Method and system for assessing structural integrity of hollow expandable structures

Abstract

Methods and systems are disclosed for assessing the structural integrity of a hollow expandable structure subject to expansion and contraction. The disclosed methods use a combination of expandable structure wall strain calculation and expandable structure wall tension calculated from 3D images (or 3D images assembled from 2D images) of the expandable structure captured at different states of expansion of the expandable structure. The calculated wall strain and wall tension are independent of wall thickness and wall material properties.

Description

[0001] METHOD AND SYSTEM FOR ASSESSING STRUCTURAL INTEGRITY OF HOLLOW EXPANDABLE STRUCTURES Technical field The disclosure relates to automated analysis of captured images to identify structural impairment of a hollow expandable structure, and potentially identify weaknesses in the structure from the image analysis. A particular application of embodiments is for analysis of flexible expandable structures, such as those given by medical images of organs or vessels, such as the aorta, to identify indicators of potential risk, such as aneurysm disease progression and aneurysm rupture risk. Background Aortic aneurysm (AA), or more specifically Abdominal Aortic Aneurysm (AAA) is a chronic asymptomatic disease of the elderly (> 65 years). AAA rupture is a catastrophic event with mortality exceeding 90%. Clinical decisions (essentially whether to operate or to put a patient on surveillance) are currently based on AAA maximum diameter without any consideration for mechanical / biomechanical factors. Most AAAs are asymptomatic, and they are often diagnosed opportunistically during clinical examination or investigation for another condition. The most important complication of AAA, aortic rupture, is a catastrophic clinical event. Most patients will not survive and overall AAA causes ~200,000 deaths per year worldwide. Australia has a high overall prevalence (7.2%) of an AAA defined as 30 mm or larger in diameter in men over 64 (in women it is ~4 times lower). Although the overall mortality has halved in the last decade, Australia has a very high rate of surgical intervention compared to other western countries. In 2019 the European Society for Vascular Surgery and National Institute for Health and Care Excellence (UK) published updated guidelines on AAA management confirming the burden of disease and indications for interventional treatment, which is based on a maximum AAA diameter > 5.5 cm for men and 5 cm for women. Yet, in Australia 40% of all AAA undergo intervention below this threshold despite the fact that data from the National Health System (NHS, UK) screening programme show that, for aneurysms below 5.5 cm, the rupture rate is 0.4% per year, which is lower than the risk from operation, and many AAA cases remain quiescent in a patients’ lifetime. This raises the question on how to best manage AAA’s as there is a balance between intervention to prevent AAA rupture versus overtreatment that may cause harm. The current management of intact AAA’s is based primarily on the maximum aortic diameter. If the diameter is < 5.5 cm for men and 5 cm for women, the patient is usually placed on a program of surveillance, with regular ultrasound examinations or CT scans to monitor growth. If the diameter exceeds 5.5 cm for men and 5 cm for women, or the AAA is expanding rapidly (> 4 mm in 6 months or >10 mm in one year), surgical intervention is typically recommended. Regardless of the type of repair planned, it is the decision and timing of intervention that causes the most concern amongst patients and clinicians. Currently a 'one size fits all' approach is applied to AAA care, and as such is not suitable for all patients. A rupture prediction criterion derived from population statistics does not take into account the particular circumstances of a given patient. It is estimated that as many as ten operations are performed to prevent one AAA rupture and probably at least 75% of AAAs do not actually rupture, yet as many as 0.4% per year smaller aneurysms in patients under surveillance do rupture. Therefore, there is an unmet need for improved patient stratification. Given the many limitations of the current clinical definition of ‘high-risk’ of rupture, based mainly on the maximum diameter of the AAA, many researchers across both engineering and medical disciplines believe that biomechanics-based patient-specific modelling (PSM) could have major clinical potential to provide more accurate patient-specific rupture risk assessment. Summary of the Invention According to one aspect there is provided a method of assessing the structural integrity of an expandable structure subject to expansion or contraction, using a combination of expandable structure wall strain calculation and expandable structure wall tension calculation, calculated from 3D images of the expandable structure captured at different states of expansion of the expandable structure, wherein the calculated wall strain and wall tension are independent of wall thickness and wall material properties. In some embodiments the method comprises the steps of: obtaining a first set of 3D images (possibly of different modalities) of the expandable structure at a first state of expansion; obtaining at least one second set of 3D images (possibly of different modalities) of the expandable structure, each second set of images captured at a state of expansion different from the first state of expansion; calculating wall strain (ε) between the first and second expansion states based on relative displacement of a plurality of points on the structure between at least one 3D image from the first set and at least one 3D image from the second set; obtaining data indicative of a pressure load on the expandable structure; generating a 3D discretisation of geometry of the wall of the expandable structure based on any one or more of the 3D images, providing a sample of wall characterising points defining the wall; calculating wall stress based on solid mechanics; calculating wall tension from the calculated wall stress for the plurality of wall characterising points by stress field integration over the wall thickness; and calculating a structural integrity index (SII) based on a comparison between the calculated tension and the computed strain for each one of the plurality of wall characterising points. In some embodiments wall strain is calculated by: registering at least one 3D image from the first set and at least one 3D image from the second set to obtain a displacement field between the first and second expansion states based on relative displacement between corresponding voxels in registered images; regularisation of the obtained displacement field between the first and second expansion state; computing deformation gradient components of the wall of the expandable structure based on the displacement field; and computing strain (ε) of the wall for at least a plurality of the wall characterising points from the wall deformation gradient or estimating wall strain from selected components of deformation gradient In some alternative embodiments wall strain is calculated by: generating a first state 3D model of geometry of the expandable structure based on the segmentations of at least one 3D image of the first set of images; generating a second state 3D model of geometry of the expandable structure based on the segmentations of at least one 3D image of the second set of images; registering the first state 3D model of geometry to the second state 3D model of geometry to determine relative displacement of the plurality of points characterising expandable structure between the first state 3D model of geometry and the second state 3D model of geometry; and calculating strain between each of the wall characterising points from relative displacement between the two expansion states of the expandable structure or estimating wall strain from selected components of deformation gradient. In some alternative embodiments wall strain is calculated by: generating a first state 3D mesh of the expandable structure based on at least one 3D image of the first set of images or their segmentation; generating a second state 3D mesh of the expandable structure based on at least one 3D image of the second set of images or their segmentation; registering the first state 3D mesh to the second state 3D mesh to determine relative displacements of the plurality of points characterising expandable structure between the first state 3D mesh and the second state 3D mesh; and calculating strain between each of the wall characterising points from relative displacement between the two expansion states of the expandable structure. In some alternative embodiments wall strain is estimated from selected components of a deformation gradient, the deformation gradient being determined from the first state 3D mesh and the second state 3D mesh. In some embodiments strain is replaced by stretch and principal strain by principal stretch. In some embodiments principal strain is replaced by tangential strain and maximum principal strain by maximum tangential strain. In an embodiment