly reduce radiation dose to surrounding healthy tissues and organs. The position of the Bragg peak, near the end of travel for the protons, is determined by the proton stopping power of the tissues encountered and the incident energy of the protons. The energy of the incident protons may be varied, during treatment, to allow full coverage of the tumour. This is shown as a Spread-Out Bragg Peak (SOBP). Figure 2 shows an example of a treatment delivery system which uses electro-magnetic scanning of a narrow-focussed beam. This is called pencil-beam scanning. The energy and intensity modulated beam 1 is focussed by a pair of quadrupole magnets 2. A pair of orthogonal magnets 3 deflect the beam in x and y directions 4 so that the tumour 5 can be scanned with a specified pattern 6. The energy of the incident beam is changed so that different slices of the tumour can irradiated 7 to provide full coverage of the target region. Pencil-beam scanning gives much greater precision to individual treatments by enabling more compliant dose distributions. Before treatment can begin, information is acquired about the treatment site by x-ray imaging. Computed Tomography (CT) is an imaging technique which acquires information about a subject by performing a plurality of scans of a treatment site from different directions. This provides a plurality of cross-sectional images at different directions. These can be combined into a 3D data set. Currently, treatment is usually planned by CT imaging using x-rays. However, there are disadvantages with treatment planning using x-ray imaging. It is desirable to combine with proton CT imagery for treatment planning. Imaging requires irradiation of a large area. The area scanned by current PBT systems can be up to 40 cm square. This implies large and expensive sensors where most of the sensor is not exposed to the pencil beam at any one time. It is not possible to defocus the beam to very large cross-sections due to the relatively narrow throat of the scanning nozzle. Introducing a passive scatter after the nozzle will affect the beam quality, introduce wider and more diffuse divergence and, may change the geometry used for treatment. It is worth noting that the narrow, typically a few mm in diameter, beam can be scanned at high speed - up to 30 m / s - but with a higher proton flux density compared to passively scattered delivery systems. Figure 3 schematically shows an arrangement for recording a proton CT. As proton trajectories are non-linear due to multiple Coulomb scattering, it is necessary to track the paths of individual protons. This tracking demands strict requirements of the instrumentation system and the delivery of incident protons. There is a beam tracker 9 on a proximal side of the subject and a beam tracker 10 on a distal side of the subject 11. For each proton, the beam trackers provide an estimate of the trajectory of the proton and of: (i) a position A on the subject’s surface where the proton entered; and (ii) a position B on the subject’s surface where the proton exited. The proton loses energy in passing through the subject. A Residual Energy-Resolving Detector (RERD) 12 records, directly or indirectly, the remaining energy, Er, of the exiting proton. The RERD 12 is a form of calorimeter. The initial energy of the proton, Ei, is known from the settings of the proton accelerator. Knowing both the initial energy Ei and the remaining energy Er, it is possible to determine the energy lost across the subject (Ei - Er). These triplets of data [A(x,y), B(x,y), (Ei - Er)] are obtained for many thousands of protons for each orientation of the subject and the instrument. These triplets can be used to construct a radiograph in terms of proton relative stopping power. A proton CT can be created by combining a series of such radiographs acquired at different rotations of the subject and the instrument about the isocentre. There are several algorithms for CT reconstruction, such as filtered back-projection or iterative methods. Figure 4 shows two possible ways of implementing the RERD 12. In Figure 4(a), the RERD is a calorimeter which records the total residual energy. The calorimeter can comprise a monolithic block 17 of scintillator plastic. The incident proton 16 loses energy as it penetrates the scintillator 17 and so produces fluorescent light proportional to the energy lost. The light is collected by a detector 18 and converted to an electrical signal. As there is no spatial information as to where the light is generated, such a RERD can only reliably work for single protons. In Figure 4(b) the RERD is a range telescope where the energy is detected by determining the distance travelled through layers of calibrated material. A plurality of thin layers or plates 19 are arranged orthogonally to the primary direction of the incident proton beam. As the proton traverse the layers it will deposit energy, recorded as light or electronic charge, up until the Bragg Peak. By recording the layer number of the last detected signal and the proton stopping power of the layers, the residual energy can be calculated. The beams used during CT scanning are pulsed beams, where each pulse comprises a bunch of one or more protons. The average number of protons in a bunch is dependent on the proton beam current. This number varies as it depends on the random emission of protons and follows a Poisson distribution. One issue with implementing the RERD is in detecting the individual energy of a single proton. Most RERDs cannot cope with more than one proton at a time. RERDs able to record individual energies from a bunch of protons have been proposed, but they are complex and costly to implement. It is an aim of the present invention to address at least one disadvantage associated with the prior art. SUMMARY OF THE INVENTION There is provided a method of determining residual energy of an individual particle of hadron radiation according to claim 1. Optionally, the set of equations is a set of linear equations. Optionally, the method comprises: identifying groups of particles with an incomplete set of determined trajectories; and removing the total residual energy data forthose groups of particles with an incomplete set of determined trajectories. Optionally, the method comprises: determining a number of particles in one of the groups; determining a number of trajectories for the group; comparing the determined number of particles in the group with the determined number of trajectories for the group; and removing the total residual energy data for the group of particles when the determined number of particles in the group does not equal the determined number of trajectories for the group. Optionally, the method comprises: (i) determining an estimate of a number of particles in each of the plurality of the groups of particles; (ii) determining an average residual energy value per particle of the plurality of the groups of particles based on the estimates; (iii) sorting individual particles into subsets based on the trajectory data, where each sorted particle is associated with an average residual energy value; (iv) identifying outlying average residual energy values in a distribution of the residual energy values for a subset. Optionally, the method comprises determining an adjusted estimate of the number of particles in at least one of the plurality of the groups of particles and repeating (ii)-(iv) with the adjusted estimate. Optionally, the method comprises removing data for individual particles with the outlying average residual energy values. Optionally, the method comprises removing data for individual particles with the outlying average residual energy values and for other individual particles in the same group of particles. Optionally, determining trajectory data for individual particles comprises: determining proximal position data at a proximal beam tracker on an input side of a subject, wherein the proximal position data indicates incident positions of individual particles in the groups of particles; and determining incident trajectories of the individual particles using the proximal position data. Optionally, determining trajectory data for individual particles comprises: determining distal position data at a distal beam tracker on an output side of a subject, wherein the distal position data indicates incident positions of individual particles in the groups of particles; and determining exit trajectories of the individual particles using the distal position data. Optionally, determining trajectory data for individual particles comprises: determining proximal position data at a proximal beam tracker on an input side of a subject, wherein the proximal position data indicates incident positions of individual particles in the groups of particles; determining distal position data at a distal beam tracker on an output side of a subject, wherein the distal position data indicates incident positions of individual particles in the groups of particles; determining incident trajectories of the individual particles using the proximal position data; determining exit trajectories of the individual particles using the distal position data; and determining a full trajectory comprising one of the determined incident trajectories and one of the determined exit trajectories. Another aspect of the present invention provides a method of determining residual energy of an individual particle of hadron radiation according to claim 11. This method may be performed by a processing apparatus which is connected to one or more beam trackers and a residual energy measurement unit (e.g. RERD). Optionally, the method comprises one or more of the steps of the previous aspect. Another aspect of the present invention provides computer readable instructions which, when executed by a computer, are arranged to perform the method according to the previous aspect. Another aspect of the present invention provides an apparatus for determining residual