Classifications

• • G—PHYSICS
  • G06—COMPUTING; CALCULATING OR COUNTING
  • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
  • G06T11/00—2D [Two Dimensional] image generation
  • G06T11/003—Reconstruction from projections, e.g. tomography
  • G06T11/005—Specific pre-processing for tomographic reconstruction, e.g. calibration, source positioning, rebinning, scatter correction, retrospective gating

Definitions

• the present invention relates to the field of image tomography, and in particular to methods of identifying, locating or analysing objects of interest in single-photon emission tomography (SPET) or PET studies.
• SPET single-photon emission tomography
• the technique is used to construct a three-dimensional map of radioactivity sources within an entity or target body, providing relative levels of radioactivity emanating from each of a plurality of volume elements making up the entity.
• the radioactivity sources are gamma radiation emitters which have been injected into the body of a patient, and these are detected by a gamma camera which images a plurality of views of the body as illustrated in figures 1 and 2.
• three dimensional mapping of other entities is also achieved with this technique.
• the imaging system typically comprises a detector 10 and a coliimator 15 adapted to image emissions parallel to the axis of the coliimator, ie. as depicted in figure la, in the x-direction.
• images are taken every 2 — 6° .
• the resulting set of images each provide total radiation counts for, or projections of, a plurality of parallel columns 22 passing through the body.
• back-projection techniques are well-known in the art, but all of them make a substantial number of approximations and assumptions about the data which result in an effective filtering of the data when reconstructing the voxel data.
• back-projection techniques necessarily use an averaging process to determine the values of individual voxels, and thus introduce a smoothing effect, ie. a high-frequency filtration of the data.
• the voxel map produced in the reconstructed image cannot be considered as "raw data” and further processing (ie. filtering for image enhancement or quantitative analysis) of this data can cause problems with unwanted filtering artefacts such as aliasing and the like.
• a digital data processing system must, in creating a reconstructed image, back-project to a predetermined back- projection matrix 35 or grid, such as that shown in figure Id. Because of this, a substantial amount of inte ⁇ olation of the data is required when a projection such as that shown in figure lb is not aligned with the back- projection matrix (figure Id). In other words, the quantized x' axis ofthe camera must be mapped to the quantized x-y axes of the matrix 35.
• Various schemes exist for such inte ⁇ olation varying from "nearest-pixel" mapping to linear and even more complex interpolation methods, all of which introduce a further element of data filtration. Filtering is required, subsequent to this inte ⁇ olation, in particular to remove the "star” artefact, which also introduces interdependence of voxel values that prevents derivation of quantitative parameters.
• a further example is attenuation and scatter correction.
• Each projection image provides a total radiation count for a given column 22.
• a simple, but unsophisticated technique for back-projection is to assume, in the first instance, that the radiation count derives from sources distributed evenly throughout the length of the column, before weighting the data with counts from other images transverse thereto in the reconstruction process.
• this simplistic approach ignores known attenuation and scatter factors for radiation passing through the body 20, for which approximate corrections can be made during the back-projection process.
• such corrections also introduce filtering artefacts which can cause problems with later data processing.
• the ability to provide quantitative measurement of radiation sourced from a region of interest within a body is a highly desirable goal in a number of fields.
• there are many clinical benefits such as enabling a clinician to more accurately locate and analyse a disease site in a scanned patient.
• the ability to use time as an additional factor in deriving quantitative data further enhances the ability to make dosimetry measurements for radionuciide therapy of cancer and other diseases.
• such techniques have a far wider applicability beyond aiding diagnosis and therapy of the living body.
• the present invention provides a method of deriving quantitative data from a raw projection data set of an entity in a tomographic image by the steps of:
• the present invention provides a method of enhancing portions of an entity in a tomographic image by elimination of contributions thereto from a selected object within the entity by the steps of: (a) segmenting out the selected object in the projected images; (b) modifying the raw data set to form a second data set in which contributions from the selected object have been eliminated; and
• the present invention provides a method of segmenting out at least one selected object from a raw projection data set of an entity in a tomographic image and modifying the raw projection data set to form a second data set comprising data relating only to the at least one selected object, comprising the steps of: forming a sinogram for a given transverse plane; identifying the edges of a selected object for a selected theta value; tracking the edges of the object through its sinusoidal path on the sinogram for all theta to determine an object extent; modifying the raw data set to form the second data set by using only data corresponding to the object extent.
• the methods are useful in imaging the body of a patient.
