WO2013053007A1

WO2013053007A1 - System and method for analysing a heterogeneous, three-dimensional object having an amorphous shape

Info

Publication number: WO2013053007A1
Application number: PCT/AU2012/001232
Authority: WO
Inventors: Nicholas Delanie Hirst Dowson; Pierrick Bourgeat; Michael Francis FAY; Paul Anthony Thomas
Original assignee: Commonwealth Scientific And Industrial Research Organisation
Priority date: 2011-10-11
Filing date: 2012-10-11
Publication date: 2013-04-18

Abstract

A computer implemented method and system of analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, enables improved analysis and display of information about the structure of complex 3D objects, such as tumours. The method includes normalising the amorphous shape of the object to a predetermined three-dimensional template to define a normalised shape of the object (step 1905). A plurality of three dimensional regions within the normalised shape is then defined (step 1910). A value of the at least one parameter for each of the regions is then determined (step 1915). Each of the values is then assigned to a unique location on the normalised shape, wherein each location corresponds to a position of one of the regions within the object (step 1920).

Description

TITLE

SYSTEM AND METHOD FOR ANALYSING A HETEROGENEOUS, THREE-DIMENSIONAL OBJECT HAVING AN AMORPHOUS SHAPE FIELD OF THE INVENTION

The present invention relates to computer-assisted analysis of parameters of three-dimensional objects. In particular, although not exclusively, the invention relates to displaying graphical representations of parameters of tumours.

BACKGROUND TO THE INVENTION

The study of tumours has many pitfalls, many of which are not generally accounted for when analysing and treating tumours. Individual tumours are biologically heterogeneous, with individual cell lines highly adapted to their immediate environment, be it hypoxic, well perfused, or in regions of oedema. However, most studies appear to examine tumours as a whole, essentially averaging away the rich information contained within three dimensional (3D) images. This not only makes it difficult to deal with the confounding effects of biological heterogeneity but also artificially limits the power of studies, for example, of rare diseases, or where recruitment is limited, or complications frequent.

Many studies also require the measurement of tumour statistics as they change over time in longitudinal studies, such as when calculating local volume to measure growth, or when estimating predictive capabilities of different biomarkers. However, the spatial correspondences in tumours between different time-points are often ambiguous, even with state of the art registration algorithms. That is because events such as surgery, treatment, and tumour growth often significantly change local tumour characteristics.

Many prior art algorithms either assume that tumour variations are primarily due to spatial movement (such as non-rigid algorithms), or that variations are due primarily to changes in intensity (such as rigid algorithms). In reality the image variations are usually a combination of both intensity changes and spatial movements. But even with algorithms based on mechanical properties of tissues, such as finite element modelling approaches, the choice between the two effects is often itself ambiguous.

Tumours are generally solid, three dimensional, heterogeneous objects having an amorphous shape, making individual regions difficult to refer to in text, on paper, or even on computer screens, which are limited to displaying 3D surfaces or 2D planes. Advanced cancer tumours generally consist of a core of necrotic tissue or fluid, surrounded by a shell of active tissue, and have very amorphous 3D boundaries including outgrowths and extrusions. Such tumours often change radically over time, due for example to surgery, treatment and tumour growth. In addition, even individual tumours are biologically heterogeneous, so treatment often should be tailored to different parts of the tumour. However, the above factors make analysis of tumours, such as the tracking of local progression for purposes of treatment or research, difficult.

Other complex three dimensional objects can similarly be difficult to analyse and characterise. Therefore there is a need for an improved system and method for analysing a heterogeneous, three dimensional object having an amorphous shape.

OBJECT OF THE INVENTION

It is an object of some embodiments of the present invention to provide improvements and advantages over the above described prior art, and/or overcome and alleviate one or more of the above described disadvantages of the prior art, and/or provide a useful commercial choice.

SUMMARY OF THE INVENTION

According to one aspect, the invention resides in a computer implemented method of analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, including: normalising the amorphous shape of the object to a predetermined three-dimensional template to define a normalised shape of the object;

defining a plurality of three dimensional regions within the normalised shape;

determining a value of the at least one parameter for each of the regions; and

assigning each of the values to a unique location on the normalised shape, wherein each location corresponds to a position of one of the regions within the object.

Preferably, the method further comprises displaying representations of the values on a two-dimensional projection of the outer surface of the normalised shape.

Preferably, the predetermined three-dimensional template is a spheroid.

Preferably, the method further comprises simultaneously displaying a second two-dimensional projection that displays previous values of the at least one parameter of the object.

Preferably, the method further comprises simultaneously displaying representations of the values of a plurality of parameters on the two- dimensional projection of the outer surface of the normalised shape.

Preferably, the plurality of three dimensional regions within the normalised shape are defined by the outer surface of the normalised shape, an inner surface of the normalised shape, and a plurality of rays extending from a centre of the normalised shape.

Preferably, the plurality of three dimensional regions within the normalised shape are defined by the outer surface of the normalised shape, an inner surface of the normalised shape, and four rays extending from a centre of the normalised shape.