the structural integrity index (SII) is a ratio of the calculated tension and strain. In some embodiments the method further comprises calculating a relative structural integrity index by dividing structural integrity index by its average value. In some embodiments the wall stress is calculated using a finite element method. In some alternative methods the wall stress is calculated using a meshless method. In some embodiments the SII is calculated SII = Wall tension / (1+strain magnitude)= Wall tension / (1+|ε|). In some embodiments the SII is calculated for every wall characterising point of the expandable structure wall. Some embodiments of the method further comprise the step of visualising the ratio of Wall Tension / Strain (SII) and Relative ratio of Wall Tension / Strain (RSII). In some applications the expandable structure is a flexible expandable structure. For example, the flexible expandable structure can be a biological expandable structure. Expandable structures to which the current methods may apply can also include other hollow flexible structures or frameworks, for example, pneumatic tyres, expandable frames or stents. In one example the hollow expandable structure is an aortic aneurysm. In this example the sets of 3D images can include a systolic image and a diastolic image. The images may be of different modalities, for example CT, MRI, ultrasound. However, the images do not need to be the systolic and diastolic images, and images taken at other states of expansion (not the extremes) may be used. An embodiment of the method further comprises, a) calculating further wall strain between any previous state and a further state of the expandable structure based on a further one of the second sets of images; b) calculating a structural integrity index (SII) for each one of the plurality of wall characterising points based on comparison between the calculated tension for the point and the further calculated strain for each point. This embodiment may further comprise the step of choosing a further one of the sets of second images and repeating steps a) and b) for the further set of second images. In some embodiments the wall characterising points can be located on an inner wall surface of the expandable structure. In alternative embodiments the wall characterising points can be located on an outer wall of the expandable structure. Another aspect provides a system configured to implement the method as described above. Brief Description of the Drawings Figure 1 is a flowchart showing a schematic overview of a method in accordance with an embodiment of the invention. Figure 2 shows the Basic Registration Components as are applied for registering two 3D images in an embodiment of the invention. Figure 3 shows an example of the outcome of the registration process. Figure 4, which is a flowchart showing steps used to calculate the deformation gradient and wall strain in an embodiment of the invention. Figure 5, shows an example of automatic finite element mesh creation. Figure 6 is an image of a 3DSlicer interface showing an example of extracted patient specific AAA geometry from a diastolic CT scan. Figure 7 shows an example of a cross sectional view of AAA finite element meshes. Figure 8 shows an example of fixed boundary conditions applied to the top and bottom edges of the AAA geometry. Figure 9 shows an example of Maximum principal stress (in MPa) distribution maps and their directions (indicated by arrows) for an AAA patient. Figure 10 illustrates an example of maximum principal tension (N / mm). Figure 11 illustrates and example of structural integrity index (SII) distribution maps (in N / mm). Figure 12 illustrates examples of results of different RSII calculation scenarios. Figure 13 is a block diagram of an embodiment of a system for implementing an embodiment of the invention. Detailed Description Glossary Acronyms used within the specification include: AA Aortic Aneurysm. An aortic aneurysm is an abnormal bulge that occurs in the wall of the major blood vessel (aorta) that carries blood around the body from the heart. Aortic aneurysms can occur anywhere in your aorta and may be tube-shaped (fusiform) or round (saccular). AAA Abdominal Aortic Aneurysm. This is an aortic aneurysm located in the abdominal aorta, the lower part of the body’s main artery. CT or CTA Computed tomography (CT) or computed tomography angiography (CTA) uses x-rays to provide detailed pictures of the heart and blood vessels. 3D CT or 3D CTA compiles a three-dimensional image rendering from the captured CT images. 4D CT or 4D CTA adds the dimension of time to 3D CT or 3D CTA. In 4D CT timing of image capture, which may be relative to a respiratory or cardiovascular cycle, is used to order images based on time to render dynamic 3D CT images. 4D CT-Angiography (CTA) is an imaging technique that provides a time history of sequential volumetric (3D) scans. This allows time- resolved tracking of the 3D motion of a specific region of tissue. RPI Rupture potential index. SII Structural Integrity Index. Structural Integrity Index is a term introduced in this specification to refer to a function of wall tension to wall strain – a measure of the structural integrity of regions within the assessed structure that shows variation in wall stiffness in regions of the structure. Strain is a dimensionless measure of deformation representing the displacement between particles in a material body. Stretch is a measure of deformation of a material and is defined as the ratio of the deformed length to the original length. RSII Relative structural integrity index, is another term introduced in this specification. Relative structural integrity index is a term introduced in this specification to refer to a ratio of SII to its average value over the surface. It is a self-calibrating relative measure of the structural integrity of regions within the assessed structure that displays variation in wall stiffness in regions of the structure. As this measure is relative to other regions of the structure, this measure is not dependent on knowledge of exact wall thickness and wall material properties, instead this provides an indicator a structural integrity that shows local changes in wall stiffness. Additional clarification of terms: Pixels are rectangular building blocks of 2D images. Voxels are rectangular prism building blocks of 3D images. A 3D image is an object on its own, it is not a collection of 2D images. A 3D image may, however, be assembled from a collection of 2D images. It should be understood that references in this specification to 3D images encompasses 3D images from any source, including assembled from a collection of 2D images, or equivalent of 3D image data extracted from a set of 2D images. Calculating wall stress based on solid mechanics: “solid mechanics” refers to any experimental, analytical or numerical method describing the behaviour of solid objects, and calculating stress in solid objects including finite element method, finite volume method, finite difference method, and other methods using mesh-based and meshless discretisation. Image registration generates mapping between two images (a fixed and a moving / floating image) and identifies correspondence between voxels in two images. Image segmentation is the process of partitioning a digital image into multiple segments. Image segmentation is typically used to locate objects and boundaries (lines, curves, etc.) in images. More precisely, image segmentation is the process of assigning a label to every pixel in an image such that pixels with the same label share certain characteristics. In the case of AAA, image segmentation identifies the wall, intraluminar thrombus and lumen. This information can then be used to create a 3D model of geometry. Detailed Description of Embodiments Disclosed herein are methods for assessing the structural integrity of an expandable structure subject to expansion and contraction, using a combination of expandable structure wall strain calculation and expandable structure wall tension calculation from 3D images (or 3D images assembled from 2D images) of the expandable structure captured at different states of expansion of the expandable structure. The calculated wall strain and wall tension are independent of wall thickness and wall material properties. In application to AAA the disclosed methods and algorithms allow robust, accurate, quantitative, patient-specific assessment of structural integrity of an aneurysm wall and can enable identification of localised weakening of the wall. Although the examples and research referred to in the present specification relate to Abdominal Aortic Aneurysms, embodiments of this method and system can be applied to any other aneurysm of the vascular system, including cerebral aneurysms. Further, embodiments may be applied to any other hollow (or sack-like) organ, where the organ is subject to expansion or compression, for example, a bladder at various stages of inflation. This methodology may also be applied to other types of hollow expandable structures subject to expansion or contraction due to changes in internal pressure. For example, engineered or manufactured hollow expandable structures