• a still further aspect of the invention provides a method of locating a disease site in a patient, the method comprising the method of the first or second aspects of the invention wherein the entity is the body of the patient and the at least one selected object is either: (a) the disease site, or (b) a site which partially obscures the disease site.
• disease site we include any site in the body which exhibits abnormal characteristics.
• a disease site includes a tumour which may be a primary tumour or may be a secondary tumour or metastasis.
• the disease site may be a prostate tumour and a typical site which obscures this is the bladder of the patient.
• Figures 1(a) to 1(d) show schematic diagrams in the x-y plane useful in the explanation of back-projection tomography techniques
• Figure 2 shows a perspective schematic view of a plurality of images or projections formed from a single transaxial plane or "slice" through a body
• Figure 3 shows a schematic view of a sinogram presentation of the images in figure 2;
• Figures 4(a) and 4(b) show a further schematic view of a sinogram presentation of a more complex set of images together with a corresponding plot of total counts per angle of the sinogram for an object therein;
• Figure 5 shows a further schematic view of the sinogram presentation of figure 4(a);
• FIG. 6 shows a flow diagram of the principal steps of the present invention
• Figure 7 shows a flowchart for the initialization of a forward projection image matrix
• Figures 8(a) to 8(f) show a flowchart indicating the steps taken during automated segmentation of data in each sinogram;
• Figure 9 shows a flowchart indicating the steps taken during manual segmentation of data in each sinogram;
• Figures 10 and 11 show the steps taken during the forward projection of the segmented data to estimate counts contributed from segmented objects
• Figure 12 to 17 show exemplary images illustrating use of the techniques of the present invention, in which:
• Figure 12 is a conventionally back-projected reconstruction of a transverse section at human kidney level
• Figure 13 is a hybrid image with both kidneys and spleen in an estimated body outline
• Figure 14 shows the result of the first iteration of an algorithm according to the present invention to remove the contribution of the right kidney to the raw data
• Figure 15 shows the result of the final iteration of the algorithm according to the present invention having removed the right kidney without affecting the left kidney or spleen;
• Figure 16 shows a transverse section of a conventionally reconstructed image at bladder level
• Figure 17 shows a transverse section corresponding to figure 16, but with pre-processing of the raw data set according to the present invention prior to reconstruction;
• Figure 18 shows a diagram illustrating a sinogram row presentation of raw data according to one aspect of the present invention
• Figures 19(a), 19(b) and 19(c) show actual image raw data in the sinogram row presentation of figure 18;
• Figure 20 shows a diagrammatic three dimensional view of the sinogram row presentation of data of figure 18;
• Figures 21(a), 21(b) and 21(c) are diagrams useful in explaining data processing techniques according to one aspect of the present invention.
• Figure 22 shows a diagram of a panspectral version ofthe sinogram row presentation of figures 18 to 20.
• a body 20 located at the centre of rotation of a gamma camera is imaged in a transaxial or transverse (x-y) plane to produce a plurality of projections 30 0 to 30 n , each at an angle theta to the back-projection matrix 35 in the x-y plane.
• the projections 30 are shown as having finite dimension in the z-direction.
• a gamma camera will comprise a two- dimensional array coliimator thereby providing simultaneous data collection for several transaxial planes at once.
• An object of interest 40 located within the body 20 at position i,j,k is imaged on the projections 30 at varying positions as indicated, representing an increased or decreased number of counts usually displayed as intensity of the image.
• FIG. 3 there is shown a sinogram presentation 50 of the data collected in figure 2.
• the sinogram trace 45 can be predicted in both phase and amplitude (which correspond to the location of the object in the x-y plane) and in variation of the number of counts (or intensity) along the trace (which corresponds to the effects of physical factors such as attenuation and scatter).
• the change in counts between the first few projections 30 0 , 30 t etc and the last few projections 30 n . ⁇ , 30 n represent any changes in activity within the period of acquisition.
• the shape of the object of interest will manifest itself as a variation in the thickness a,b of the trace 45 with varying theta, the edges of the object of interest typically being discernable by changes in intensity.
• a sinogram 60 is shown for two objects spatially separated within the body being scanned.
• Trace 62 represents an object for which quantitative data is required.
• Trace 64 represents an interfering object in which we have no interest. For a large part of the sinogram, the traces do not meet, eg.
• the selected object for segmentation may take one of two forms. In the first scenario, it is only the selected object for which the user requires detailed or quantitative count information, or a detailed three dimensional image. In this case, all other data in a sinogram is discarded, leaving only data corresponding to the selected object as an object of interest.