Preferably, the plurality of rays are defined by a centre point of the object and the intersections of latitudes and longitudes on the surface of a sphere.

Preferably, the plurality of rays are non-linear. Preferably, the plurality of rays conform to an intensity gradient of an image of the object.

Preferably, each ray in the plurality of rays follows the shortest path to the outer surface of the object.

Preferably, the object is a biological object or tumour.

Preferably, a boundary of a necrotic core of the tumour is approximated as an inner surface of the sphere.

Preferably, each segment approximates a segment of an active tissue shell of the tumour.

Preferably, the at least one parameter is selected from the following: density, temperature, glycolitic volume, mean uptake, and percent volume with blood brain barrier breakdown.

Preferably, the at least one parameter is selected from the following: a histogram of values, an at least one parameter derived from a plurality of values (e.g. a dynamic scan or a diffusion weighted image), and an at least one parameter derived from a linear or non-linear combination of values.

Preferably, the method further comprises simultaneously displaying a second two-dimensional projection that displays previous values of the at least one parameter of the tumour.

Preferably, the plurality of three dimensional regions define a plurality of shells of the tumour.

Preferably, the representations of the values are selected from the following: colours, symbols, character strings, and patterns.

According to another aspect, the invention resides in a system for analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, including:

a computer readable memory; and

a processor operatively connected to the memory, wherein the memory includes computer readable program code for:

normalising the amorphous shape of the object to a predetermined three-dimensional template to define a normalised shape of the object; defining a plurality of three dimensional regions within the normalised shape;

determining a value of the at least one parameter for each of the regions; and

BRIEF DESCRIPTION OF THE DRAWINGS

To assist in understanding the invention and to enable a person skilled in the art to put the invention into practical effect, preferred embodiments of the invention are described below by way of example only with reference to the accompanying drawings, in which:

FIG. 1 is a composite of 2D scan images and a 3D model illustrating the location and shape of a brain tumour present inside a human skull;

FIG. 2 is a close up view of the 3D model of FIG. 1 ;

FIG. 3 illustrates the same tumour as shown in FIG. 2, but where the amorphous shape of the model has been normalised to the shape of a sphere, according to an embodiment of the present invention;

FIG. 4 is a Mercator projection of values of a particular parameter, such as total glycolitic volume, of the segments of an outer shell of an object, according to an embodiment of the present invention;

FIG. 5 is a diagram of cross sectional contours of an amorphous, heterogeneous object in the form of a tumour;

FIG. 6 is a diagram illustrating a three dimensional region in the form of a segment of the tumour of FIG. 5;

FIG, 7 is a diagram of a three dimensional region of an object, and a set of nearby regions that potentially correspond with the first at a second time point after the object has changed in geometry (possibly in the future), illustrating how uncertainty arising from various errors can be managed; FIG. 8 is a histogram showing the value of a statistic Si measured from a distribution of voxel intensities within a segment, and a Gaussian distribution that approximates the histogram;

FIG. 9 illustrates a joint distribution of statistics si and s₂, as the accumulation of four Gaussian joint distributions, each having a different weight;

FIG. 10 is a diagram illustrating the registration of a plurality of images, according to an embodiment of the present invention;

FIG. 11 shows a series of images illustrating a manually contoured tumour on two images at both a time point 1 and at a time point 2;

FIG. 12 illustrates four Mercator projections of four tumour statistics: total glycolitic volume at time point 1 , percentage of volume with BBB breakdown at time point 1 , mean uptake at time point 1 , and total glycolytic volume at time point 2;

FIG. 13 illustrates joint distributions of a time point 2 and a time point 1 ;

FIG. 14 illustrates a particular type of tumour that is sufficiently amorphous that folds occur, where a ray extending from the centre of the tumour passes outside the tumour and then back into the tumour;

FIG. 5 illustrates another type of tumour that consists of multiple or amorphous necrotic cores;

FIG. 6 illustrates yet another type of tumour where no active shell exists, or where the active shell is beyond a scanner resolution;

FIG. 7 is a diagram illustrating a cross section of a tumour having vasculature extending into and out of the tumour;

FIG. 18 is a diagram illustrating a cross section of a tumour modeled using non-linear rays;

FIG. 19 is a flow diagram illustrating steps of a method of analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, according to an embodiment of the present invention;

FIG. 20 diagrammatically illustrates a computing device, according to an embodiment of the present invention; FIG. 21 diagrammatically illustrates a cross section of a tumour modelled using linear rays projected from the vertices of a geometric primitive, according to an embodiment of the present invention;

FIG. 22 diagrammatically illustrates a tumour modelled using linear rays projected from the vertices of a geometric primitive in three dimensions, according to an embodiment of the present invention; and

FIG. 23 diagrammatically illustrates the efficacy of a method for examining the relationship between at least two measured statistics, according to an embodiment of the present invention.