such as pneumatic tyres, balloons, pneumatic balls, tubes, hoses, packages etc. As the methodology described herein is based on analysis of images captured of the surface of the expandable structure wall (internal or external) at different states of expansion, this data can be captured using know image capture technologies including cameras, radar, lidar etc. The captured images can be processed to calculate wall strain and wall tension to assess rupture risk in the same manner as described herein for biological structures such as AAA, examples will be described in further detail later in this description. Deformation in the AAA wall is driven by variations in the internal blood pressure. The forces applied by the blood to the internal AAA wall are balanced by stresses which develop in the wall. The maximum principal stress S (unit [Pa]) develops predominantly tangentially to the wall (see Figure 9) and leads to an increase in AAA diameter when the internal pressure increases, due to the tangential strain ε (non-dimensional) induced in the wall. We compute wall stresses using the inventors’ well-established, published methods that are insensitive to (unknown) patient-specific mechanical properties of the aneurysm wall. The tension in the wall is computed by integrating the stress field (examples of some methods by which this may be found are described below) over the thickness of the wall. Tension computed this way is insensitive to estimated wall thickness for a given patient (as the thickness is “integrated out”). The wall strain (dimensionless) is computed from the wall deformation field measured from images captured in two different states of expansion. For ease of use in relation to AAA from systolic and diastolic Computed Tomography images. Sophisticated existing image registration methods can be used to obtain this deformation field. Advanced methods of differential geometry and approximation theory are deployed to compute strains from this deformation field. The wall strain can be determined based on image analysis, and mapping of points or voxels to identify difference in relative position, and difference in distance between adjacent points in images captured at different states of hollow structure expansion. Wall stress can be determined based on known 3D modelling stress calculation approaches to provide a 3D stress tensor field, which can be integrated over thickness to provide a wall tension. The tension and strain thus calculated from the image analysis are used to provide a structure integrity index for each region of the structure. The structural integrity index is a function of tension to strain at each point on the aneurysm surface. The essence of our approach is point-by-point comparison of the wall tension (measured in N / mm) and wall strain (dimensionless), which we call Structural Integrity Index (SII). Further, scaling this SII by its average yields Relative Structural Integrity Index (RSII). Localised abnormal ratio of SII to average SII (i.e. abnormally low or high as compared to the rest of the wall RSII) is an indication of localised impairment of the wall’s structural integrity. The local SII characterising a function of the maximum principal tension and maximum principal strain is colour coded and displayed on as surface of an aneurysm. This is a very easy to interpret picture that helps with diagnosis, prognosis and treatment planning. An advantage of the methods and algorithms described herein is that they provide an approach that is entirely patient-specific and do not rely on any population-based statistics, as is often the case with other approaches utilising population-derived tissue properties, wall strength and wall thickness. These methods and algorithms have a potential to revolutionise aneurysm disease management leading the way to truly personalised treatment plans. An embodiment will now be described in further detail with reference to Figure 1, which is a flowchart providing a schematic overview of a process according to an embodiment of the invention using the example application of assessment of an aneurysm. Image acquisition (110) The first steps 110 and 115 concern acquisition of the images upon which the assessment is based. At least two images are required, each at a different state of expansion of the structure of interest. Multiple images may be captured, each at different times during a cycle of expansion and contraction 110 and the two or more images for analysis selected from this data set 115. Also, during this image capture, data regarding internal pressure of the structure can also be captured at the same time as each image, so the image and associated pressure data are recorded. However, this is not necessary for calculations and utilised as indicative of the state of expansion only in some embodiments. In this aneurysm example, the images may be acquired from CT (computerised tomography) scans 110, the scan being taken at different times during a cardiac cycle. The blood pressure may be captured for enabling indexing of the images to stages within the cardiac cycle, which may be useful for indexing or comparison of sets of images taken at different times or other analysis, such as tracking disease progression for a patient. The selected at least two images 115 preferably include one systolic image and one diastolic image, showing the smallest and largest size of the aneurysm respectively. For example, a standard 4D CT can be used, where 3D images are captured successively at predetermined time intervals. This imaging technique is commonly used in cardiology and available widely.4D CT-Angiography (CTA) is an imaging technique that provides a time history of sequential volumetric (3D) scans. This allows time-resolved tracking of the 3D motion of a specific region of tissue. As a result, measurements of trajectories of discrete material points of the arterial wall can be recorded. The relative motion between different material points can be used to defines the strain in the aortic wall. In their research the inventors used a SOMATOM Definition Flash CT Scanner (Siemens Healthineers AG, Forchheim, Germany) at Fiona Stanley Hospital in Perth, Western Australia. Although this example uses CT scan data, for other applications image data may be acquired using other modalities, for example MRI (magnetic resonance imaging), ultrasound, 3D photography, stereo vision, etc. As should be apparent from the following explanation the method of image acquisition is not critical to the subsequent analysis process. For non- biological applications (for example application to manufactured articles such as pneumatic tyres, balloons, balls or tubes) any suitable imaging modality may be used, for example cameras, lidar etc. to capture data for characterising a 3D images of a wall surface of the article in two different expansion states. It should be appreciated that the 3D images may be of a surface of a wall only. The wall surface may be an internal wall surface or an external wall surface. 3D non-linear image registration of systolic and diastolic data sets (120) After at least two 3D images are selected, these images are registered to find positions of corresponding voxels (i.e.3D pixels) in each of the images 120. For this registration process, one image is selected to be the fixed image, with the other images considered moving / floating images. The registration process involves finding the spatial transformation that maps each point in the fixed image to corresponding points of the moving / floating image. Furthermore, the mapping of each registered point is regularised so that the transformation is constrained by a selected physical law. In the context of image registration, regularization refers to techniques used to impose additional constraints or incorporate prior knowledge into the registration process. This helps to ensure that the resulting transformation is smooth, realistic, and robust, especially in the presence of noise or when data is sparse. Regularization is crucial in preventing overfitting and producing physically meaningful deformations. The regularization term is added to the objective function to control the smoothness and physical plausibility of the transformation. It penalizes undesirable properties of the transformation, such as excessive warping or irregularities. In particular, Physical Model-Based Regularization incorporates biomechanical or physical models (e.g., tissue elasticity) to ensure the deformation adheres to known physical properties. In at least one embodiment of the present method uses a deformable image registration with isotropic total variation regularization of displacement (for example, see Vishnevskiy, V., Gass, T., Szekely, G., Tanner, C., Goksel, O., 2017. Isotropic Total Variation Regularization of Displacements in Parametric Image Registration. IEEE T Med Imaging 36, 385-395). Isotropic total variation (TV) regularization of displacement is a technique used in image registration and other applications to enforce smoothness and reduce noise while preserving edges in the displacement field. This regularization method is particularly useful when you want to maintain sharp discontinuities or edges in the