• the selected object may be an obscuring object, the data from which is masking or interfering with the data required during the reconstruction process. For example, there may be an accumulation of radioactive material in a particular organ in a patient's body which is not of interest, but the high counts generally obscure other regions in which smaller, but nevertheless crucial quantities of radioactive material are accumulated. In this case, data corresponding to the selected object are discarded, leaving all other raw data intact and more clearly showing any objects of interest.
• an image may be formed from the remaining data, and quantitative measurements made.
• the raw image data from projections 30 j to 30 n are loaded into the computer system (step 101).
• a sinogram representation 60 of the data is formed (step 102) and, based on operator analysis of the sinogram, the sinogram trace 62 relating to a selected object is identified (steps 103, 104).
• the edges of the selected object are defined (step 105), and the count data from the object isolated from the raw data (step 106) to form a second data set (step 111), either by segmenting out the selected object to leave the selected object data only (steps 107, 108), or by segmenting out the selected object to leave all other data (steps 109, 110) more clearly showing any objects of interest within the body.
• This modified data set may then be used to form an image (step 1 12), or to provide quantitative data such as volume of the object, activity within the object and activity variation with time (steps 1 14-1 16), providing output either on a suitable display device or print out (step 1 17).
• step Al parameters for the forward projection of matrix 35 are specified for each transverse (x-y) image plane, including matrix size (resolution) and number of projections 30 comprising the raw data set.
• Other display parameters may be set, and the method of inte ⁇ olation to be used for back-projection of the projections 30 onto the non-aligned matrix 35 is specified.
• step A2 a matrix is constructed which gives the mapping of a point (i,j) in the x-y plane of the transverse image onto the sinogram at values (x',k).
• step Bl the raw data from gamma camera 10 is loaded into the computer system.
• the data is re-formed into a set of sinograms as illustrated in figures 3 and 4, each corresponding to a transaxial slice.
• the user For the pu ⁇ oses of segmenting out the data, the user first selects the sinogram to display (step B2). The selection depends upon the location of the object relative to the z-axis, and the relative positions of other traces. For example, the projection may be clearer in some sinograms than others.
• the user then opts (step B3) for either automatic object definition (step B5) or manual object definition (step B4).
• Manual object definition is necessarily substantially more labour intensive, but may offer advantages in respect of the skill of the user in assessing the shape and extent of objects and will be discussed in greater detail later with reference to figure 9.
• step B6 the user first selects a designation number to define a selected object (Object Number), which object will comprise a number of segments, ie. a number of trace portions Sl, S2 and S3 relating to the same selected object within the sinogram.
• the user displays the chosen sinogram which will best show the object (step B7), and identifies, on the sinogram, a selected trace portion or segment Sl of the object, by marking the upper and lower limits of the segment (ie. at maximum and minimum theta values thereof) and a seed position P within the selected segment Sl of trace 64 (step B9A). Other segments S2 and S3 of the trace 64 are similarly marked (step B9B).
• the system then allows the user to select (step BIO) one of a number of predetermined global (e.g. Sobel) or direction biased (e.g. Edge Compass) edge-detection algorithms well known in the art to locate the edges 80,81 of the object segment in the positive and negative x' directions from point P and over the selected range of theta values for the segment on the sinogram.
• predetermined global e.g. Sobel
• direction biased e.g. Edge Compass
• steps B12 to B22 the system uses the edge-finding algorithms to determine an outline shape or two-dimensional "edge map" 85,86,87 (on the sinogram, ie. in x'-0 space) of the various segments Sl, S2 and S3 identified with the object trace 64. From the sinogram view, the system generates either a first or second derivative image (steps B 12-B15). This image may be displayed to the user (step B16) and saved for further use during edge tracing. In steps B19 to B22, the edge tracing procedure is carried out from the derivative edge map. Starting from the seed position P identified by the user, the algorithm hunts for the nearest edge moving across the spatial derivative at that particular angle 0.
• the system Upon finding the nearest edge, the system then attempts to locate a new, and corresponding edge point for the adjacent ⁇ value above or below in the sinogram. This procedure is carried out subject to the constraints that the new edge point should be within a user specified target range of the previous edge point detected and that the changes in the counts at the edge detected should exceed a user specified "edge sha ⁇ ness" expressed as a percentage of the maximum counts in the object at that angle. The process is terminated if the constraints are not met and results in a series of discrete points mapping the edge (eg. 85, 86 or 87, figure 5) in the defined segment. The procedure is repeated for both left and right edges of the sinogram trace, and for all segments.