Those skilled in the art will appreciate that minor deviations from the layout of components as illustrated in the drawings will not detract from the proper functioning of the disclosed embodiments of the present invention. DETAILED DESCRIPTION OF THE INVENTION

Embodiments of the present invention comprise a system and method for analysis of a heterogeneous, three-dimensional object having an amorphous shape. Elements of the invention are illustrated in concise outline form in the drawings, showing only those specific details that are necessary to the understanding of the embodiments of the present invention, but so as not to clutter the disclosure with excessive detail that will be obvious to those of ordinary skill in the art in light of the present description.

In this patent specification, adjectives such as first and second, left and right, front and back, top and bottom, etc., are used solely to define one element or method step from another element or method step without necessarily requiring a specific relative position or sequence that is described by the adjectives. Words such as "comprises" or "includes" are not used to define an exclusive set of elements or method steps. Rather, such words merely define a minimum set of elements or method steps included in a particular embodiment of the present invention.

Advantages of some embodiments of the present invention include enabling the analysis and display of information about the structure of a complex 3D object, for example the internal parameters of an amorphous, heterogeneous biological object such as a tumour. For example, the information can be simplified so that it can be easily interpreted by a lay- person or untrained clinician, and so that it can be easily displayed in two- dimensions, such as on paper or on a display screen. Further, an analysis according to some embodiments of the present invention can account for the inherent biological heterogeneity in tumours, which may enable tissue specific treatment - rather than patient or population specific treatment. Also, some embodiments of the present invention can explicitly account for uncertainty in spatial correspondences over time (e.g., despite brain shift, surgery and tumour growth). That can enable a local correlation between different biological phenomena, treatment coverage, and success or failure.

The above advantages can be achieved through the computer- assisted analysis of parameters of three-dimensional objects as described herein.

FIG. 1 is a composite of 2D scan images and a 3D model 100 illustrating the location and shape of a brain tumour present inside a human skull 105.

FIG. 2 is a close up view of the 3D model 100. The amorphous and heterogeneous features of the tumour are recreated in the model 100. In this specification, the word "amorphous" refers to any non-uniform shape, such as the shape of the model 100. Such amorphous shapes are common in tumours, which often include various outgrowths and extrusions. The word "heterogeneous" refers to a tumour where a parameter or statistic under measurement varies across regions.

FIG. 3 illustrates the same tumour as shown in FIG. 2, but where the amorphous shape of the model 100 has been normalised to the shape of a sphere 300. According to embodiments of the present invention, various statistics and parameters of different regions of an amorphous tumour can be more effectively analysed using clearly defined three dimensional segments and shells of a predetermined three-dimensional template, such as the sphere 300. For example, an outer shell 305 of the sphere 300 can be used to model an outer active shell of the tumour, which active shell overlays a necrotic/excised core of the tumour. Here, the necrotic core of the tumour is modelled as an inner sphere 310.

Three dimensional regions or segments of the outer shell 305 are defined on their sides by lines of longitude and latitude of the sphere 300. The ends of the segments are defined by the outer and inner surfaces of the outer shell 305. According to embodiments of the present invention, parameters and statistics of each segment then can be used to track changes in the tumour over time.

FIG. 4 is a Mercator projection of values of a particular parameter, such as total glycolitic volume, of the segments of the outer shell 305. The Mercator projection is achieved by assigning the value of the particular measured parameter of each segment to a voxel on the outer surface of each segment. Then, just as geographical boundaries and locations on the surface of the earth can be represented on a two dimensional Mercator world map, the values of the measured parameter can be represented in 2D using a grey scale or colour spectrum. The segments that were cut-away to display the inner core are highlighted by the lighter rectangle in FIG. 4 to show the correspondences between FIG. 3 and FIG. 4.

FIG. 5 is a diagram of cross sectional contours of an amorphous, heterogeneous object in the form of a tumour. As described above, a tumour can be normalised to the shape of a spheroid and treated as having a centre 500, and a necrotic core 505 or excised centre surrounded by an active shell 510 of active tissue.

According to some embodiments of the present invention, an object can be normalised to the shape of various predetermined 3D templates, such as a spheroid, cylinder, or other geometric shape. The process of normalising the shape of an object can be done manually or automatically. For example, to normalise an object manually, contours can be drawn on images of an object. In the medical field, contour lines drawn on fused Positron Emission Tomography (PET) and Magnetic Resonance (MR) images can be used to define the outer extent of a tumour. The necrotic core 505 can be approximately delineated by thresholding the tumour centre 500 in a PET image. A mean point within the necrotic core 505 is then calculated to define the centre 500.

Next, according to an embodiment of the present invention, a plurality of three-dimensional regions are defined within the normalised shape. As shown in FIG. 5, rays 515 corresponding to each combination of longitude and latitude of a spheroid are projected from the centre 500 to the contour denoting the outer surface 520 of the tumour. The PET value at the outer extent of the tumo r is extracted and used as a ray threshold. PET values are then measured proceeding backwards along a ray 515. The first time a PET value below the ray threshold is encountered, that point is denoted as an inner surface 525. Together the inner surface points define the necrotic core 505. The active shell 510 is defined as the region of tissue between the inner and outer surfaces 525, 520. The inner surface 525 could also be defined by considering selecting one connected region of voxels with intensities below a defined threshold.