transformation while ensuring overall smoothness. Total variation measures the integral of the gradient magnitude of a function. In the context of displacement fields, it quantifies the amount of change or variation in the displacement field. Isotropic TV regularization treats all directions uniformly and penalizes the total variation of the displacement field without preference to any particular direction. This means the regularization is applied equally in all spatial directions, preserving the isotropic nature of the image or displacement field. Isotropic total variation regularization of displacement is a powerful tool in image registration, offering a good balance between smoothness and edge preservation, making it suitable for a wide range of applications where maintaining structural integrity is crucial. The output of this registration process is a transformation containing the deformation field mapping the moving / floating image onto the fixed image. The registration process involves finding the spatial transformation, ^(^), that maps each point in the fixed image, ^^(^), to corresponding points of the moving / floating image ^^(^(^)). Let us denote this transformation by ^(^) = ^ + ^(^). This registration problem is often formulated as a simplified parametric optimisation problem: ^^^= ^^^^^^^^^(^; ^^, ^^) Equation [1] Where ^(^; ^^, ^^) = −^(^; ^^, ^^) + ^^(^). Equation [2] The quality of the alignment depends on the similarity measure function (S). The term ^ weigh the similarity measure against the regularity or penalty term, P, and as a result constrains T. This is due to the problem being ill-posed for non-rigid transformations. The output of the registration is the registered moving image ^^^^^^(^)^, and a description of the transformation ^^^, that can be used to compute the As this is based on a parametric approach, algorithms embedded in codes such as BRAINS and ELASTIX (which are known algorithms with available software) have been developed to allow for testing of different parameters, . Figure 2 shows the Basic Registration Components as is known in the art. The Image pyramid 220 is used in multi-resolution framework to avoid local minima and increases the capture range of registration. The sampler 230 determines how the fixed image 210 is sampled. Interpolator 240 interpolates intensities of images 215 and deformation of transformations. Optimiser 260 optimises the similarity measure. Considering the aneurysm example, aneurysm wall deformations can be extracted from the 4D-CT images using one of many non-linear medical image registration techniques. In this example, intensity-based non-rigid image registration algorithms (as available for example, in BRAINS, ELASTICS and PTVreg) have been applied from the 3D Slicer open-source software platform for medical image analysis. Any suitable 3D analysis technique or software package may be utilised to process the input 3D images to extract the data required as input to the mathematical processes as described below, the primary purpose for the 3D analysis is identification of corresponding vessel wall voxels in the two or more images and tracking of these voxels between images. Embodiments of the present invention use the following parameters: 1. Fixed image (βF): systolic image. 2. Moving image (βM): diastolic image. 3. Transformation type: BSpline transform. 4. Sample percentage: 20% of the fixed image voxels were used as an input for the mutual information (similarity measure). 5. Similarity measure: Mean Square Error (MSE): MSE =$% ∑%+,$(β(− β))*, n: number of voxels Equation [3] The main components that can be adjusted are the cost metric 250 and the transformation model 270, along with others such as the optimizer 260, pyramid 220, sampler 230 and interpolator 240. The cost metric 250 measures the similarity of the fixed image 210 and the registered moving image 215. In our case, we use MSE as defined in equation 3. The transformation model determines the degree-of-freedom of the deformation, ^^^. In the aneurysm example, we use B-Spline Transformation as it is recommended for non-rigid registrations. These parameters are adjusted until we find the most our application. This is verified (130) through a visual assessment analysis with the support of Canny edges, an edge detector based on image intensity as well as the following image similarity measures commonly used in medical image analysis field: The structural similarity index measure SSIM, Peak signal-to-noise ratio PSNR, mean squared error MSE and Dice similarity coefficient DICE. This methodology may equally be applied to non-biological image data. Figure 3 shows the outcome of the registration process, showing in pane a) a section through 3D CT; in pane b) the automatically generated Canny edges. In this example, the “small circle” 310 is a lumen; the “large circle” 320 is the external contour of the wall. White edges indicate perfect overlap of edges in the fixed and registered floating image. Green edges are on the fixed image, pink are on the floating image. If the accuracy of the registration process is not satisfactory, the analysis will be stopped 135. For example, problems with quality of the input images may have caused registration errors, so further images may be acquired to restart the process. Alternatively, the image registration step may be repeated using adjusted transform parameters. Computation of the deformation gradient (150) We take the points representative of the aneurysm wall 140 (also see 160 below) and these can be labelled for reference. For example, wall characterising points may be points on the internal wall surface, external wall surface or within the wall surface. In the example discussed in detail points on the external wall surface are used, however other wall characterising points are contemplated within the scope of the invention. Labelling is also used when combining strain and stress calculations, which is described in further detail below. The labelling of voxels / points allows identification of the same point / voxel in each of the images. Thus, a difference in distance between two points on, or in, the artery wall on the first image and the same two points on the artery wall in the second image is a result of deformation (changing shape) of the wall due to change in internal pressure. In an example the deformation gradient is determined based on points on the external surface of the aneurysm wall, and wall characterising points represent the external wall surface. In this example we are using wall characterising points on the external wall. From image registration 120, we know the displacements between corresponding wall characterising points in the systolic and diastolic images (∆u). The deformation gradient field on the external surface wall is computed from these displacements. Sophisticated methods of differential geometry and interpolation theory can be deployed to compute the deformation gradient field on the external surface of the wall. Examples of known meshless methods that may be used are: modified moving least squares (MMLS), interpolating modified moving least squares (IMMLS), Discretization-Corrected Particle Strength Exchange (DC PSE) and an improved DC PSE developed by the inventors. The last two appear to be the most efficient and appropriate. It should be appreciated that these same methods are equally applicable to processing images of non-biological structures, to obtain a deformation gradient field. As an example, we provide a detailed description of Discretization-Corrected Particle Strength Exchange (DC PSE) The DC PSE method computes spatial derivatives using a set of points distributed (uniformly or randomly) over the spatial domain. Initially, DC PSE was introduced as a Lagrangian particle-based numerical method, based on Particle Strength Exchange (PSE) operators. An example of one method that may be employed for these calculations is described in further detail below. The DC PSE operators were introduced to reduce the discretization error -.( / )in the PSE operator approximation. In DC PSE approximation we define a kernel function 01( / ) = ψ3401( / ⁄5 ) (scaled to width 5 (kernel width)) which minimizes the difference this operator and the actual derivative. To achieve this, we use the following expression for the derivative approximation: 7.18( / ) =(3$)|1|1!;.1<18( / ) + ∑>|=|,$(3$)|=|=!5|=|3|1|;.=<=8( / ) + ^@Equation [4] =?1, 1D), E1F being an nodal spacing, H1the partial |1| differential operator expressed as H1=II / AI / 1B 1D, AB …I / DJK= LK |1| MNBM3|1|OKMD Equation [5] FG( / ) |1| PQQ O= / 3 / = / 3F =ARQ∑S∈V( / ) ^SR^T1^ / SR^Equation [6] in a neighbourhood around the point / Swith cut-off radius JW. The set of moment conditions becomes |1|;X =(−1) 1! = = 1.Y 0 = ≠ 1^gh4≤ |=| ≤ |1| + ^ − 1 Equation [7] where the kernel 01is chosen as: 01( / , j)= ^∑||1n||,l=m3$opq^k( / )jk^ r3|j|s= ^( / , j)t(j), j = / 3 / uv Equation [8] Equation [9] For the approximated derivative 7.18( / ) at node / ^, the coefficients are computed by solving the above linear system of equations for / = / ^. Given our choice of kernel function, the DC PSE derivative approximation becomes: } / ~ / B / 3 / 3| u ^}^Equation