energy of an individual particle of hadron radiation according to claim 12. Optionally, the apparatus is configured to perform one or more steps of the method of the previous aspects. Optionally, the residual energy measurement unit comprises: at least one scintillator element configured to emit a quantity of light in response to energy of incident particles of hadron radiation passing through or along that scintillator element; and a detector to convert the light from the at least one scintillator element into an electrical signal. Optionally, the residual energy measurement unit comprises a two-dimensional array of scintillator elements each configured to emit a quantity of light in response to energy of one or more incident particles of hadron radiation passing through or along that scintillator element. Optionally, the proximal beam tracker comprises a position sensitive detector configured to determine a position of a particle in a two-dimensional plane at a plurality of spaced-apart positions and the distal beam tracker comprises a position sensitive detector configured to determine a position of a particle in a two-dimensional plane at a plurality of spaced-apart positions. Another aspect of the present invention provides a computed tomography scanner apparatus comprising the apparatus of the previous aspect. The proximal beam tracker is for positioning on an input side of a subject and the distal beam tracker is for positioning on an output side of the subject. The scanner apparatus is configured to use the determined energy of the individual particles to construct an image of the subject. Another aspect of the present invention provides a processing apparatus configured to determine residual energy of an individual particle of hadron radiation according to claim 18. The functionality described in this document can be implemented in hardware, software executed by a processing apparatus, or by a combination of hardware and software. The processing apparatus can comprise a computer, a processor, a state machine, a logic array or any other suitable processing apparatus. The processing apparatus may be a general-purpose processor which executes software to cause the general-purpose processor to perform the required tasks, or a plurality of general-purpose processors which collectively execute software to cause the processors to perform the required tasks. Alternatively, the processing apparatus can be dedicated to performing the required functions. Another aspect of the invention provides machine-readable instructions (software) which, when executed by a processor, perform any of the described methods. The machine-readable instructions may be stored on an electronic memory device, hard disk, optical disk or other machine-readable storage medium. The machine-readable medium can be a non-transitory machine-readable medium. The term “non-transitory machine-readable medium” comprises all machine- readable media except for a transitory, propagating signal. The machine-readable instructions can be downloaded to the storage medium via a network connection. The term “particles of hadron radiation” includes protons and any other penetrating charged particles, such as helium ions. An advantage of at least one embodiment or example of the present invention is determining accurate residual energies for individual protons over the full clinical energy range and for multiple protons per cyclotron period. An advantage of at least one embodiment or example of the present invention is that requirements of the RERD are considerably simplified. The RERD only has to determine total residual energy for a group of particles. It does not need to separate contributions of each incident particle from other particles arriving in the same group of particles. This can allow a much simpler RERD, such as a device with a single block of scintillating material, or a device with a relatively small number of scintillator elements. Embodiments of the invention may be understood with reference to the appended claims. Within the scope of this application, it is envisaged that the various aspects, embodiments, examples and alternatives, and in particular the individual features thereof, set out in the preceding paragraphs, in the claims and / or in the following description and drawings, may be taken independently or in any combination. For example, features described in connection with one embodiment are applicable to all embodiments, unless such features are incompatible. For the avoidance of doubt, it is to be understood that features described with respect to one aspect of the invention may be included within any other aspect of the invention, alone or in appropriate combination with one or more other features. BRIEF DESCRIPTION OF THE DRAWINGS One or more embodiments of the invention will now be described, by way of example only, with reference to the accompanying figures in which: Figure 1 shows absorbed radiation dose versus tissue depth for x-rays and proton radiation; Figure 2 shows a proton CT scanner; Figure 3 shows use of position-sensitive detectors to determine a vector of a proton path; Figure 4(a) shows a calorimeter and Figure 4(b) shows a range telescope for determining residual energy in a proton; Figure 5 shows an example of a proton CT apparatus; Figure 6 shows a RERD with a single block of scintillator material; Figure 7 shows a series of machine cycles of operating the proton CT apparatus; Figure 8 shows position data acquired by a beam tracker; Figure 9 shows paths of protons during a series of machine cycles of operating the proton CT apparatus; Figure 10 shows a RERD with a plurality of scintillator elements; Figure 11 shows part of a processing chain of the RERD; Figure 12 shows another part of a processing chain of the RERD; Figure 13 shows data acquisition for a scanned beam; Figure 14 shows a data structure; Figure 15 shows matching of inlet and exit trajectories; Figure 16 shows collection of data for groups of protons; Figure 17 shows sorting of proton trajectories; Figure 18 shows identifying and removing outlying data; Figure 19 shows processing to determine residual energy per proton; Figure 20 shows matrices used to solve residual energy per trajectory; Figure 21 shows two examples of position-sensitive detectors for use in the beam trackers; Figure 22 shows a method of determining residual energy data; Figure 23 shows a processing apparatus for performing the method. DETAILED DESCRIPTION Figure 5 schematically shows an example of a proton Computed Tomography (CT) apparatus. The following description refers to protons but can be applied to other charged particles. The apparatus comprises a source 70 of protons, such as a cyclotron. The apparatus comprises a first beam tracker (proximal beam tracker) 20P on a proximal side of a patient 25 and a second beam tracker (distal beam tracker) 20D on a distal side of the patient. Each of the beam trackers 20P, 20D comprises a pair of position-sensitive detectors (PSD) 20. Each of the position-sensitive detectors 20 is configured to determine position, in a two-dimensional x-y plane, of an incident proton. The positions detected by each pair of position-sensitive detectors 20 can be used to determine a straight-line estimate of a trajectory (path) 26 of an individual proton. The apparatus comprises a Residual Energy-Resolving Detector (RERD) 60. This can be called a residual energy measurement unit or a calorimeter. In its simplest form, the RERD 60 comprises a single block of scintillating material 21 coupled via a light guide 22 to a photodetector 23. The scintillating material converts energy of an incident proton into light energy. The light energy is detected by the detector 23. A broad beam 24 of essentially monoenergetic protons is emitted by the cyclotron 70. The term “monoenergetic” means that the protons have substantially the same initial energy. This beam may be scanned across the region to be imaged. For CT creation, there is a relative rotation of the instrument and the patient about the iso-centre in small angular steps. The CT reconstruction volume is effectively a cylinder 27. The initial energy of the proton, Ei, is known from the settings of the cyclotron 70. Knowing both the initial energy Ei and the residual energy Er, it is possible to determine the energy lost across the subject (Ei - Er). The energy lost across the subject is indicative of density of the part of the subject that the proton passed through and can be used to construct an image of the subject. A processing apparatus 50 is connected to the beam trackers 20P, 20D and the RERD 60. The processing apparatus 50 receives proximal position data 51, 52 from the positionsensitive detectors 20 of the proximal beam tracker 20P. The proximal position data 51, 52 indicates positions (e.g. in terms of (x, y) co-ordinates) of incident protons detected by the position-sensitive detectors 20 of the proximal beam tracker 20P. The processing apparatus 50 receives distal position data 53, 54 from the position-sensitive detectors 20 of the distal beam tracker 20D. The distal position data 53, 54 indicates positions of incident protons detected by the position-sensitive detectors 20 of the distal beam tracker 20D. The processing apparatus 50 may receive the position data directly from each PSD 20, or from circuitry associated with the beam tracker 20P (i.e. the processing apparatus 50 receives position data from circuitry associated with the beam tracker 20P for the pair of PSDs 20 of that beam tracker 20P). The processing apparatus 50 receives total residual energy data for each of a plurality of groups of protons received by the RERD 60. The total residual energy data for each of the groups of protons is indicative of residual energy contributed by that group of protons. The processing apparatus 50 is configured to use the position data 51-54 to determine trajectory data for individual protons. That is, the processing apparatus 