FIG. 6 is a diagram illustrating a three dimensional region in the form of a segment 600 of the tumour of FIG. 5. The collection of rays 515, inner surface 525 and outer surface 520 define the tumour within a spherical coordinate system. Within this system each set of four adjacent rays 515 defines an approximately conical three dimensional segment, such as the segment 600, within the tumour.

Relative to regions of similar tumour biology the segments are arbitrary. However, measuring changes in parameters of the segments over time can be very useful in enabling a local correlation between different biological phenomena, treatment coverage, and treatment success or failure.

For the purpose of extracting statistics from the images each segment can be drawn on a label mask, l(x). For example, volume can be determined b the following equation 1 :

Eq. and mean PET intensity can be determined by the following equation 2: ¾ - ^-∑['(*)-Λ· *⁾._. Eq. 2 where [ ] is the indicator function ([0]=1. [a≠ o J=0), x is a voxel location, Nj is the number of voxels with label j, l^x) is the intensity of a voxel at position x within the PET image, and V_voxei the volume of a single voxel in an image.

A value of at least one parameter for each of the regions is then determined. For example, for a tumour the parameters can be any variable of interest such as density, temperature, glycolitic volume, mean uptake, and percent volume with blood brain barrier breakdown. In a heterogeneous tumour, such parameters can vary significantly at different locations. For inanimate objects, other parameters such as hardness, porosity, molecular structure, or material composition can be determined.

Next, a value for each of the at least one parameter for each region is assigned to a unique location on the normalised shape, where each location corresponds to a position of one of the regions within the object. For example, the values can be assigned to a point on an outer surface of each region, such as a square as shown in Fig. 4. That can facilitate effective analysis of changes to the parameters within each region over time. For example, monitored statistics of the values of different parameters can include a wide range of statistics such as: mean, standard deviation, kurtosis, histogram, sum, product, maximum, minimum, range, N% population range, median, and population.

Further, to facilitate analysis, representations of the values assigned to each region can be displayed on a two-dimensional projection of the outer surface of the normalised shape, such as a spheroid. Thus the various statistics of a complex 3D medical image can be conveniently visualised on a plane using a standard two-dimensional projection, such as a Mercator projection.

According to some applications of the present invention for analysing tumours, longitudes and latitudes can be oriented relative ίο the anatomy of a patient. For example, zero longitude corresponds to the patient anterior; the 180 and -180 longitudes correspond to the posterior; longitudes of -90 and 90 correspond to the patient's right and left, respectively; and latitudes of -90 and 90 respectively correspond to the patient's inferior and superior. Also, the same ray directions can be used In all time-points for a given patient, i.e., no spatial normalisation apart from a rigid registration needs to be performed.

As will be understood by those having ordinary skill in the art, various two-dimensional projections can be used, such as Mercator projections, Winkel-Tripel projections, Lambert projections, and Dymaxion projections.

When using embodiments of the present invention to analyse brain tumours in longitudinal studies with the purpose of finding correspondences between various statistics, e.g. FDOPA uptake and local growth, errors can arise from at least four sources:

· Heterogeneous biological regions are lumped together into a single segment. Similarly, homogeneous biological regions can also be separated;

• Segments with the same latitude and longitude may be assumed to correspond directly. However, spatial correspondences between segments at two time-points can be imprecise due to brain shift arising from phenomena such as tumour growth, oedema and surgery. Hence correspondences between a given segment at time-point 1 and multiple surrounding segments at time-point 2 may be considered in addition. It is assumed that rigid registration removes errors due to misalignment of the images;

• Tissue might change (e.g., in some areas tissue might die or grow); and

• Image noise.

There is a necessary trade-off between the above errors, because the larger individual three dimensional regions or segments are, the larger the risk of lumping heterogeneous regions together. However the correspondence error between segments is reduced. Similarly, image noise can be reduced by averaging.

Reducing the size of segments decreases the lumping of tissues, but when the segment size approaches that of spatial accuracy the uncertainty of spatial correlations can be significantly reduced. Likewise, the signal to noise ratio for the statistics being measured increases.

To account for biological heterogeneity, it is assumed that the voxel intensities in each image are independent and identically distributed with a normal distribution around the measured value, with standard deviation, σ, that is independent of location and intensity. The standard deviation may be estimated from a background region in the image. The measurements within each segment are accumulated into a histogram, which is convolved using the Parzen window with standard deviation, σ. A particular distribution may optionally be fitted to the histogram of each segment, e.g. a mixture model, to reduce computation.

FIG. 7 is a diagram of a three dimensional region of an object, illustrating how uncertainty arising from the above errors can be managed. Consider that the segment 700 is a defined three dimensional region within a normalised shape of a brain tumour. The spatial uncertainty is estimated from the measurements of brain-shift. This is treated as uncertainty in the relationship between the segment 700 at one time-point and its correspondence to all nearby segments at a second time-point. This uncertainty is represented as a weighting factor between statistic Si (which is a value of a parameter, such as mean uptake, of the segment 700) and the statistics from each of the nearby segments in the second time-point s∑. The uncertainty around each sample of Sf is accumulated into a joint histogram, which is simply a continuous version of a scatter plot from which the relationship between the two statistics under investigation can be estimated with a known confidence.