• the user may view these points either on the original sinogram image, or on the edge image (step B21) and can toggle the display between the two (step B22).
• a curve fitting algorithm is carried out to map the closest possible pair of sinusoidal waveforms respectively to the left-hand edges and the right-hand edges of individual segments S1-S3 which form the object trace 64. These waveforms are then drawn onto the displayed sinogram for confirmation by the user (steps B23 to B28), which finalises the object definition.
• the separation of the sinusoidal traces for each theta value are used to calculate the object width and shape, and to calculate the total number of pixel counts attributable to the object (step B30). This is preferably carried out by plotting the number of counts along the sinusoidal trace, against angle 0 (see figure 4(b)).
• This plot yields a trace having a relatively slow variation in count as a function of theta, representing variations arising from differing levels of attenuation through the body (eg. at segments Sl , S2 and S3), upon which is superimposed relatively sharp deviations from the slowly varying trace where the counts of interfering traces combine with those of the selected object (eg. at areas 70,71).
• Known inte ⁇ olation techniques are used to eliminate these sha ⁇ deviations, resulting in a slowly varying trace which corresponds to the counts deriving from the selected object only.
• the system may also use the trace 64 width to assume an ellipsoidal shape of the object and represent it as such, or to represent the object as irregular in shape (step B31), as appropriate.
• edges of an object have been delineated in the sinogram, it is possible to represent them in the transverse plane via a reverse Radon transform. Since the detected edge 85,86,87 has a binary form, it does not require any filtering for moving between the planar (x-y space) and sinogram (x'-0 space) representations of the raw data set. This means that there is now an enclosed area that represents the location of the object whose edges have been traced. In order to estimate the activity within this region, the forward projection procedure as shown in figure 10 is used.
• the body 20 outline is defined in the transverse section and the object of interest 40 outlined within it (step Dl). It will be understood that additional objects of interest may also be added as ellipsoidal or irregular shapes (step D2).
• the total number of counts attributable to the object of interest is distributed into the transverse plane as a number of counts per voxel within the area of the object of interest (step D2). This is based upon the fact that radiation emission is isotropic. As an example, this means that if there are 6400 gamma rays emitted from the object of interest 40 (derived from the count vs. 0 plot), we are likely to get on average 100 events detected in the object's projection in each of the 64 views acquired under ideal conditions.
• an array of expected attenuation factors for the body 20 outline are generated and stored, or retrieved from memory (steps D3 to D8). These attenuation factors provide an estimate of the expected attenuation occurring for each angle 0 for the segmented object of interest given its position within the body outline.
• step D9 account is taken of the observed phenomenon of line spread by setting a suitable line spread function. This compensates for a number of effects such as scattering, equipment and acquisition parameters which diffuse the image from, for example, a point source into an approximate Gaussian distribution.
• step D10 account is taken of known background noise effects by defining a suitable noise function, eg Poisson distribution.
• the counts within the object are forward projected (steps Dl 1 , D12) and this distribution of counts obtained in each projection are compared with the counts that were actually obtained for the selected object in the raw data set (step B35).
• the simulation parameters may then be adjusted to minimise the Chi-squared statistic (step B36) in order to get a forward projection count distribution result as close as possible to the actual counts obtained from the selected object 40 in each of the projections.
• the cycle of steps B34 - B37 are repeated until a convergence criterion is satisfied (step B37), although in practice it is found that very few iterations, if any, are required.
• the convergence criterion may be chosen according to a clinical situation governing the desired accuracy.
• the operation steps B2 to B39 must be repeated for each transverse slice. Since adjacent slices will be substantially similar to one another, with slowly varying values of the sinusoidal traces for successive slices, it is possible to carry out a repetitive process on the succeeding slice substantially automatically. Providing that the axial distance between transverse slices is not large compared with the dimensions of the object of interest, the seed position P will still be contained within the object of interest, and the upper and lower limits for theta will vary only slightly and the object edges will have varied only slightly. Thus edge finding algorithm at steps BIO to B21 can operate automatically on the new slice, with confirmation from the user if necessary.
• step B39 we have, by addition, both the location of, and the counts within, the selected object for all the transverse planes that the object occupies by using only the raw data without any reconstruction.
• step Cl the left or right hand side of the " sinogram trace is first selected (step Cl) and a sinusoidal waveform is displayed superimposed thereon. Phase and amplitude coefficients are adjusted by the user until a close match with the edge of the object trace edge is obtained (steps C2, C3). The exercise is repeated for the opposite trace edge (step C4).