50 is configured to use the position data 51-54 to determine an estimate of at least part of a trajectory, or path, followed by the individual protons. The processing apparatus 50 is configured to determine residual energy of the individual protons using the determined trajectory data for the individual protons and the total residual energy data for each of the plurality of groups of protons, wherein protons having the same, or a similar, trajectory are assumed to have the same residual energy. The block of scintillating material 21 may be a plastic (polymer) scintillating material. This type of material has advantages of high light output, fast response, availability of large sizes and the material is machinable. Figure 6 shows features of a plastic scintillator calorimeter. The scintillating material 21 converts energy of an incident proton into light energy. The depth / length of the scintillating material 21 is selected based on the maximum expected proton energy. A clinical proton beam therapy facility has a range of energies up to around 230 MeV. This requires a depth of scintillating material of around 300 mm, or a larger depth such as 360 mm. The light guide 22 concentrates the light to a photodetector 23. The photodetector 23 may be a photomultiplier (PMT), photodiode, silicon PMT or other suitable device. The light collection efficiency is limited by the ratio of the detector area to the scintillator cross-section area (a consequence of Liouville’s theory). This phenomenon is often referred to as the “etendue” of an optical system. Figure 6 shows an example path 28 of a decaying proton across the block of scintillating material 21. Light is emitted along the entire path 28. The emitted light is collected by the light guide 22 and detected by the photodetector 23. Figure 7 shows an example timeline of operation of a cyclotron and photodetector. Operation is in the form of a sequence of machine cycles. Four machine cycles are shown. Protons 28 are emitted from the cyclotron in short groups, or bunches, over a period of around 2 - 4 ns. A new group of protons 28 is emitted each machine cycle. In this example the machine cycle is 8 - 14 ns. The number of protons in each group may be zero, one, two or a higher number. The photodetector 23 is configured to integrate an electrical signal (responsive to light energy from the protons) over the machine cycle. This integrated signal is proportional to the proton energy deposited in each bar. The integrated signal is sampled 29 towards the end of the machine cycle, prior to the start of the next machine cycle. In an alternative implementation, the integration of the signal can be achieved by sampling with a very fast analogue-to-digital convertor (ADC) and the effective integration performed in the digital domain. Clinical quality proton CT imagery requires about 100 proton tracks and their corresponding individual residual energies per reconstruction voxel. This should achieve about 1% material density resolution. A 300 mm diameter reconstruction cylinder, 300 mm high, is 21 million 1-mm3 voxels. So, 2.1 x 109 tracks and residual energies are required in total, or about 107 per projection, with 180 such projections. A 10 pA beam current is equivalent to 6.25 x 107 protons / s. If this beam covered the full 300 mm square projection, then 160 ms of beam time would deliver 107 protons. In practice, not all incident protons will produce recoverable tracks or reach the RERD. It is reasonable to expect an overall efficiency of about 50%, after considering protons undergoing nuclear interactions, scattered by large angles out of the system, and inevitable noise contributions from the trackers and other components. So, about 300 ms of beam time is required per projection at 10 pA beam current. Figure 8 shows one of the beam trackers 20P, 20D in more detail. The beam tracker 20P, 20D comprises two x-y position-sensitive detectors (PSD) 20. Each of the PSDs 20 can determine a position of incident radiation as an x-y coordinate. The two recorded coordinates (Xi, Yi) and (X2, Y2) may then be used by the processing apparatus 50 to provide an estimate of the trajectory 14 of the proton. Each of the beam trackers 20P, 20D outputs position data which can be used to determine the positions of the incident proton, and the trajectory 14 of the proton. The position data may be in the form of (x, y) co-ordinates, or other data which can be converted to (x, y) co-ordinates. For example, each of the PSDs 20 may be implemented in the form of a set of 1D strip sensors which output 1D co-ordinates. The 1D co-ordinates can be converted to (x, y) co-ordinates by processing circuitry associated with the beam tracker, or by the processing apparatus 50. Each of the PSDs 20 is a 2D plane. The co-ordinate (Xi, Y1) is a position on the 2D plane of the first PSD 20, and the co-ordinate (X2, Y2) is a position on the 2D plane of the second PSD 20. The trajectory 14 is a vector in 3D space between the two positions (Xi, Y1) and (X2, Y2). The trajectory 14 can be projected (extended) beyond the PSDs 20. Figure 8 shows a projection of the trajectory 14 to a 2D plane 85. Trajectory 14 intersects the plane 85 at position 86. The plane 85 may represent an outer surface aligned with the CT reconstruction volume 27 (Figure 5). The trajectory 14 may be projected to any desired 2D plane or 3D surface. Figure 9 shows the CT scanning apparatus during four different time intervals. Each time interval shows a multi-proton bunch passing through the scanning apparatus. Protons emitted by the cyclotron follow different paths through the scanning apparatus. The path of a proton passing through the scanning apparatus is known from the x-y locations detected by the beam trackers 20P, 20D. For the k® proton, the trajectory Tk is: where: (xi, yi) and (X2, y2) are the co-ordinates from beam tracker 20P; and (xs, ys) and (X4, y4) are the co-ordinates from beam tracker 20D. Protons following the same path will result in nearly the same residual energy, There will be statistical variations about this value, such as due to the stochastic nature of multiple Coulomb scattering. The proton of interest is denoted by a dotted-line path 41 and residual energy is denoted by a solid star 42. The RERD outputs a signal 45 which is proportional to the total energy deposited in one machine cycle. Other protons are marked by dashed-line paths 43 and corresponding residual energies by open stars 44. These concurrent protons are uncorrelated in terms of paths and energies with the proton of interest. It is possible to use various computational methods to recover individual residual energy per proton per trajectory from the output of the RERD. The scintillator unit 21 may be a single block of scintillating material, as shown in Figure 6, or an array of scintillator elements. The scintillating material has reflective and opaque boundaries. The reflective boundaries ensure that a high portion of emitted light reaches the photodetector. Light which is initially emitted in a direction towards one of the boundaries is reflected by the boundary and eventually reaches the light guide 22 and detector 23. The opaque boundaries prevent external light from entering. A large single block of scintillator material (e.g. 40 x 40 x 36 mm) will result in long light paths of the emitted photons. Performance can be improved with an array of scintillator elements. Figure 10 shows an array of scintillator elements 29. Each scintillator element 29 is in the form of an elongated bar. The bar is coated with a highly reflective coating, such as titanium dioxide. This causes light emitted within the bar to remain trapped within that single bar. The overall assembly can be wrapped with an opaque layer to prevent any external light entering the assembly. Figure 10 shows an example path 28 of a decaying proton across the array of scintillator elements 29. Light is emitted along the entire path 28. The path 28 crosses a plurality of the scintillator elements 29. Light is emitted within each of the scintillator elements 29 crossed by the proton. Emitted light from the plurality of scintillator elements 29 is collected by the light guides 22 and detected by the detectors 23. Typical photon yields for plastic scintillators are about 1 photon per 100 eV of energy deposited. So, for 20 MeV - 230 MeV, 2 x 105 - 2.3 x 106 photons are generated. However, these scintillators do not respond linearly to the ionisation density. Very dense ionization regions will emit less light than expected based on dE / dx for minimum-ionising particles. Birks’s Law (Birks, J.B. (1951). "Scintillations from Organic Crystals: Specific Fluorescence and Relative Response to Different Radiations". Proc. Phys. Soc. A64: 874-877) for scintillator quenching (as it is termed): ' S’ rfe ““ 14-^3 . where: dY / dx is the luminescence yield per unit length for the scintillator given in 1 / cm; S is the light production efficiency for the sensor given in 1 / MeV; dE / dx is the proton stopping power in MeV / cm; kB is the quenching factor. If kB = 0, then no quenching, but in practice kB is ~0.2 mm / MeV. There are more refined relationships. Archambault et al. (Archambault L, Polf JC, Beaulieu L, Beddar S. Characterizing the response of miniature scintillation detectors when irradiated with proton beams. Physics in Medicine &Biology. 