FIG. 8 is a histogram showing the value of s» measured from a distribution of voxel intensities within the segment 700. This can be approximated as a single Gaussian with a standard deviation a. Similarly, another statistic, s_∑, is measured in all nearby segments at a second time point 2, where each segment has its own uncertainty.

FIG. 9 illustrates a joint distribution of s* and s₂, as the accumulation of four Gaussian distributions, each having a different weight. The spatial correspondence between the various segments at time point 1 and at time point 2 are inexact, and thus a weight, w, is used to represent a level of correspondence between the segments at the two different time points.

As will be understood by those having ordinary skill in the art, according to the present invention almost any image or modality can be used to define a spatial reference model that is the subject of analysis. For example, that includes PET, MRI, CT, 3D SPECT, simulations of 3D environments, 3D fields, computer derived 3D images (e.g., atlas based label images), four dimensional dynamic images, N-dimensional images, parameters within 3D images derived from multi-dimensional images, and combinations of 3 and 4D images. Modalities can be scalar (e.g., PET) or vector fields (e.g.; tensors from diffusion weighted MR images). Also, statistics from pairs of images can be combined, such as when multiplying the maximum PET intensity by the segment volume to obtain total glycolytic volume. Also, both linear and non-linear combinations are possible, and the combinations can be optimized according to the content of the images.

Example

Data used in the example described below were obtained from patients who received a fluorine-18 l-3,4-dihydroxyphenylalanine (18F- FDOPA) PET scan and an MRI scan at two time-points: one four weeks after a six-week course of chemo-radio-therapy (three months after surgery), and another three months after the first follow-up (six months after surgery). The PET and MRI scans at each time point were taken within two days of each-other.

The MRI images consisted of pre- and post-contrast Magnetization- prepared Rapid Acquisition Gradient-echo (MPRAGE) images on a 3 Tesla Siemens Magnetom Trio scanner. PET imaging was performed using a Philips Allegro GXL scanner. A transmission computed tomography (CT) scan was acquired first. Subsequently, FDOPA was administered intravenously and a 75-minute acquisition initiated. The images were reconstructed using ordered subset expectation maximisation with corrections for attenuation and scatter. The final volume has a matrix size of 128x128, consisting of 90 planes of 2x2x2mm³ voxels.

FIG. 10 is a diagram illustrating the registration of a plurality of images, according to an embodiment of the present invention. All PET scans were motion corrected subsequent to acquisition and reconstruction using a method described in Mourik JEM, Lubberink M, van Velden FHP, Lammertsma AA, Boellaard R. Off-line motion -correction methods for multi-frame PET data. Eur J Nucl Med Mol Imaging. 2009 Dec;36(12):2002-13. Within each time-point all images were aligned to the pre-contrast MRI, to avoid the enhancing regions introducing bias. All registrations were performed with a block matching algorithm at the coarse scale (such as described in Greene FL, editor. AJCC Cancer Staging Manual. Springer; 2002. p. 387-90.) and refined using a standard hierarchical Mutual Information based optimiser (such as described in Nekolla SG, Miethaner C, Nguyen N, Ziegler SI, Schwaiger M. Reproducibility of polar map generation and assessment of defect severity and extent assessment in myocardial perfusion imaging using positron emission tomography. European Journal of Nuclear Medicine and Molecular Imaging. 1998 Sep 1,25:1313-21.) Connected boxes show multiple series within a single study. Arrows indicate registrations computed and the series used for this purpose. The dotted boxes indicate all studies taken at a particular time-point.

An experienced nuclear medicine physician (PT) manually contoured each tumour for each time point based on abnormal FDOPA uptake in the FDOPA PET image. The fused CT (from the PET/CT acquisition) and the fused post-contrast MR image were available to assist contouring by providing anatomical landmarks. An experienced nuclear medicine physician (PT) also manually marked out several anatomical landmarks in normal brain tissues adjacent to the tumour that correspond across the time points. This was done in order to obtain an estimate of brain shift or deformation within and around the tumour of each patient.

FIG. 11 shows a series of images illustrating a manually contoured tumour at both a time point 1 and at a time point 2. The top row of three images represent time point 1 , and the second row of three images represent time point 2. Each segment within the tumour is shown overlayed on a single slice of the PET and MRI scans through the tumour equator at both time points. Three dimensional renderings of the tumour are also provided. As shown, the extrusions to the left and right of the tumour die back by time point 2, and the main body of the tumour shrinks back to the region of blood brain barrier breakdown. However the excised core of the tumour is re-colonised, such that a core is no longer discernable. This is well represented in the reference model.

24 latitudes and longitudes were used to divide the space resulting into segments of 15° by 7.5°. In total there were 576 segments. The following three statistics were measured at time point 1 :

1. Total glycolytic volume in units of Bq/ml * ml.

2. The mean PET uptake in units of Bq/ml.

3. The fraction of tissue with blood brain barrier (BBB) breakdown, measured as the fraction of the volume with hyper-intensity in the post-contrast MR.