• a raw data set contains all the information necessary to characterise the distribution of radioactivity in three dimensions, and that, for a given data set, it is possible to describe the relationships between the entire set of projections as a set of mathematical functions. Once this description is made, it is possible to manipulate the data set to predict clinically advantageous "what if" scenarios that maintain the relationships and provide quantitative parameters. The steps have been described in connection with Figure 6.
• the algorithm starts off with user identification of the object that is to be segmented and quantitated in the raw projection data, which is usually best done in the projection with the maximum counts from the object itself, and with minimal interference from any over- or underlying structures.
• a user defined seed pixel within this object starts off a three dimensional edge detector that produces a series of discrete points defining the boundaries that satisfy a preset target range and edge sha ⁇ ness, and terminates when all such points have been identified.
• a least squares fit to this set of edge pixels defines the boundary of the object according to an assumed ellipsoid or irregular shape selected by the user.
• the algorithm then forms an estimate of the outline of the patient's body according to a preset threshold from the limits as seen in all the projections, and also the mean background counts free from all other major objects.
• a copy of the delineated object as well as the estimated body outline is produced in a new data set to form the basis of the forward projection simulation module.
• An attenuation map is generated by associating the path lengths stored in a lookup table for each of the pixels located within the object of interest to the edge of the body outline with the attenuation coefficient.
• the pixels within the body outline are given an initial count value based on the estimate of the mean background and the pixels within the object of interest are given an arbitrary initial count value by the user.
• a Monte Carlo subroutine that isotropically distributes these initial estimates of counts per voxel for each projection angle.
• This subroutine takes into consideration the aforementioned attenuation maps (and any additional attenuation corrections if required), noise, Modulation Transfer Function and time variance of activity within the segmented organ due to pharmacokinetic redistribution or radionuclidic decay.
• a Chi-squared statistic is calculated to compare the simulated data with the actual data based on the projections with the majority of the counts arising from the object of interest, and used to revise the initial estimates iteratively. This procedure converges to a point when the simulation mirrors the original data closely for only the delineated object independent of all others.
• the algorithm can branch one of two ways by either deleting the segmented object from the raw data set, or keeping the object but deleting out everything else, ie. image surgery.
• This decision is made by the user based on the clinical situation for which the study was performed.
• the quantitative data about the object namely, volume, activity and time variance during the period of acquisition are inferred from the values of these parameters used during the simulation to get the minimum Chisquared statistic. All the above steps and their resultant output can be overridden or modified by the user should the need be felt.
• the entire sequence is repeated several times till all objects of interest have been segmented and quantitated independent of each other using the raw data set only, and a new data set is generated that includes the appropriate objects of interest only, in any combination dictated by the clinical situation.
• the algorithm may then terminate at that point without attempting to form images.
• the new data set which contains the quantitated object can be reconstructed using back projection with no prefiltering and a simple ramp filter to obtain images for comparison with conventionally filtered and
• Table 1 gives quantitative data for a phantom with six spheres, ranging in volume from 0.6 to 24 cL and with activities from 7.8 to 312
• MBq put in water, r values for both volume and activity are >0.99 showing good concordance between actual volumes and activities and those measured from regression lines fitted to the program output.
• Figure 12 shows a conventionally backprojected reconstruction of a transverse section at the level of the kidneys of an Indium-Ill Octreotide study using no prefiltering and a simple ramp filter.
• Figure 13 shows a hybrid image with both the kidneys and spleen from the original data placed in the estimated body outline, while Figure 14 shows the first iteration of the algorithm to remove the contribution of the right kidney
• FIG. 15 shows the final iteration showing same section with the right kidney completely removed from the raw data set without affecting the left kidney or the spleen. It can be seen that the artefactual cold area in the area between the kidneys is reduced.
• Figure 16 shows a transverse section of a conventional postreconstruction image at the level of the bladder in a Tc-99m labelled CYT-351 study of prostate cancer at 24 hours with Weiner prefiltering and attenuation correction
• Figure 17 shows the result of processing of the raw data set to reduce selectively the counts originating from the bladder prior to similar reconstruction.
• the conventional image shows the effects of a wide range of contrast values, accumulation of activity in the bladder over the hour long acquisition, and poor count statistics.
• the two external iliac vessels at approximately 10 and 2 o'clock position (with respect to the bladder), the two internal iliac vessels at 5 and 7 o'clock and the extraprostatic extension of the carcinoma at 6 o'clock are visualised.