2008 Mar 10;53(7):1865) investigates energies 73 - 230 MeV and derives the following relationship: Quenching correction factor (QCF, kB) = 0.881 + 0.00796 LET with LET (linear Energy Transfer) having units of MeV / cm. Supporting evidence suggests correction can be within 0.1 % of true energy and the correction is stable over time. Quenching effects can be rectified in subsequent processing. Figure 11 shows an example of a processing chain for a single block of scintillator material 21 or a single one of the scintillator elements 29. A Silicon PMT 31 is optically coupled to a bar with integral taper 30. The processing chain comprises a pre-amplifier 32, a gated integrator circuit 33, a sample-and-hold stage 34 and an analogue-to-digital converter (ADC) 35. As discussed earlier, in an alternative implementation, integration of an electrical signal (responsive to light energy from the protons) can be performed in the digital domain. This can be achieved by sampling an output of the silicon PMT 31, or an output of the pre-amplifier 32, a (high) number of times during a machine cycle to give a set of digital values. The digital values are summed to give a value representing energy deposited during the machine cycle. Figure 12 shows an example of a subsequent stage. Outputs of the ADCs 35 are summed 38 to provide a signal representing total light output. Prior to summing individual channels, it is possible to correct for differences between channels (bars). Differences may arise due to one or more of: gain (of channels / bars and / or electronics 31-35), thresholds, etc. Outputs of individual ADCs 36 are corrected by a dedicated correction unit 37 and then summed 38. The correction factors may be determined experimentally, theoretically or from simulations. For pencil-beam scanning systems (Figure 2) only a small portion of the area of the array of scintillator elements is likely to be in use at any point in time. Further noise reduction can be achieved if the position of the beam is known in real-time. Figure 13 shows a proton beam 39 moving across an array of bars. It is assumed that, for the position of the proton beam shown, only scintillator elements A will output any emitted light. A scintillator element 29 and an associated processing chain 31-35 will be called a channel. The apparatus is configured to only activate those channels A in the neighbourhood of the current position of the beam. Figure 14 shows an example of a data structure which may be used by the processing apparatus 50. This data relates to a single machine cycle N of operation. Similar data is acquired for each machine cycle. Each of the PSDs 20 in the beam trackers 20P, 20D records the position of an incident proton as an “event”. An “event” or “hit” is a triggering of a strip sensor channel (or other position-sensitive device) in a beam tracker 20P, 20D. Each PSD 20 records the position of the detected incident proton as an x,y co-ordinate. In this example, each of the PSDs (PSD 1 to PS4) detects K events. PSD1 detects K events: xi, yi (1); Xi, yi (2);.... xi, yi (K). Similarly, PSD2 detects K events X2, y2 (1); X2, y2 (2);.... X2, y2(K). The processing apparatus 50 receives the co-ordinate data. Residual energy, Er, is the output of the RERD 60 for the same machine cycle as the event data. The maximum number of protons that can be tracked, K, will be determined by the capabilities of the beam trackers 20P, 20D and their data acquisition system. Each of the PSDs 20 may detect the same number K of events, as shown in Figure 14. Alternatively, the number of events detected by the PSDs 20 may differ. Not all protons in a particular group / bunch may reach the calorimeter and deposit their residual energy. Some protons may be lost due to nuclear interactions with intervening material or may be scattered out of the instrument. The energy deposited in the beam trackers 20P, 20D follows a Landau distribution (Grupen C. Physics of particle detection. InAlP Conference Proceedings 2000 Sep 13 (Vol. 536, No. 1, pp. 3-34). American Institute of Physics). There is a small probability that the charge deposited is less than the threshold set for each PSD. In addition, the data acquisition system will exhibit noise. The threshold for each PSD may be programmable to remove any variation between PSDs. It is also possible to provide a mechanism to control the ratio between false events and missed true events. Figure 15 shows the scanning apparatus with incident trajectories A, B of protons through the proximal beam tracker 20P and exit trajectories C, D of protons through the distal beam tracker 20D. In one example, the processing apparatus 50 determines a combined trajectory of a proton through the scanning apparatus. The combined trajectory comprises an incident trajectory of the proton through the proximal beam tracker 20P and an exit trajectory of the proton through the distal beam tracker 20D. For a machine cycle with multiple protons, there is a plurality of candidate incident trajectories (for each of the protons detected by the proximal beam tracker 20P) and a plurality of candidate exit trajectories (for each of the protons detected by the distal beam tracker 20D). The processing apparatus 50 determines a suitable match between the incident trajectories and exit trajectories. Figure 15 shows one possible method of matching the incident trajectory and exit trajectory of a proton. Several approaches are possible, from simple geometric considerations to machine learning approaches. The incident and exit trajectories are extended into the CT reconstruction volume with a cone-shaped projection. The cone has an angle 0 which represents the typical maximum scattering angle of protons. These cones are projected on to the iso-centre of the CT reconstruction volume. The incident and exit trajectory pair with the greater overlap of these projections is chosen as the full trajectory. As indicated by 40, this is essentially a Venn Diagram, where the task is to locate the greatest intersection of two sets, AB and CD, and form pairs of corresponding incident and exit trajectories. During this procedure of connecting incident and exit trajectories most incoming and outcoming protons trajectories will be correctly mapped, although some proton trajectories could be lost. Figure 16 shows acquisition of additional information about groups (bunches) of protons. The RERD 60 can only determine a total residual energy for a group (bunch) of protons received during a machine cycle. However, the beam trackers 20P, 20D provide information about the number of protons passing through the scanning apparatus during the same machine cycle as the RERD 60 determines total residual energy. The number of protons in a group (bunch), Nc, that deposit their energy in the RERD 60 is recorded. Nc may be estimated by the number of events recorded in the last PSD 43 of beam tracker 20D. PSD 43 may be positioned close to the front of the RERD 60 to ensure that the acceptance of the RERD closely matches that of PSD 43. Nc can sometimes be higher or lower than the number of identified trajectories in a bunch, Ntr. For example, Nc can be higher than Mr due to incomplete trajectory restoration. In this case, the RERD 60 measures total residual proton energy, but no information is available on the trajectories of the protons. It is also possible for Nc can be lower than Ntr due to noise. Advantageously, the system only uses data for groups (bunches) of protons for which all of the trajectories are available, i.e. when Ntr = Nc. Our extensive Monte Carlo simulations suggest that this condition is met for a large fraction of groups (bunches). The next stage is to determine the individual residual energies associated with each proton trajectory. Useful results can be obtained by sorting the trajectory data into bins, or compartments, of similar trajectories. The subsequent processing uses these bins of trajectories and determines a residual energy per proton per trajectory bin. Protons having similar trajectories are assumed to have the same residual energy. The size of the bins / compartments can be selected as a compromise between computational load (smaller bins requires more computation) and accuracy of the final energy determination (smaller bins offers higher accuracy). Figure 17 schematically shows sorting of proton trajectories into different bins / compartments. Each bin / compartment 81 represents a range, or subset, of trajectories. Each bin / compartment 81 is an approximation of a proton trajectory. There are various ways of performing the sorting. In one example, trajectories may be binned based on a 2D plane positioned at the proximal side of cylinder 27, Figure 15. All protons that enter this 2D plane at the same location are considered to have the same trajectory. This form of binning ignores the outgoing trajectory and also the direction of travel of the incoming protons. In another example, trajectories may be binned based on a first 2D plane positioned at the proximal side of cylinder 27 and a second 2D plane positioned at the distal side of cylinder 27. All protons that enter the first and second 2D planes at the same location are considered to have the same trajectory. In another example, trajectories may be binned based on a 2D plane positioned at a centre of cylinder 27. A trajectory of a proton is calculated as a mean position of: (i) a projection of the incident trajectory and (ii) a projection of the distal trajectory. Other schemes for binning are possible. Each proton trajectory is allocated to a specific one of the bins 81 which best matches the trajectory of that proton. For example, consider that two protons P1, P2 are identified during a machine cycle k. Proton P1 has a trajectory T1 and proton P2 has a trajectory T2. The protons are sorted into the best trajectory bins. In this example, the best fit for trajectory T1 is trajectory bin Tn and the best fit for trajectory T2 is trajectory bin Tn+2. Figure 17 shows the accumulated results after a number of machine cycles. Trajectory bin Tn has four entries which represent protons with closely similar trajectories; trajectory bin Tn+1 has five trajectories entries which represent five protons with closely similar trajectories; and so on. The actual number of protons per bin will typically be much higher than shown in these simple examples. In the later steps of the method, protons with similar trajectories falling within the same bin will be assumed to have a similar residual energy. For each bunch measurement there is a relationship between the