The following one statistic was measured at time point 2, for the purposes of measuring co-variance:

4. Total glycolytic volume in units of Bq/ml * ml at time-point 2. FIG. 12 illustrates four Mercator projections of the four tumour statistics: total glycolitic volume at time point 1 , percentage of volume with BBB breakdown at time point 1 , mean uptake at time point , and total glycolytic volume at time point 2. At time point 1 , three regions with high total glycolitic volume are visible: the largest is centralised at 60°S 75°W, with two others centralised at 30°S 90Έ (the extrusion on the left) and 30°N 180Έ. This geometry is mirrored in the projection of mean uptake. Blood brain bamer breakdown is common everywhere around the tumour core, except to the patient's right inferior. By time-point 2, several changes are visible with die-backs in the first and second major hotspots visible at time-point 1. ^' _} .

FIG. 13 illustrates joint distributions of time point 2 and time point 1. According to some embodiments of the present invention, to account for uncertainty, joint distributions between statistics-Obtained at different time points can be presented and analysed. In the present example, there was little correlation between mean PET uptake and time-point 2 total glycolytic volume (R—0.1 ). There was a slight correlation with blood brain barrier breakdown (R=0.39) and time point one glycolytic volume (R=0.55). In the percentage blood-brain-barrier breakdown, three populations are clearly visible, two where BBB breakdown values are linked to total-glycolitic load, and one where growth occurs in a segment with little BBB breakdown.

As shown, the Mercator projections allow the individual regions of a tumour to be easily and effectively compared across time-points, despite the occurrence of brain shift. Moreover, an entire tumour can be easily and naturally visualised on paper without the need for electronic storage and image viewing software and its associated issues (e.g., availability, compatibility, obsolescence of formats, etc.).

Further, the division of a tumour into individual segments can result in a better interrogation of data, with greatly reduced tissue heterogeneity within each segment relative to the tumour as a whole. In the above described example, despite the brain shift between time points and the changes in PET uptake, the spatial relationship between the various segments of the tumour is clearly visible, as is the effect of treatment on each individual region. The inherent uncertainties in the measurements at each time point and the spatial correspondence between them are explicitly accounted for, allowing the relationship statistics at various time points to be extracted. In particular, the sometimes complex non-linear relationship between BBB breakdown and future tumour infiltration is visible by the three clusters shown in the far right image of FIG. 13.

According to the prior art, a summary of statistics across an entire tumour model, and associated information loss, would lose such a relationship.

However, the likewise reference system enabled by the present invention allows different parts of the tumour at different time points to be referred to naturally and intuitively.

In some cases, a large distance between the inner and outer surfaces of a tumour means that multiple heterogenous and biological regions of the tumour may be included within each segment. This suggests that in such circumstances a multilayer shell should be used.

Embodiments of the present invention can easily accommodate this. A third intermediate surface can be generated just below the outer surface.

Statistics between the inner and intermediate, and intermediate and outer surfaces can be extracted and displayed as two separate Mercator projections. For example, this can be useful in cases where it is suspected that hypoxic regions along the edge of the active tumour shell are to be found.

FIG. 14 illustrates a particular type of tumour that is sufficiently amorphous that folds occur, where a ray 1400 extending from the centre of the tumour passes outside the tumour and then back into the tumour. As illustrated, only the fold of the tumour closest to the core is considered (bold line). According to some embodiments of the present invention, two options exist: treat the separated part of the segment as a separate segment, or simply include it in the existing one. Since segments can be large and include heterogeneous regions anyway, the latter approach can ' be effective for assisting analysis of the tumour.

FIG. 15 illustrates another type of tumour that consists of multiple or amorphous necrotic cores 1500. Here, each core can be treated independently, with an interpolated boundary between regions belonging to each core. The inner surface of the shell (necrotic core surface) is interpolated between rays which smooths away folds. This can mean parts of the necrotic core are inadvertently included, but relative to the size of each segment these regions are small. FIG. 16 illustrates yet another type of tumour where no active shell exists, or where the active shell is beyond a scanner resolution. In this case, an inner surface 1600 and an outer surface 1605 of the shell coincide. Likewise, when no core exists then the inner surface is defined at the origin at the centre of the tumour.

FIG. 17 is a diagram illustrating a cross section of a tumour 1700 having vasculature 1705 extending into and out of the tumour 1700. If a clustering algorithm is used to divide a tumour up into connected regions with similar statistics, the regions need not be fixed to conical segments. Rather, the data can be displayed as a series of slices at different distances from a tumour centre. Even if no such clustering is performed, certain parts of segments can be masked out (i.e., ignored) if they are known to correspond to certain phenomena such as the vasculature 1705. That enables an analysis to focus solely on relevant parts of a tumour.

FIG. 18 is a diagram illustrating a cross section of a tumour 1800 modeled using non-linear rays 1805. For very amorphous tumours, nonlinear rays can be projected from the centre (or inner surface of the core) to the edges. The rays can be made to follow paths of highest intensity gradient, or generated using some other measure, such as a method that enforces minimum angular spacing and shortest total path.