[0010] where p( / )=[p1( / ), p2( / ),…, pm( / )], with m being the number of monomials (m=6 and m=10 for second order monomials in two and three dimensions, respectively), and =( / ) =^=A, =B, … , =^^are the vectors of terms in the monomial basis and their coefficients, respectively. By using the DC PSE method, the spatial derivatives E1up to second order are given as: EA,K≡II / , EK,A≡II^Equation

[0011] Equation

[0012] Standard textbook methods are available to compute strain from the deformation gradient field. The schematic of the computations in steps 150 and 155 is given in Figure 4, which is a flowchart showing steps used to calculate the deformation gradient from the displacements (using a meshless method such as DC PSE), the Right Cauchy-Green deformation tensor (C) and Alamansi strain ε from the deformation gradient. The aneurysm displacement field (∆u) is calculated as a difference between the systolic (x,y,z)sand diastolic (x,y,z)dcoordinates of AAA wall points. The Alamansi strain ε is calculated from the Right Cauchy-Green deformation tensor (C = FTF). The deformation gradient tensor (F) is calculated from the spatial derivative (∇u) at each point of the diastolic geometry using the formula F = I + ∇u (where I is the identity matrix / unit tensor). One of many meshless numerical methods can be used to obtain ∇u or analytical derivatives of B- Splines can be evaluated. DC PSE is preferable as it is a robust and stable method for calculating the spatial derivate without introducing the shape functions when clouds of points are used as computational grids (digital images are collection “cloud” of points, centres or vertices of voxels). In an alternative embodiment instead of registering 3D images directly, 3D segmented models of geometry may be registered to provide displacement fields for strain calculations. For example, 3D geometries may be characterised using sets of images captured for two different states. Registration of these respective geometries may be used to obtain displacement fields, and deformation gradients. In other embodiments, common nodes may be labelled in the 3D geometry for each state, and comparison of relative distances between nodes in each state used to calculate strain. Alternatively, comparison of 3D meshes may be used to provide displacement fields subsequently used for calculation of deformation gradients and strain, as described above. It should be appreciated that a number of known methods for strain calculation may be employed, and all are contemplated within the scope of the present method. As described above the relative positions of points on the external wall surface in the two images are used to calculate the amount of strain caused in different regions of the wall due to the cyclic change in pressure. However, the amount of strain alone is not necessarily a reliable indicator of wall integrity. Embodiments of the invention combine calculation of strain with wall tension to provide an indicator of wall integrity. The following section describes the process for calculating wall stress. It should also be noted that the strain calculation need not be based on the external wall surface, an internal wall surface or points interior to the wall may also be used. The nature of the structure may cause internal or external wall to be more computationally convenient. In the exemplary embodiments discussed the external wall is used, however alternatives (internal or interior) may also be used. The calculation of wall strain is independent of calculation of wall stress. Although some input data for the calculations may be the same, input image data, the computation of wall stress involves separate calculations. Estimating wall strain from selected deformation gradient components In some embodiments selected components of the deformation gradient can be used for estimating wall strain. In some embodiments, certain components of the deformation gradient can be determined more accurately from registration than others. For example, components derived from the change in an expandable structure’s radius can be measured with higher precision. In such cases, only these accurately determined components are obtained from the registration, for use in estimating wall strain. Some components for estimating wall strain can also be derived using the incompressibility condition. The incompressibility condition is a constraint applied in solid mechanics to describe materials that do not change in volume when subjected to deformation. In other words, for incompressible materials, the density remains constant, regardless of the applied forces or deformations. For an incompressible solid, the determinant of the deformation gradient tensor F must be equal to one, det(F)=1. This equation, together with symmetry considerations, allows estimating all deformation gradient components from a component measured in a specific direction. Biological tissues, such as arterial walls, are often modelled as incompressible materials due to their high water content, which makes them nearly incompressible. Also rubbers and polymers from which engineered and manufactured hollow expandable structures are made, are also considered incompressible. Computation of wall stress field (160,165,170). Generation of model geometry, finite element meshing, application of boundary conditions, application of (blood) pressure loading and computation of the stress can be conducted using the inventors’ well established and published methods. These methods are known internationally and have been used by the inventors and others to compute stress in large number of patients, demonstrating that stress alone is not an adequate biomarker of the severity of the aneurysm disease. Figure 5 shows an example geometry model and mesh. Figure 5 shows an example of automatic finite element mesh creation in BioPARR for an AAA case. BioPARR is a Biomechanics based Prediction of Aneurysm Rupture Risk software system that facilitates analysis of abdominal aortic aneurysms and evaluation of rupture risk using a finite element analysis-based approach. It should be noted that this is only one example of a software package that may be utilised to implement embodiments of the invention and other tools may be utilised to extract the required information and perform calculations. For the purpose of the present analysis this software is used only for the initial steps of extracting the mesh geometry 160, as, for the invention as disclosed, this mesh geometry is utilised to produce a finite element model 165 for calculation of wall stress 170. As illustrated in Figure 5, pane a) shows the input consisting of AAA segmentation from CT. The contour of the AAA is shown in white (dotted line) 510 and the lumen segmentation is indicated as 520. Pane b) shows geometry extracted from a label map; of which the low quality triangular elements are not suitable for analysis. Pane c) shows re-meshed geometry. Pane d) shows final geometry (AAA exterior surface 530, interior surface 540 and interior intraluminal thrombus (ILT) surface 550). Pane e) shows the final mesh with a configurable number of element layers. Considering each of the steps for stress calculations: 1. Geometry extraction: The patient-specific AAA 3D geometry is extracted from the diastolic CT image using 3D Slicer, see Figure 6. Figure 6 is an image of a 3Dslicer interface showing an example of extracted patient specific AAA geometry from a diastolic CT scan. 2. Creation of computational grid: Patient-specific finite element (FE) meshes are created from the AAA geometries (extracted from diastolic CT images) using the open source Gmsh mesh generator that is called within BioPARR. Figure 7 shows a cross sectional view of AAA finite element meshes 700 showing ILT (intraluminal thrombus) 710, blood channel (lumen) 720, and AAA external wall (constant wall thickness 1.5 mm) 730 created automatically by BioPARR. 3. External load and boundary conditions: BioPARR generates input files ready for finite element simulation, by assigning boundary conditions and load (patient-specific blood pressure). The top (level of renal arteries) and bottom (level of aortic bifurcation) points of the aneurysm are rigidly constrained (Figure 8). Blood pressure changes within the patient’s cardiac cycle. Thus, mean arterial blood pressure MAP =$^ (systolic + (2 × diastolic)) applied to the external surface of ILT is used as external load in AAA stress calculation. Figure 8 shows fixed boundary conditions applied to the and bottom edges of the AAA geometry. It should be appreciated that methods or systems other than BioPARR may be utilised to generate the finite element meshes used in the stress calculations. Methods other than the BioPARR method (as discussed below) may also be used for stress calculations. The BioPARR system has been used for convenience as this system can be used for wall stress calculation in addition to meshing. An advantage of the BioPARR method described above is that results of this method of computing wall stresses are not dependent on mechanical properties of the wall material. Thus, patient specific mechanical properties of the wall need not be determined, estimated or assumed using this method. 4. Maximum principal stresses: The predicted principal stresses are extracted from the finite element solver. Many commercial and open source finite element solvers provide this output option and can be utilised to implement embodiments of the invention. As anticipated (typically), the maximum principal stress acts in the tangential direction (hoop direction) of the aneurysm surface, this is consistent with pressure vessel theory. Figure 9 shows Maximum principal stress (in MPa) distribution maps and their directions (indicated by arrows) for AAA patient, in this example the stresses are obtained using the previously verified BioPARR software package for AAA stress calculation. Other methods for stress calculation may also be used. Calculation of wall tension (175) Tension (a stress resultant with dimension N / m or N / mm) is computed through stress field integration over the wall thickness. This method has an advantage of eliminating the dependence of the results on an assumed or inaccurately measured wall thickness. While the method of computing tension is from standard textbooks on walled structure analysis, this methodology has not been applied in the context of vascular medicine. The ith component of the stress resultant ^h(N / m) is computed as ^h=^^^^p^h(^)d^ Equation