residual energies related to the various bins associated with the bunch. The size of the bins is chosen in such a way that there are multiple measurements within each bin during the acquisition time for one projection. Typically, the bins are of equal size, but this is not strictly necessary. For example, one or more of the bins may have a narrower range compared to other bins. Optionally, the method can remove outliers in the set of data to improve accuracy of the residual energy calculation. For example, consider that a single proton enters the RERD 60 and the RERD 60 outputs a total residual energy measurement, but the beam tracker incorrectly determines Nc =2. The residual energy data associated with this machine cycle can be removed. Figure 18 illustrates a process for identifying and removing outlying data. This process may be performed per bin / compartment of trajectory data, such as each bin 81 of Figure 17. To recap, during each machine cycle a group of protons passes through the scanning apparatus. The following data is acquired: (i) trajectory data for each of the protons in the group; (ii) one total residual energy data value (Er) for the group of protons; (iii) a number of protons (Nc) in the group. Residual energy data is also allocated to trajectory bins 81. For each machine cycle, the quantity Er 82 represents total residual energy for the group of photons. The individual residual energy per proton is unknown. However, it is possible to calculate an average residual energy per proton Ea. One way of calculating Ea is to calculate the ratio of Er and Nc, 83. The result of this calculation 84 is not the actual residual energy per proton, but an approximate exit energy per proton in the bunch. This is a useful quantity for identifying erroneous data. Referring again to the list, during each machine cycle the following data is acquired: (i) trajectory data for each of the protons in the group; (ii) total residual energy data (Er) for the group; (iii) an estimated number of protons (Nc) in the group; (iv) average residual energy per proton (Ea) in the group. The “average residual energy per proton” Ea is assigned as the exit energy Ee for each of the protons in the group. The exit energy Ee is entered into a trajectory bin 81 for each of the protons. For example, consider that two protons are identified during a machine cycle k. The protons are sorted into the best trajectory bins. In this example, the protons are sorted into bins Tn and Tn+2. The exit energy Ee is stored in bins Tn and Tn+2. After a number of machine cycles, each compartment contains a number of entries from different groups of protons. These entries include exit energy Ee values for the protons. These exit energy values form a statistical distribution. An example statistical distribution is shown in Figure 18(a). Typically, the distribution has a narrow peak and some outlying data. Outlying data falling outside a certain distance of the central peak or mean of the distribution can be removed at this stage. Figure 18(b) shows the portions of the distribution which are identified as outlying data. Figure 18(c) shows the remainder of the distribution, after removal of the outlying data. When a data value is deemed to be an outlier, all data associated with that group of protons is removed. So, in the example above, the entries in bins Tn and Tn+2 for other protons in machine cycle k are removed. The aim of this outlier detection stage is to identify cases where Ncwas incorrectly estimated and, if possible, to correct the estimate to obtain a better fit to the data. If a better estimate of Nc is not possible, protons having outlying energy values are discarded. An example of identifying outlying data is now described: - For each trajectory bin 81, perform a Gaussian fit to determine the mean and standard deviation on Ee for that bin; - For each group, count how many of the protons have an EEthat lies within 3 sigma of the mean of their respective bins. If most of the protons are not within 3 sigma of the mean, it is assumed that Nc was incorrect. An updated estimate of Nc is tried for groups of protons associated with that trajectory bin 81. This can involve recalculating data for multiple groups of protons and calculating new values of Ea and Ee. This is repeated until all of the protons have an EEthat lies within the expected 3 sigma range of the mean. - If, after trying to find a new estimate of Ncfor every bunch, some of the protons still do not lie within 3 sigma of the mean, protons having outlying Ee values are discarded. The improved estimate of Nc is used in the comparison with the determined number of trajectories per group (Ntr = Nc). Groups which do not meet the requirement of Ntr= Nc are removed. This leaves a more reliable set of total residual energy data for groups, and a complete set of trajectories for the individual protons in those groups. Each group measurement can be represented by an equation which equates the sum of the individual residual energies per trajectory bin 82 to the total residual energy measured by the calorimeter 83. During the acquisition of a specific CT projection many such equations are obtained. The total number of equations is determined by: the trajectory bin size; the total number of protons; and the average number of protons per group (bunch). The total number of protons is on the order of 107 per angle, and there are typically 1-5 protons per group, so that the total number of equations is on the order of 106. Figure 19 shows how this set of equations can be rewritten in a matrix equation. The trajectories 91 of individual protons in the groups (bunches) is a known quantity. The total residual energy per group (bunch) 93 is also a known quantity. The residual energy per trajectory bin 92 is an unknown quantity. This will be generally an overdetermined system, and an approximate solution can be found by various methods. One possible method is by using a conventional least squares method. QR factorisation is, in practice, infeasible because of the inefficient scaling with the number of equations, which is typically very large. The matrix associated with the system of equations is sparse in nature. Efficient iterative solvers that solve approximately linearly in time with the number of equations are available. The paper “LSMR: An iterative algorithm for sparse leastsquares problems”, DCL Fong and M Saunders, SIAM J. Sci. Comput., 2011, Vol. 33, No. 5, pp. 2950-2971, describes a suitable approach to solving this problem. The exit energy of each individual proton is associated with its trajectory bin energy, which is the solution of this system of equations. This process is explained below. Consider a set of linear equation where the coefficients, 3mn, represent a proton trajectory through the system and Xn is its residual energy. On the right-hand side, is the combined residual energy values for a group of protons, bm. Here 1<n<N, where N is the total number of bins. Furthermore, 1<m<M, where M is the total number of groups (bunches). anxi + 312X2 +...+ aiN xn = bi a2ixi + 822X2 +...+ a2N xn = b2 aiVHXl + 3M2X2 +...+ aMN Xn = blVI These equations can be written in matrix form, AX=B where: A is a matrix formed of the 3mn coefficients, X is a vector (N x 1 matrix) formed of the Xn coefficients, and B is a vector (M x 1 matrix) formed of the bm coefficients. This is shown in Figure 20. The trajectories are known. The total residual energy per group of protons, bm, are also known. The residual energy Xn is unknown. Typically, M»N and hence the matrix equation AX =B is overdetermined. Due to a spread of proton energies per bin, the system does not have a solution. Instead, X is solved by minimizing the difference between the left and right-handed side. One way would be to minimize the loss function ||AX - B||2, i e., the difference between the left-hand side and right-hand side is minimized in a least-square fashion. Other loss functions (such as with a power different from 2, or a different function) are also possible. Another option is to add an Nc-dependent factor for each relation (i.e. each group), although this does not affect the results much. Groups (bunches) that contain only single protons may, or may not, be excluded from binning and / or from determining their residual energy as a result of such iterative methods. Alternative binning procedures could also be employed, such as inverse bi-linear or inverse-multi-linear interpolation. For a CT scanner, four (x, y) co-ordinates from the beam trackers have a 500 x 500 pixel resolution. Each beam tracker can produce one in 5002 values = 250,000 values. There are four beam trackers, so there are up to 250,0004 (around 4 x 1021) possible trajectories. To decrease the number of possibilities, we could assume that the residual energy of a proton is predominantly determined by the incoming (proximal) position, leading to N=250,000 values. The number of protons per angle is on the order of 5,000,000. Depending on the current, the number of groups is of the order of M=2,000,000 and hence the matrix A is still very large. With these numbers it contains 5 x 1011 elements (2 TB of 32 bits floats). However, the nonzero coefficients of the matrix A are sparsely distributed. Solving the minimization procedure on X may use iterative methods, which makes a guess at the “x” values and refines gradually. One example method of solving uses a least square error function to refine. This converges to a result with low computational cost. Any of the aforementioned variations or methods of a similar spirit could be used and are (for simplicity) referred to as solving a system of equations. Trajectory data In the examples described above, the method determines a trajectory of a proton through the scanning apparatus. The trajectory comprises an incident trajectory of the proton through the proximal beam tracker 20P and an exit trajectory of the proton through the distal beam tracker 20D. This