As suggested by the above alternatives, those having ordinary skill in the art will appreciate that the examples described herein do not represent the only means for implementing the present invention, and a wide variety of alternative embodiments are also enabled by the present disclosure. For example, three dimensional regions of an object do not need to be defined by lines of longitude or latitude, but alternatively can be defined by other features such as an internal similarity of a particular statistic (e.g., a standardised PET value of around 5) within the enclosed region.

Still other applications of the present invention include, for example, melanoma scans. Three dimensional optical scans of a person at multiple time points can be stored and then presented on a sphere or projection thereof using the teachings of the present invention. That can be used to either automatically detect melanoma or observe existing cases of it. The parameters for projecting the scans to a sphere also can be recorded.

Yet another application of the present invention includes capturing 3D scans of multiple motor vehicles in car crashes and storing them. The deformations can be normalized to a sphere, and later scans can be added to a library of stored parameters to establish the position, direction and force of impact of future car crashes.

FIG. 19 is a flow diagram illustrating steps of a method 1900 of analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, according to an embodiment of the present invention.

At step 1905 the amorphous shape of the object is normalised to a predetermined three-dimensional template to define a normalised shape of the object.

At step 1910 a plurality of three dimensional regions within the normalised shape is defined.

At step 1915 a value of the at least one parameter for each of the regions is determined.

At step 1920 each of the values is assigned to a unique location on the normalised shape, wherein each location corresponds to a position of one of the regions within the object.

FIG. 20 diagrammatically illustrates a computing device 2000, according to an embodiment of the present invention. For example, the method 1900 of FIG. 19 can be implemented using the computing device 2000 and appropriate computer readable program code. Thus, according to some embodiments, the computing device 2000 can function as a system for analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape.

The computing device 2000 includes a central processor 2002, a system memory 2004 and a system bus 2006 that couples various system components, including coupling the system memory 2004 to the central processor 2002. The system bus 2006 may be any of several types of bus structures including a memory bus or memory controller, a peripheral bus, and a local bus using any of a variety of bus architectures. The structure of system memory 2004 is well known to those skilled in the art and may include a basic input/output system (BIOS) stored in a read only memory (ROM) and one or more program modules such as operating systems, application programs and program data stored in random access memory (RAM).

The computing device 2000 can also include a variety of interface units and drives for reading and writing data. The data can include, for example, image data of a three-dimensional object such as a tumour.

In particular, the computing device 2000 includes a data storage interface 2008 and a removable memory interface 2010, respectively coupling a solid state or hard disk drive 2012 and a removable memory drive 2014 to the system bus 2006. Examples of removable memory drives 2014 include magnetic disk drives and optical disk drives. The drives and their associated computer-readable media, such as a Digital Versatile Disc (DVD) 2016 provide non-volatile storage of computer readable instructions, data structures, program modules and other data for the computer system 2000. A single hard disk drive 2012 and a single removable memory drive 2014 are shown for illustration purposes only and with the understanding that the computing device 2000 can include several similar drives. Furthermore, the computing device 2000 can include drives for interfacing with other types of computer readable media.

The computing device 2000 may include additional interfaces for connecting devices to the system bus 2006. FIG. 20 shows a universal serial bus (USB) interface 2018 which may be used to couple a device to the system bus 2006. For example, an IEEE 1394 interface 2020 may be used to couple additional devices to the computing device 2000. Examples of additional devices include cameras for receiving images or video, or microphones for recording audio.

The computing device 2000 can operate in a networked environment using logical connections to one or more remote computers or other devices, such as a server, a router, a network personal computer, a peer device or other common network node, a wireless telephone or wireless personal digital assistant. The computing device 2000 includes a network interface 2022 that couples the system bus 2006 to a local area network (LAN) 2024. Networking environments are commonplace in offices, enterprise-wide computer networks and home computer systems.

A wide area network (WAN), such as the Internet, can also be accessed by the computing device, for example via a modem unit connected to a serial port interface 2026 or via the LAN 2024.

It will be appreciated that the network connections shown and described are exemplary and other ways of establishing a communications link between computers can be used. The existence of any of various well-known protocols, such as TCP/IP, Frame Relay, Ethernet, FTP, HTTP and the like, is presumed, and the computing device 2000 can be operated in a client-server configuration to permit a user to retrieve data from, for example, a web-based server.

The operation of the computing device 2000 can be controlled by a variety of different program modules. Examples of program modules are routines, programs, objects, components, and data structures that perform particular tasks or implement particular abstract data types. The present invention may also be practiced with other computer system configurations, including hand-held devices, multiprocessor systems, microprocessor-based or programmable consumer electronics, network PCs, minicomputers, mainframe computers, personal digital assistants and the like. Furthermore, the invention may also be practiced in distributed computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed computing environment, program modules may be located in both local and remote memory storage devices.

FIG. 21 is a diagram illustrating a cross section of a tumour 3010 modelled using linear rays 3030 projected from a geometric primitive 3040, according to an embodiment of the present invention.