• Two wedge shaped cold artefacts are present on either side of the bladder.
• the iliac vessels are seen in essentially the same places as before, but the extension due to the prostate cancer is now separated from the bladder, and without the artefactual addition of counts originating from the bladder.
• the wedge artefacts have disappeared and the contrast range is now balanced over the entire image.
• the processing illustrated above is possible only after accurately reproducible derivation of both the size and activity within the object by the algorithm.
• the program returns a series of numbers in terms of counts, pixels and percent kinetic variation, which can be calibrated easily to yield MBq.cm "3 .
• Any method that aims to provide clinically useful quantitative parameters must satisfactorily take into account all the variability in the entire expanse of factors affecting the acquisition of data in the routine environment of a Nuclear Medicine department if it is to achieve widespread acceptance. It is preferable if the inco ⁇ oration of the corrections involves as little processing and user interaction as is technically possible so that the accuracy, reproducibility and confidence in the quantitative parameters is increased.
• the method described here begins the processing, using the raw projection data only, before any artefacts are introduced by any reconstruction process. It then segments organs of interest and provides a simulated data set for each, independent of all others, that is capable of taking into account all the major factors affecting acquisition eg. the Modulation Transfer Function, noise, attenuation, large contrast values and time variance of the activity distribution due to pharmacokinetics.
• the simulated data sets are forward projected to assess the accuracy ofthe simulation and the parameters used for the simulation are used to manipulate the original data set to compensate for acquisition limitations and quantify volume and activity. The compensation and quantitation are done before the reconstruction introduces interdependence of voxel values.
• the processing can be tailored to the pharmacokinetics and biodistribution of any particular agent. This is important in cases of those radiopharmaceuticals which offer low normal: abnormal ratios, have rapid redistribution kinetics or with wide variations in uptake in adjacent organs. It may be possible to have less stringent goals for new radiopharmaceuticals in terms of pharmacokinetics and biodistribution.
• the ability to quantify objects independent of any process of image formation means that more rigorous comparisons can be made between studies carried out at different times, centres or protocols. Such an exacting basis is a prerequisite for the development of standardised databases of images and protocols, and in the assessment of equipment and software performance.
• the mathematically defined relationships used by the algorithm may be able to form the basis of optimised acquisition protocols for new types of studies, for example, a reduced number of views but with a longer time per image over an arc or set of arcs that offer the best visualisation of a particular organ, or studies using rapidly distributing tracers that offer a combination of functional information and three dimensional visualisation.
• the technique previously described herein uses an implementation which segments out a part of the raw projection data and then generates a simulated data set that closely resembles the contribution from the object of interest within this part of the data. Once this condition is met, it is inferred that the parameters used during the simulation are directly comparable to the object of interest. This provides the clinically important estimates of volume, activity and time variance.
• Avoidance of this simulation process can be useful as simulation processes can be quite elaborate and complex in order to achieve optimal results. This requires considerable computing power to implement and can be time consuming to program, debug, optimise and check for accuracy under varying conditions.
• the simplification of the edge detection / object delineation process can be desirable as although the techniques described above can utilize a number of well developed techniques, no single method can be applied to the wide range of tomographic data which can be found in nuclear medicine. This means that a preferred implementation will include several different edge detectors. It may therefore be necessary to select the type of detector used and operating parameters thereof dependent upon a particular clinical study. Whilst there is no problem with this, there are circumstances in which it is also desirable to offer a standardized analysis technique.
• the alternative embodiment now to be described makes further use of a number of periodicities found in the sinogram representations of the raw data.
• the alternative embodiment has particular applicability for camera systems in which, for each value of 0, information is collected simultaneously for all z. That is to say, the camera includes a detector 10 and coliimator 15 which extend in two dimensions for simultaneous collection of x' data in all transaxial planes (z) at once, as previously discussed.
• the data acquired and represented in the sinograms of figures 3, 4 and 5 essentially relate to the following dimensions: a) the three physical dimensions identified previously in figure 1 as x, y and z; b) the time during acquisition and therefore rotation of the camera head, ie. 0; c) the energy of the counts arising from the volume imaged, hereinafter referred to as E; d) the change in counts within objects during a period of acquisition; and e) the time between sets of acquisitions.
• the sinograms 50 of a raw data set as depicted in figure 3 are each rotated by 90° anticlockwise, and laid end to end in order of the successive transaxial slices, ie. for increasing, or decreasing values of z.
• a sinogram row 200 is thereby formed comprising successive sinograms 50 ⁇ to 50 n representing successive z values.