full trajectory (incident trajectory and exit trajectory) is used when sorting trajectories of protons into trajectory bins. In other examples, the method uses a simpler representation of the trajectory. For example, only the incident trajectory is used. The incident trajectory is used when sorting trajectories of protons into trajectory bins. Where only the incident trajectory is used, the method may still use data from the distal beam tracker 20D. For example, data from the distal beam tracker 20D may be used to obtain the number of protons in a group (bunch), Nc and / or for image generation (backprojection + filtering type step that converts the energies and trajectories into a 3D image of the patient.) Position sensitive detectors Figure 21 shows two examples of a position-sensitive detector which may be used to implement the beam trackers 20P, 20D. In Figure 21(a) the position-sensitive detector 20 comprises an array of crossed silicon strip detectors or crossed scintillator fibres. In the case of a silicon strip sensor a single proton will create excess charge. In the case of a scintillator fibre sensor a single proton will create excess light. The charge or light is detected at the end of each strip, thereby providing an x-y location. Figure 21(b) shows an improved positionsensitive detector with three or more sets of rotated strips 210A1, 210A2, 210A3. Each set of strips has an associated readout circuit 210A1R, 210A2R, 210A3R which outputs a data signal 210A1D, 210A2D, 210A3D indicating detected position of an incident proton. This PSD is described in WO 2015 / 189601 A1. Other types of PSD may be used. For example, the PSD may be pixellated such as Active Pixel Sensors (CMOS Imagers). Pulsed scanning beams The cyclotron which generates the scanning beam has an operating envelope in terms of current. Operating below a current of a few pA poses challenges in changing the operational envelope of the cyclotron and the delivery system. This can create unacceptable delays in switching between imaging and treatment modes. For a 10 pA current (72 MHz cyclotron frequency), then 42% of proton bunches will contain no protons, 36% will contain one and 22% contain two or more. Hence the use of a RERD that can only correctly respond to single proton bunches will be inefficient so extending the overall data collection time. By providing a RERD which can determine individual energies for up to 6 protons in a bunch, the efficiency can be greater than 99.9%. If the preceding trackers can resolve up to 7 trajectories per pulse and the beam current is increased to a more realistic 50 pA, the system would be 85% efficient. The overall data acquisition time will be greatly reduced. The total beam time required to acquire this dose when accepting up to 7 protons per bunch at 50 pA is 11 s, while operating at 10 pA and only accepting single protons would require 114 s (assuming 3 x 109 protons recorded for an entire data set). Figure 22 shows a method which may be implemented by the processing apparatus 50 of Figure 5. Figure 23 also shows functionality 102, 104 performed by beam trackers 20P, 20D and RERD 60. At block 102, beam trackers 20P, 20D determine position of individual incident particles. Each beam tracker detects position of a plurality of simultaneously, or near simultaneously, incident particles within one machine cycle. Each beam tracker outputs position data. The position data may be in the form of co-ordinates indicating positions in two position sensitive detectors 20. At block 104, RERD 60 determines total residual energy per group (bunch) of particles. As described above, this represents the total residual energy for a group of one, two or more particles which arrive at the RERD within one machine cycle. At block 106 the processing apparatus 50 receives the position data. At block 108 the processing apparatus 50 receives the total residual energy data. At block 110 the processing apparatus 50 determines trajectory data for individual particles using the position data. As described above, this block may determine an incident trajectory of a particle based on position data, which may be in the form of positions detected by spacedapart PSDs of a proximal beam tracker 20P. This block may determine an exit trajectory of a particle based on position data, which may be in the form of positions detected by spacedapart PSDs of a distal beam tracker 20D. This block may compare incident and exit trajectories and attempt to find the best match. At block 112 the processing apparatus 50 determines residual energy of individual particles. At block 114 the processing apparatus 50 allocates, or partitions, the trajectories of individual particles (block 110) into subsets of trajectories. This can be considered allocating trajectories to bins or compartments, each defining a range of trajectories. Optionally, at block 116, the method removes outliers. These are values which lie outside an expected range. This block may remove residual energy data associated with groups of outliers. At block 118 the processing apparatus 50 retains total residual energy data for groups of particles with complete trajectory data. One way of implementing this block is to compare, for a group of particles, a number of events Nc reported by the distal beam tracker with a number of determined trajectories Ntr from block 110. This block removes residual energy data associated with those groups where Nc does not equal Ntr. At block 120 the processing apparatus solves a set of data to determine an unknown quantity of residual energy per particle per trajectory (subset). As described above, this block may solve a set of linear equations or matrices which define: (i) total residual energy per group of particles; and (ii) trajectory subsets (bins) for data acquired during a scanning projection. At block 122 the processing apparatus uses the residual energy data to determine energy lost across the subject. Knowing the initial energy of a particle and the residual energy of the particle gives the energy lost across the subject (patient). This is indicative of density of a part of the subject that the particle passed through. At block 124 the processing apparatus uses the energy lost across the subject in CT imaging. The energy lost across the subject is used to construct the CT image. Blocks 102-112 are performed for every single group of protons from the cyclotron. Blocks 114-120 are applied once for each relative orientation of the patient (i.e. 180 times). Blocks 122 and 124 are performed once after data has been processed for all patient orientations. Figure 23 shows an example of a processing apparatus 300 which may implement at least part of the processing of the invention, such as the method of Figure 22. The processing apparatus 300 can be the processing apparatus 50 shown in Figure 5. Processing apparatus 300 comprises one or more processors 301 which may be any type of processor for executing instructions to control the operation of the device. The processor 301 is connected to other components of the device via one or more buses 306. Processor-executable instructions 303 may be provided using any data storage device or computer-readable media, such as memory 302. The processor-executable instructions 303 comprise instructions for implementing the functionality of the described methods. The memory 302 is of any suitable type such as nonvolatile memory, a magnetic or optical storage device. The processing apparatus 300 comprises input / output (I / O) interfaces 307. The I / O interfaces 307 can receive signals from other apparatus, such as the beam trackers 20P, 20D and RERD 60. The I / O interfaces 307 can output signals to other apparatus. The processing apparatus 300 connects to a user interface 308. Memory 302, or a separate memory, stores data used by the processor. This can include: position data 311; trajectory data 312; total residual energy per group of particles data 313; total residual energy per particle data 314. The functionality shown in blocks 102 and 104 is performed during a data acquisition period, during the machine cycles of the cyclotron. It acquires raw data about position of incident particles and residual energy. The functionality shown in blocks 110 and 112 may be performed offline. That is, it can be performed during a later period of time, after the data acquisition period, using the raw data from blocks 102 and 104. The processing apparatus 50 is shown in Figure 5 as a single unit. Processing functions may be distributed among two or more processors which collectively perform the overall functionality. As described above, some functionality may be performed by processing circuitry (such as a Field Programmable Gate Array (FPGA)) associated with the beam trackers 20P, 20D or the RERD 60. For example, incident trajectories may be determined by processing circuitry (such as a FPGA) associated with the proximal beam tracker 20P and exit trajectories may be determined by processing circuitry associated with the distal beam tracker 20D. Throughout the description and claims of this specification, the words “comprise” and “contain” and variations of the words, for example “comprising” and “comprises”, means “including but not limited to”, and is not intended to (and does not) exclude other moieties, additives, components, integers or steps. Throughout the description and claims of this specification, the singular encompasses the plural unless the context otherwise requires. In particular, where the indefinite article is used, the specification is to be understood as contemplating plurality as well as singularity, unless the context requires otherwise. Features, integers, characteristics, compounds, chemical moieties or groups described in conjunction with a particular aspect, embodiment or example of the invention are to be understood to be applicable to any other aspect, embodiment or example described herein unless incompatible therewith.