FIG. 22 is a diagram illustrating a tumour 3110 in three dimensions modelled using linear rays projected from a three dimensional geometric primitive 3 40, according to an embodiment of the present invention. In this case the 3D geometric primitive 3140 is a tetrahedron. Any geometric primitive could be used, including non-Platonic solids. The outer surfaces of two regions 3150, 3160 in the tumour 3110 are shown in different shades of gray. Dividing a tumour in this manner reduces the effects of geometric distortions when projecting data onto a plane.

FIG. 23 shows an example demonstrating the efficacy of a method for examining the relationship between at least two measured statistics, according to an embodiment of the present invention. One point 3210 for each region in a set of tumours is represented on a plane. The horizontal position of each point 3210 indicates an average intensity 3220 within the region within a Positron Emission Tomography (PET) image covered by a tumour segment. The vertical position indicates an extent 3230 by which the volume of a given segment changed over time. A vertical coordinate of 100 indicates no change in size and is indicated by a line 3240. An analysis of four different tumours is shown, each indicated by the markers in the legend 3250. Linear regressions 3260 were applied to each individual tumour. In every case a positive correlation was obtained between Positron Emission Tomography intensity and changes in volume over time. Also, the amount of growth varies within tumours, indicating that the effect of therapy varies within tumours. The method of the present invention enables the latter result to be obtained, and this result has implications for the way cancer is treated and studied. In particular, the present method enables the tailoring of treatment within tumours.

The above description of various embodiments of the present invention is provided for purposes of description to one of ordinary skill in the related art. It is not intended to be exhaustive or to limit the invention to a single disclosed embodiment. As mentioned above, numerous alternatives and variations to the present invention will be apparent to those skilled in the art of the above teaching. Accordingly, while some alternative embodiments have been discussed specifically, other embodiments will be apparent or relatively easily developed by those of ordinary skill in the art. Accordingly, this patent specification is intended to embrace all alternatives, modifications and variations of the present invention that have been discussed herein, and other embodiments that fall within the spirit and scope of the above described invention.

Claims

Claims:

1. A computer implemented method of analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, including:

normalising the amorphous shape of the object to a predetermined three-dimensional template to define a normalised shape of the object;

defining a plurality of three dimensional regions within the normalised shape;

determining a value of the at least one parameter for each of the regions; and

assigning each of the values to a unique location on the normalised shape, wherein e_^ach location corresponds to a position of one of the regions within the object.

2. The method of claim 1, further comprising displaying representations of the values on a two-dimensional projection of the outer surface of the normalised shape.

3. The method of claim 1 , wherein the predetermined three- dimensional template is a spheroid.

4. The method of claim 2, further comprising simultaneously displaying a second two-dimensional projection that displays previous values of the at least one parameter of the object.

5. The method of claim 2, further comprising simultaneously displaying representations of the values of a plurality of parameters on the two-dimensional projection of the outer surface of the normalised shape.

6. The method of claim 1 , wherein the plurality of three dimensional regions within the normalised shape are defined by the outer surface of the normalised shape, an inner surface of the normalised shape, and a plurality of rays extending from a centre of the normalised shape.

7. The method of claim 1 , wherein the plurality of three dimensional regions within the normalised shape are defined by the outer surface of the normalised shape, an inner surface of the normalised shape, and four rays extending from a centre of the normalised shape.

8. The method of claim 6, wherein the plurality of rays are defined by a centre point of the object and the intersections of latitudes and longitudes on the surface of a sphere.

9. The method of claim 6, wherein the plurality of rays are non-linear.

10. The method of claim 6, wherein the plurality of rays conform to an intensity gradient of an image of the object.

11. The method of claim 6, wherein each ray in the plurality of rays follows a shortest path to the outer surface of the object.

12. The method of claim 1 , wherein the object is a biological object or tumour.

13. The method of claim 12, wherein a boundary of a necrotic core of the tumour is approximated as an inner surface of the sphere.

14. The method of claim 12, wherein each segment approximates a segment of an active tissue shell of the tumour.

15. The method of claim 12, wherein the at least one parameter is selected from the following: density, temperature, glycolitic volume, mean uptake, and percent volume with blood brain barrier breakdown.

16. The method of claim 12, wherein the at least one parameter is selected from the following: a histogram of values, an at least one parameter derived from a plurality of values (e.g. a dynamic scan or a diffusion weighted image), and an at least one parameter derived from a linear or non-linear combination of values.

17. The method of claim 12, further comprising simultaneously displaying a second two-dimensional projection that displays previous values of the at least one parameter of the tumour.

18. The method of claim 12, wherein the plurality of three dimensional regions define a plurality of shells of the tumour.

19. The method of claim 1 , wherein the representations of the values are selected from the following: colours, symbols, character strings, and patterns.

20. A system for analysing at least one parameter of a heterogeneous, three dimensional object having an amorphous shape, including:

a computer readable memory; and

defining a plurality of three dimensional regions within the normalised shape;

determining a value of the at least one parameter for each of the regions; and