[0013] where and ^hand ^^are the inner and outer radii, respectively. We compute this integral numerically using Gauss quadrature as follows ^h= ∑4^^,$^hz^^{^^Equation

[0014] where are quadrature point coordinates and weights, respectively. Figure 10 illustrates maximum principal tension (N / mm). It should be appreciated that by integrating the stress field over the thickness of the wall, this eliminates dependence on assumptions or potentially inaccurate measurements of wall thickness. Essentially the estimated wall thickness (and any associated inaccuracies and / or assumptions) is “integrated out” by the calculation. It should also be appreciated that the results of these calculations are patent specific and do not rely on any population-based statistics. At the time of filing known techniques require assumptions or estimations to be made for parameters such as wall thickness or wall strength utilising population-derived tissue properties. This can result in undesirable inaccuracies, which presents particular risks for patients with unusual physiology. For example, where the actual wall thickness and strength measurements (which may be costly, impractical, unsafe or impossible to measure in a live patient) deviate significantly from normal. As the wall stress and tension calculations discussed above are calculated using a model of the patient specific geometry of the AAA, there is no need to apply population-based assumptions. It should be appreciated that for AAA the geometry of the vessel is complex and there can be wide variation in geometry between patients. As such, individualised geometry modelling of the patient anatomy for application in stress and tension calculation enables localised comparison with the strain calculations based on the displacement fields derived from the patent specific images. Similarly for other organs (i.e. other blood vessels, stomach, bladder etc.) such patient specific geometry modelling and calculations can also be applied. It should be appreciated that for manufactured articles, such as pneumatic tyres, balls or tubes, there may little geometric variation between articles and the geometric modelling less complex. For example, the geometric modelling may be based in part on a combination of measurements, engineering drawings, or computer aided design (CAD) data with captured 3D image data of the surface of the article in the two expansion states. For example, radii and wall thickness data may be measured or obtained from engineering / production data to generate the model for stress and tension calculation as described above. Calculation and visualisation of Structural Integrity Index SII and Relative Structural Integrity Index RSII (180, 185) An indicator of the structural integrity is a comparison between the tension and strain in a region of the structure. This may be ratio or other comparative measures utilising a combination of the strain and tension calculated within the material. The mismatch between the wall tension and the corresponding strain, as compared to the rest of an expandable structure, is an indication of the impairment of the structural integrity. It is the comparison between strain and tension that provides the indicator of structural integrity, and rupture risk. One should appreciate that structural integrity and rupture risk are two different ways of considering the likelihood of mechanical failure of a structure. Identification of a weak area can be based on relative structural integrity between regions of the structure. The structural integrity can be determined for given points in the structure. The resolution of the structural integrity and relative structural integrity calculations is based on the number and density of points chosen for these calculations. In an embodiment, as an indicator of the local AAA structural integrity the inventors use a function of maximum principal tension, calculated from the stress field (in steps 165, 170, 175), to maximum principal strain at a given point. We refer to this function as the Structural Integrity Index (SII), Equation 15. We note that SII is independent of AAA wall material properties and assumptions regarding the AAA wall thickness. ^ ¡ «SII =+^¢^ £¤+%¥+£ ¦ §¨%©+ª% (¬)$l ^ ¡+^¢^ £¤+%¥+£ ¦ ©§¤ +% (­+^¨%©+ª%¦¨©©)Equation