Claims

1. A method of determining residual energy of an individual particle of hadron radiation in a system in which groups of particles are transmitted, the method comprising:determining trajectory data for individual particles in each of a plurality of the groups of particles, wherein the trajectory data for one of the individual particles is indicative of at least part of a trajectory through the system for that individual particle;determining total residual energy data for each of the plurality of the groups of particles;determining residual energy of the individual particles using the determined trajectory data for the individual particles and the determined total residual energy data for each of the plurality of the groups of particles, wherein determining residual energy of the individual particles comprises:sorting an overall set of the determined trajectory data for individual particles into subsets of trajectory data, wherein individual particles within a same subset of trajectory data have the same, or a similar, trajectory and are considered to have the same residual energy;forming a set of equations or a matrix equation which use the subsets of trajectory data for the individual particles and the total residual energy data for the groups of particles as known quantities, and residual energy of the individual particles as an unknown quantity; andsolving the set of equations or matrix equation to determine the residual energy of the individual particles per trajectory.

2. The method of claim 1 comprising:identifying groups of particles with an incomplete set of determined trajectories; andremoving the total residual energy data forthose groups of particles with an incomplete set of determined trajectories.

3. The method of claim 2 comprising:determining a number of particles in one of the groups;determining a number of trajectories for the group;comparing the determined number of particles in the group with the determined number of trajectories for the group; andremoving the total residual energy data for the group of particles when the determined number of particles in the group does not equal the determined number of trajectories for the group.

4. The method of any one of the preceding claims comprising:(i) determining an estimate of a number of particles in each of the plurality of the groups of particles;(ii) determining an average residual energy value per particle of the plurality of the groups of particles based on the estimates;(iii) sorting individual particles into subsets based on the trajectory data, where each sorted particle is associated with an average residual energy value;(iv) identifying outlying average residual energy values in a distribution of the residual energy values for a subset.