• the vertical axis represents x'
• the horizontal axis represents, within each sinogram, 0 from 0 to 360, and from sinogram to sinogram, z from z l to z ⁇ .
• the horizontal axis also represents time t in a saw tooth function 210 depicted above the sinogram row 200, from time (beginning of acquisition period) to t e (end of acquisition period).
• the number of counts, or intensity I is represented by a height of trace perpendicular to the diagram of figure 18.
• an object of interest will be represented on the sinogram row 200 as a sinusoidal trace of varying thickness according to the x-y dimensions of the object, of frequency corresponding to the one sinogram period. Variations in the dimensions of the object over the z-direction will manifest themselves as small discontinuities 202 in width and/or position of the trace at each sinogram boundary. The extent of the object in the z-direction will be manifested as the appearance of the object through a number of adjacent sinograms. Figure 18 shows this in part as a diminishing size of trace over sinogram views 50 t to 50 n , and is more clearly visible in figures 19(a), (b) and (c).
• Figures 19(a), (b) and (c) show actual data taken from human patients showing the portion of the body encompassing the liver, prostate and parathyroid respectively. In each figure, the entire length of the sinogram row 200 comprises all seven rows 200 ] to 200 7 in a continuous chain.
• the figures 19(a), (b) and (c) clearly show the plurality of interfering traces which are normally found in a sinogram view. The figures also clearly show the extent of the objects in the z direction.
• the three physical dimensions of the object of interest and its location within the volume being imaged are displayed in the phase, amplitude and length of the sinogram trace, while the counts arising from it are displayed in the height of the trace.
• the time period of the acquisition is the saw tooth function from sinogram view 50 j to 50 n in figure 18.
• a step change in the height (I) at the beginning and end of each sinogram view and from one sinogram view to the next relates to the time variance of activity over the data acquisition period t e - t b .
• a drop between the end of one view to the next one means an accumulation of activity and a rise means a decrease in activity over the period of acquisition or, comparing the beginning and end of the same view, this comparison means the reverse, ie. a drop is a decrease.
• Step changes in the phase and amplitude of the sinogram trace relate to the shape and orientation of the object.
• the characteristics of the sinogram trace relate directly to the properties of the object producing it.
• An essential aspect of this is the periodicity of these characteristics which can be exploited to segment out an object of interest.
• Figure 20 shows a schematic three dimensional visualization of the intensity data represented by just one object trace 210 within a sinogram row, with intensity I (number of counts) represented by the orthogonal axis.
• the trace 210 has finite width in x' (x-y) space as it snakes along the sinogram row, although this width is not shown in the diagram.
• the trace 210 will, of course, be typically interfered with by other traces 212 shown in dotted outline interlacing with trace 210 as previously described with reference to figure 4.
• the trace height (figure 4b and figure 20, lower inset showing I vs.
• the I vs. 0 (and also I vs. 0,z) plot for a selected object will vary sinusoidally over a period of one sinogram view.
• trace height variations from interference from interlacing traces will have a periodicity of twice that of the selected object, and these variations can be identified and eliminated accordingly.
• Local attenuation by objects eg. bone structures
• will cause dips in the intensity vs. z trace which may also be detected since they force a departure from the ideal sinusoidal trace. Thus these local dips may also be eliminated by interpolation.
• the function of intensity I versus x' (shown in figure 21(b)) is used to determine the number and location of peaks 230, 232 in the un-normalized raw data set.
• a preprogrammed suitable threshold value may be used to determine which peaks to examine on a first pass. Alternatively, this may be determined by reference to a clinical database which enables control ofthe system by defining approximate locations of major peaks for a particular clinical study.
• Each maximum point x' for any given value of 0 is related to the nearest maximum point x' for the next value of 0 forming a succession of points (hereinafter a "set") along the trace 210 in figure 21a, and similarly along the trace 212.
• the two sets of points corresponding to traces 210 and 212 will intersect twice (220, 221) per sinogram view such that, for example, only one I vs. x' peak is located at 0 B . These intersections are discounted for the time being leaving blocks of points between the intersections.
• the extent of the object is now determined within these blocks by determining an object width for each 0, ie. determining a value on each side of the peak which delineates the object.
• a pair of minimum points x' ⁇ , x' 2 are derived by computing the magnitude of the first derivative, dl/dx' (figure 21(c)). These points determine the edges of the traces 210, 212 at that value of 0.
• a least squares curve-fitting algorithm is then used to define the edges 215, 216 of each trace 210, 212. This may be smoothed using the first harmonic of the Fourier expansion of the curve.