[0015] displayed on the AAA surface are given in Figure 11. Figure 11 illustrates and example of structural integrity index (SII) distribution maps (in N / mm) for the studied patients from the posterior view: (a) Patient 1; (b) Patient 2; (c) Patient 3; and (d) Patient 4. In this example, Patient 2 appears to be more at risk than other patients. To render the final results insensitive to the choice of pressure loading, we propose a Relative Structural Integrity Index RSII as SII (at a given point P) scaled by its average value: ^^®®(^) =¯°°(±)²³´mXµ´ ¯°° ^³´m ²²² ¶·m¸X¹´Equation

[0016] To compute the RSII (at least) four scenarios about the geometry and pressure choice can be followed: Scenario 1: computational grid built from systolic geometry and loading by systolic pressure; Scenario 2: computational grid built from systolic geometry and loading by mean arterial pressure (MAP); Scenario 3: computational grid built from diastolic geometry and loading by diastolic pressure. Scenario 4: computational grid built from diastolic geometry and loading by mean arterial pressure (MAP). Figure 12 illustrates examples of each of these scenarios. However, as illustrated in the example of Figure 12, different RSII scenarios give equivalent results for practical purposes. The 3D pictures as shown in Figure 12 advantageously carry additional information, currently not available to vascular surgeons and radiologists. It would be advantageous to such practitioners to be provided with such images for use in patient diagnosis and ongoing care. The RSII, computed using the methods as described herein, has a number of properties which overcome the problems associated with Patient-Specific Modelling-based rupture risk prediction and allows us to capture the essence of structural integrity. These properties can be particularly advantageous in the application to AAA, but can also be advantageous in other applications. These properties include: i) RSII is independent of material properties. The SII is a function of computed stress and measured strains (i.e. from 4D CTA). In the AAA example, stress computed using BioPARR is independent of material properties, making SII, and therefore RSII, independent of material properties. This is of extreme importance as patient-specific material properties of AAA wall are currently impossible to measure. ii) RSII is independent of measurement conditions. This property originates from the fact that RSII is a relative measure. Therefore, any changes in the measurement conditions, such as blood pressure and its variation over the cardiac cycle, which may lead to proportional changes in SII, are eliminated when computing RSII. In the AAA example, it is proposed that, based on biomechanical principles, structural integrity of an AAA, as captured by RSII, correlates strongly with the AAA disease progression; therefore, RSII can be used for prediction of AAA diameter expansion rate (ER). ER is the indicator for disease progression currently used in clinical practice. The correlation between RSII and AAA diameter expansion rate (ER) enables RSII to be used as a predictor for AAA progression and risk of rupture. Figure 13 is a block diagram of an embodiment of a system for implementing the method as described above. The system 1300 can be implemented using one or more processors and memory, and may be implemented as a set of software modules in a generic computer or server, or integrated into a device such as a 3D / 4D scanning apparatus. The system is configured to acquire 3D / 4D images via an integrated or external image acquirer 1310 or memory storing such images post acquisition from a patient. Other data such as patient data, including measured parameters such as blood pressure measurement can be acquired with the 3D images or input from another data source, including an IO interface (not shown). The acquired 3D images are input to a 3D model generator module 1320 and a 3D image registration module 1340. The 3D model generator 1320 performs the processing as discussed above to generate 3D discretisation of geometry of the wall of the expandable structure at different states of expansion based on the input 3D image data. This wall geometry is used by the stress and tension calculator 1330 to calculate the wall stress and wall tension as described above. The 3D registration module 1340 does not require 3D modelling, but rather identifies (otherwise referred to as registers) corresponding voxels in 3D images at different states. This image registration is used to find the displacement field that is then used to compute deformation gradient field by the deformation gradient module 1350 to determine the deformation gradient between the two states (based on relative displacement between registered voxels), from which the strain calculator 1360 calculates wall strain over the wall structure as described above. The structural integrity index (SII) calculator 1370 then takes maximum principal tension and maximum principal strain at points characterising the wall to calculate the structural integrity index (SII) and relative structural integrity index (RSII) for points as described above. The renderer 1380 processes the 3D image to apply visual representation of calculated SII and / or RSII to the 3D models and control display of this data visualisation. This visualisation can be displayed to an operator on a display or in a report as is a useful aid to enable identification of risk areas in the expandable structure wall. The system 1300 may also be configured to provide data in a report form for inclusion in a test record / history. Embodiments of the system may be implemented in a distributed system, where different functional components are implemented using separate systems with data being communicated between the systems via communication networks. For example, multiple servers or distributed processing resources may be utilised to implement the system functionality described in relation to figure 13 above. In an embodiment, images may be captured at a medical facility, for example using medical imaging equipment (i.e. MRI, ultrasound, CT etc.) and uploaded or transmitted to the system from the medical imaging facility via a communication network. For example, via a web interface, software application, or API which may also enable direct upload via machine-to-machine interface from the imaging equipment. The uploaded images are processed as described above and based on this processing a report provided back to the medical facility for clinician review via the communication network. In some embodiments a step in the process may also involve a quality review of the processed images and report before transmission of the report back to the medical facility. As mentioned above, the techniques described in detail above in relation to AAA are not limited to AAA application. The same system can also be applied to other biological structures, for example other vessels, or organs such as bladder and stomach using exactly the same imaging and processing. The described techniques can also be applied to non- biological structures hollow expandable structures. Examples of such structures can include pneumatic tyres or balls, tanks, bladders, elasticised or flexible bags, hoses, tubes pipes, pressure vessels etc. For such structures the obtaining of 3D images of the structure at two different expansion states may be greatly simplified compared with biological structures, due to accessibility of the structure and control. For example, the external surface of a tyre or hose may be readily viewable and images able to be captured using a camera or other imaging device, i.e. radar, laser, or lidar. In some instances, a camera or other imaging device may be able to be placed inside the article to capture images of internal walls at two different expansion states. The images may be captured in static states with two different known internal pressures controllable by an operator or readily measurable. The images may also be captured during variable internal pressure operation. In some embodiments the article being imaged may have a random pattern applied to assist with registration of points in the 3D images. For example, if the surface of the article is without features such as pattern or variation which can assist with registration of points on the two images, the surface may have a random pattern applied (i.e. sprayed, or spattered) to simplify the image processing to register points on the two images. This is not essential but may reduce computational resources and time required for image registration. The images can be input to the system (for example as represented in Figure 13) and the system generate a 3D model for the article based on the 3D image data alone (if sufficient detail is available) or based on a combination of input engineering data and / or measurements and the 3D image data. For example, for a common structure, such as a tube, tyre, ball, cylindrical cannister etc. basic 3D models as available in computer aided design or other modelling software packages may be used by the system processor with specifications input from measurements or product data sheets to provide a base model of the article’s geometric structure. Input 3D image data can be used by the system to apply an article specific mesh to the base model to generate a model of the article at each state of expansion. This model can then be processed as described above by the system processor to: - compute the deformation gradient for the wall surface, - calculate strain over the wall structure, - calculate stress and tension over the wall structure, and - calculate the SII and RII. The output of these calculations can be output for operator interpretation. In some embodiments the system may include a renderer configured to map the RSII to the structure and output this as one or more images rendered for visual interpretation, in a similar manner to the AAA example, or a simpler rendering or description identifying a region of increased risk may be output. In some embodiments the processor may be configured to assess the calculated SII and RSII against tolerance or threshold parameter values for the article and output an assessment result. This may be a simple pass or “within tolerance” assessment if the article is assessed to be functioning within acceptable tolerance for the assessed parameters, and warning if the articles is assessed to be functioning outside acceptable tolerance for one or more assessed parameters. In some embodiments reports may also be output providing details of such test results. It should be appreciated that the method of assessing rupture risk described is based on image processing techniques and mathematical calculations, thus has broad application in medical and non-medical fields. It is to be understood that, if any prior art publication is referred to herein, such reference does not constitute an admission that the publication forms a part of the common general knowledge in the art, in Australia or any other country. In the claims which follow and in the preceding description of the invention, except where the context requires otherwise due to express language or necessary implication, the word “comprise” or variations such as “comprises” or “comprising” is used in an inclusive sense, i.e. to specify the presence of the stated features but not to preclude the presence or addition of further features in various embodiments of the invention.