5. The method of claim 4 comprising determining an adjusted estimate of the number of particles in at least one of the plurality of the groups of particles and repeating (ii)-(iv) with the adjusted estimate.

6. The method of claim 4 or 5 comprising removing data for individual particles with the outlying average residual energy values.

7. The method of claim 6 comprising removing data for individual particles with the outlying average residual energy values and for other individual particles in the same group of particles.

8. The method of any one of the preceding claims wherein determining trajectory data for individual particles comprises:determining proximal position data at a proximal beam tracker on an input side of a subject, wherein the proximal position data indicates incident positions of individual particles in the groups of particles; anddetermining incident trajectories of the individual particles using the proximal position data.

9. The method of any one of the preceding claims wherein determining trajectory data for individual particles comprises:determining distal position data at a distal beam tracker on an output side of a subject, wherein the distal position data indicates incident positions of individual particles in the groups of particles; anddetermining exit trajectories of the individual particles using the distal position data.

10. The method of any one of the preceding claims wherein determining trajectory data for individual particles comprises:determining proximal position data at a proximal beam tracker on an input side of a subject, wherein the proximal position data indicates incident positions of individual particles in the groups of particles;determining distal position data at a distal beam tracker on an output side of a subject, wherein the distal position data indicates incident positions of individual particles in the groups of particles;determining incident trajectories of the individual particles using the proximal position data;determining exit trajectories of the individual particles using the distal position data; anddetermining a full trajectory comprising one of the determined incident trajectories and one of the determined exit trajectories.

11. A method of determining residual energy of an individual particle of hadron radiation in a system in which groups of particles are transmitted, the method comprising:receiving position data for individual particles in each of a plurality of the groups of particles, wherein the position data for one of the individual particles is indicative of positions of that individual particle along at least part of a trajectory through the system;receiving total residual energy data for each of the plurality of the groups of particles, wherein the total residual energy data for one of the groups of particles is indicative of residual energy contributed by that group of particles;determining trajectory data for individual particles in each of a plurality of the groups of particles based on the received position data, wherein the trajectory data for one of the individual particles is indicative of at least part of a trajectory through the system for that individual particle;determining residual energy of the individual particles using the trajectory data for the individual particles and the total residual energy data for each of the plurality of groups of particles, wherein determining residual energy of the individual particles comprises:sorting an overall set of the determined trajectory data for individual particles into subsets of trajectory data, wherein individual particles within a same subset of trajectory data have the same, or a similar, trajectory and are considered to have the same residual energy;forming a set of equations or a matrix equation which use the subsets of trajectory data for the individual particles and the total residual energy data for the groups of particles as known quantities, and residual energy of the individual particles as an unknown quantity; and solving the set of equations or matrix equation to determine the residual energy of the individual particles per trajectory.

12. Apparatus for determining residual energy of an individual particle of hadron radiation in a system in which in which groups of particles are transmitted, the apparatus comprising:a proximal beam tracker configured to determine proximal position data for individual particles in each of a plurality of the groups of particles, wherein the position data for one of the individual particles is indicative of positions of that individual particle along at least part of a trajectory through the system;a distal beam tracker configured to determine distal position data for individual particles in each of a plurality of the groups of particles, wherein the position data for one of the individual particles is indicative of positions of that individual particle along at least part of a trajectory through the system;a residual energy measurement unit configured to receive the plurality of the groups of particles and to determine total residual energy of each of the plurality of the groups of particles, the residual energy measurement unit configured to output total residual energy data indicative of total residual energy of each of the plurality of groups of particles; anda processing apparatus configured to:determine trajectory data for individual particles in each of a plurality of the groups of particles based on the received position data, wherein the trajectory data for one of the individual particles is indicative of at least part of a trajectory through the system for that individual particle;determine residual energy of the individual particles using the trajectory data for the individual particles and the total residual energy data for each of the plurality of groups of particles,wherein the processing apparatus is configured to determine residual energy of the individual particles by:sorting an overall set of the determined trajectory data for individual particles into subsets of trajectory data, wherein individual particles within a same subset of trajectory data have the same, or a similar, trajectory and are considered to have the same residual energy;forming a set of equations or a matrix equation which use the subsets of trajectory data for the individual particles and the total residual energy data for the groups of particles as known quantities, and residual energy of the individual particles as an unknown quantity; andsolving the set of equations or matrix equation to determine the residual energy of the individual particles per trajectory.

13. The apparatus of claim 12 wherein the processing apparatus is configured to perform the method of any one of claims 2 to 10.

14. The apparatus of claim 12 or 13 wherein the residual energy measurement unit comprises:at least one scintillator element configured to emit a quantity of light in response to energy of incident particles of hadron radiation passing through or along that scintillator element; anda detector to convert the light from the at least one scintillator element into an electrical signal.

15. The apparatus of claim 14 wherein the residual energy measurement unit comprises a two-dimensional array of scintillator elements each configured to emit a quantity of light in response to energy of one or more incident particles of hadron radiation passing through or along that scintillator element.

16. The apparatus of any one of claims 12 to 15 wherein the proximal beam tracker comprises a position sensitive detector configured to determine a position of a particle in a two-dimensional plane at a plurality of spaced-apart positions and the distal beam tracker comprises a position sensitive detector configured to determine a position of a particle in a two-dimensional plane at a plurality of spaced-apart positions.

17. A computed tomography scanner apparatus comprising the apparatus of any one of claims 12 to 16, wherein the proximal beam tracker is for positioning on an input side of a subject and the distal beam tracker is for positioning on an output side of the subject, wherein the scanner apparatus is configured to use the determined residual energy of the individual particles to construct an image of the subject.

18. A processing apparatus configured to determine residual energy of an individual particle of hadron radiation in a system in which groups of particles are transmitted, the processing apparatus configured to:receive position data for individual particles in each of a plurality of the groups of particles, wherein the position data for one of the individual particles is indicative of positions of that individual particle along at least part of a trajectory through the system;receive total residual energy data for each of the plurality of the groups of particles, wherein the total residual energy data for one of the groups of particles is indicative of residual energy contributed by that group of particles;determine trajectory data for individual particles in each of a plurality of the groups of particles based on the received position data, wherein the trajectory data for one of the individual particles is indicative of at least part of a trajectory through the system for that individual particle;determine residual energy of the individual particles using the trajectory data for the individual particles and the total residual energy data for each of the plurality of groups of particles,wherein the processing apparatus is configured to determine residual energy of the individual particles by:sorting an overall set of the determined trajectory data for individual particles into subsets of trajectory data, wherein individual particles within a same subset of trajectory data have the same, or a similar, trajectory and are considered to have the same residual energy;forming a set of equations or a matrix equation which use the subsets of trajectory data for the individual particles and the total residual energy data for the groups of particles as known quantities, and residual energy of the individual particles as an unknown quantity; andsolving the set of equations or matrix equation to determine the residual energy of the individual particles per trajectory.

19. Computer readable instructions which, when executed by a computer, are arranged to perform the method according to any one of claims 1 to 11.

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