• Various refinements may be used to optimize the position of the curves defined by the x' , and x' 2 points, for example taking into account factors such as the attenuation coefficient Z, the thickness of attenuating material and energy E of the ⁇ radiation. These factors may be determined empirically or by reference to a priori knowledge of the organs being imaged.
• the number of unique sets of maximum points derived is the number of objects identified, and it is now possible to relate the phase and amplitude of each set of maximum points 230 and the length of the entire trace 210, 212 into the x, y and z dimensions of each object.
• the next task is to determine the number of counts originating from each object identified thus far.
• the count profile I vs. 0,z is plotted along the sinogram trace (figure 20, lower inset). This is smoothed to eliminate contributions from interlaced traces and to compensate for local attenuation as previously described.
• the first harmonic of the Fourier expansion of this count profile may be taken to eliminate noise from the curve fitting.
• the volume integral of this count profile relates to the number of counts originating from the object (including the background contribution at this point in the analysis). This realization makes the elimination of the Monte Carlo simulation possible, as discussed earlier. It is now possible to convert the parameters obtained above into true estimates of the physical dimensions, radioactivity and time variance for each object, providing that information relating to the characteristics of the gamma camera, the body outline and the background contribution are provided.
• the gamma camera characteristics are obtained to a required degree of thoroughness from a series of experiments calibrating the technique for a particular gamma camera set up.
• the body outline and background contributions can be assessed and calibrated using techniques described hereinbefore.
• the second sinogram data set may be back-projected for study or normalized to enable identification of a new set of peaks 230, 232 relating to objects of lower activity. A further pass can then be made to eliminate contributions from these second order objects, or to examine them in detail.
• panspectral gamma cameras may be used to acquire and assign radioactivity counts over a range of photon energies into separate energy bins which can further refine and improve the raw data segmentation process described above.
• a number of sinogram row data sets 200 A ...200 X are laid out to form a page 250 as shown in figure 22.
• Each page 250 relates to a data set acquired at a time t, over an acquisition period t+ ⁇ t, ie. from t ⁇ , to t e as shown in figure 18.
• Each page 250 comprises a number of sinogram rows in which each row corresponds to bin counts for a given photon energy (E) range. The highest energy bin corresponds to the top row (row 1) and the lowest energy bin corresponds to the bottom row (row n).
• Each row therefore comprises data from one part of the energy spectrum as indicated on the right hand side of the figure. Organising the data set in this manner enables refinements to correction methods for attenuation and scatter by exploiting information contained in the sinogram rows 2 to n.
• the probability that it will give rise to a certain pattern of counts in all of the other rows can be estimated as a probability map.
• the spread of this location further down in the energy spectrum may be estimated by a series of expanding windows 261 , 262 ... 265 (shown greatly exaggerated in the diagram) of, eg. 3 x3 data elements for rows 200 B to 200 D , 4 x4 data elements for the next row 200 E , 5 x5 data elements for the next row and 9 x9 for the remaining rows.
• the number of counts within each window are, respectively, A-f 2 , A-f 3 , ... A-f n where f n represents a parameter which is dependent upon the energy of the photon and the attenuation factor (Z value) of the attenuating medium.
• Sl counts are the result of interactions of photons arising from object 1
• S2 counts are the result of interactions of photons arising from object 2
• the probability maps also have periodic properties. For example, the spread of counts arising from a non-central object varies periodically, narrowing for 0 where the object is close to the camera and widening for 0 where the object is furthest from the camera. This means that if the counts originating from a particular point lower down in the energy range are considered, then the contributions Sl and S2 of each object can be refined still further according to the location of the object within the three ⁇ dimensional volume being imaged. This is because there is a higher probability that an object further away from the camera will give rise to an interaction because of the depth of the intervening medium than for an object closer to the camera, in proportion to the activity inside each object.
• the realisation that the variation of probabilities has periodic characteristics simplifies the implementation of the algorithm on a computer.
• the present invention therefore organizes raw acquisition data into sinogram-based data structures and exploits various periodicities in the data structure, which periodicities facilitate the segmentation from, and quantitative analysis of, object data from the raw data set without the need for data reconstruction using back projection techniques.
• the data segmented out can be the object of interest or can be an object which is obscuring remaining data in the raw data set, ie. the remaining data set essentially comprises one or more objects of interest for which quantitative data is sought without the effects of the initially segmented out object. Successive objects may be segmented to gradually leave a data set which includes the object(s) of interest.

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