Claims

CLAIMS 1. A method of assessing the structural integrity of a hollow expandable structure subject to expansion or contraction, using a combination of expandable structure wall strain calculation and expandable structure wall tension calculation calculated from 3D images of the expandable structure captured at different states of expansion of the expandable structure, wherein the calculated wall strain and wall tension are independent of wall thickness and wall material properties.

2. The method of claim 1, wherein the method comprises the steps of: obtaining a first set of 3D images of the expandable structure at a first state of expansion; obtaining at least one second set of 3D images of the expandable structure, each second set of images captured at a state of expansion different from the first state of expansion; calculating wall strain(ε) between the first and second expansion states based on relative displacement of a plurality of points on the structure between at least one 3D image from the first set and at least one 3D image from the second set; obtaining data indicative of a load pressure on the expandable structure; generating a 3D discretisation of geometry of the wall of the expandable structure based on any one or more of the 3D images, providing a sample of wall characterising points defining the wall; calculating wall stress based on solid mechanics; calculating wall tension from the calculated wall stress for the plurality of wall surface characterising points by stress field integration over the wall thickness; and calculating a structural integrity index (SII) based on a comparison between the calculated tension and the computed strain for each one of the plurality of wall characterising points.

3. The method as claimed in claim 2, wherein wall strain is calculated by: registering at least one 3D image from the first set and the at least one 3D image from the second set to obtain a displacement field between the first and second expansion states based on relative displacement between corresponding voxels, computing deformation gradient components of the wall of the expandable structure based on the displacement field; andcomputing strain (ε) in the wall for at least a plurality of the wall characterising points from the wall deformation gradient.

4. The method as claimed in claim 2, wherein wall strain is calculated by: registering at least one 3D image from the first set and the at least one 3D image from the second set to obtain a displacement field between the first and second expansion states based on relative displacement between corresponding voxels, computing deformation gradient components of the wall of the expandable structure based on the displacement field; and estimating wall strain (ε) from selected deformation gradient components.

5. The method as claimed in claim 2, wherein wall strain is calculated by: generating by segmentation a first state 3D model of geometry of the expandable structure based on one of the 3D images of the first set of images; generating by segmentation a second state 3D model of geometry of the wall of the expandable structure based on one of the 3D images of the second set of images; registering the first state 3D model of geometry and the second state 3D model of geometry to determine relative displacement of the plurality expandable structure characterising points between the first state 3D model of geometry in the second state 3D model of geometry; and calculating strain between each of the wall characterising points from relative displacement between the two expansion states of the expandable structure.

6. The method as claimed in claim 2, wherein wall strain is calculated by: generating a mesh of at least one 3D image or its 3D model of geometry from the first set of images; generating a mesh of at least one 3D image or its 3D model of geometry from the second set of images; registering the mesh of the first state 3D image or model of geometry and the mesh of the second state 3D image or model of geometry to determine relative displacement of the plurality expandable structure characterising points between the first state 3D mesh and the second state 3D mesh; and calculating strain between each of the wall characterising points from relative displacement between the two expansion states of the expandable structure.

7. The method of any one of claims 2 to 6 wherein the structural integrity index (SII) is a function of the calculated tension and strain.

8. The method as claimed in any one of claims 2 to 7 further comprising calculating a relative structural integrity index by dividing structural integrity index by its average value.

9. The method as claimed in any one of claims 2 to 8 wherein the wall stress is calculated using a finite element method 10. The method as claimed in any one of claims 2 to 9 wherein the wall stress is calculated using a meshless method.

11. The method as claimed in any one of claims 2 to 10 wherein the SII is calculated: SII = Maximum Principal Wall tension / (1+ Maximum Principal ε).

12. The method as claimed in any one of claims 2 to 10 wherein the SII is calculated: SII = Maximum Principal Wall tension / (1+Maximum tangential strain).

13. The method as claimed in claim 11 or claim 12 wherein the SII is calculated for every wall characterising point of the expandable structure wall.

14. The method as claimed in any one of claims 8, and 11, 12 or 13 when dependent on claim 8 further comprising the step of visualising the ratio of SII and RSII.

15. The method as claimed in any one of the preceding claims wherein the expandable structure is a flexible expandable structure.

16. The method as claimed in claim 15 wherein the flexible expandable structure is a biological expandable structure.

17. The method as claimed in claim 16 wherein the expandable structure is an aortic aneurysm.

18. The method as claimed in claim 17 wherein the sets of 3D images include a systolic image and a diastolic image.

19. The method as claimed in any one of claims 1 to 18 further comprising,a) calculating further wall strain between any previous state and a further state of the expandable structure based on a further one of the second sets of images; b) calculating a structural integrity index (SII) for each one of the plurality of wall characterising points based on comparison between the calculated tension for the point and the further computed strain for each point.

20. The method as claimed in claim 19 further comprising the step of choosing a further one of the sets of second images and repeating steps a) and b) for the further set of second images.

21. The method as claimed in any one of claims 1 to 20 wherein the wall characterising points are located on an inner wall surface of the expandable structure.

22. The method as claimed in any one of claims 1 to 21 wherein the wall characterising points are located on an outer wall of the expandable structure.

Images