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3D anatomical modelling and analysis of the spine

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    This work proposes 3D modelling and patient-specific analysis of the spine by integrating information on the tis

  

  This work proposes 3D modelling and patient-specific analysis of the spine by integrating information on the tissues with geometric information on the spine morphology.

  The paper addresses the extraction of 3D patient-specific models of each vertebra and the intervertebral space from 3D CT images, the segmentation of each vertebra in its three functional regions, and the analysis of the tissue condition in the functional regions based on geometrical parameters.

  Main results are the localisation, visualisation, quantitative, and qualitative analysis of possible damages for surgery planning and early diagnosis or follow-up studies.

  The framework properties are discussed in terms of the spine’s morphology and pathologies on the spine district’s benchmarks.

  The spine is a fundamental element of human anatomy that supports our body and organs, guarantees a wide range of mobility, and protects the spinal cord from injuries. All these different tasks can be accomplished thanks to the complex anatomical structure of each element composing the spine and the organisation of the different tissues in the overall district.

  Morphology As a core component of the muscle-skeletal system, the spine sustains and supports the body and organs and plays a significant role in mobility and load transfer. The vertebral spine is composed of 33 individual bones that interlock with each other to form the spinal column. Thanks to its structure, the vertebral canal, which contains the spinal cord, protects from external trauma and mechanical shocks that arise from impacts?(Sekuboyina et?al. 2021). To provide support, powerful muscles insert in the posterior portion of the vertebral column and allow the maintenance of the posture of the subject?(Mahadevan 2018). The vertebral column is divided into five regions from above downwards: the cervical, thoracic, lumbar, sacral, and coccygeal regions. When viewed from the side, an adult spine has a natural S-shaped curve that absorbs shock like a coiled spring, maintains balance, and guarantees the range of motion throughout the spinal column?(Mahadevan 2018; Hines 2018). Figure?1a shows adults’ vertebral spine’s different segments and components.

  Fig. 1figure 1

  Anatomical description of a the spine segments and physiological curves, of b the vertebral bone, and of a vertebral segment (two consecutive vertebrae with the relative intervertebral space)

  Except for the first two cervical vertebrae, all the other movable vertebrae have similar morphology, even if they present unique features in each spine region to perform their primary functions. Each vertebra has three functional parts: the vertebral body appointed to load-bearing, the vertebral arch that protects the spinal cord, and transverse processes for ligament attachment. Between the vertebral body and the vertebral arch is the vertebral foramen. Considering the whole spine, all the vertebral foramina are stacked one on the other to build the vertebral canal (Fig.?1a, b).

  Pathologies In the short term, bio-mechanical alterations can lead to pain and disability and, in the long term, even worse consequences?(Sekuboyina et?al. 2021). Moreover, damages to the spinal cord can result in a loss of sensory and motor function below the level where the damage presented, e.g., an injury to the cervical area may cause sensory and motor impairment of the arms and legs (tetraplegia)?(Hines 2018). Given the great relevance and influence of the spine, various efforts have been made to quantify and understand its biomechanics leading to various research branches that focus on the vertebral spine from different points of view. Indeed, the study of the spine should not be limited to considering either the tissue conditions or the morphology of vertebral elements.

  Thus, this work aims to provide a framework for the complete patient-specific characterisation of the vertebral spine (Sect.?2). A key element of the framework is an effective and interactive representation of the anatomical structures to facilitate the interpretation of the morphology and pathology of the input district (Sect.?3). Finally, we discuss the experimental results of the proposed approach on benchmarks of the spine district?(Sekuboyina et?al. 2021), showing the main properties of the proposed framework in terms of characterisation of the morphology and pathologies of the spine (Sects.?3,?4).

  Previous work on the characterisation of the spine and its underlying pathologies focuses mainly on imaging and 3D modelling.

  Fig. 2figure 2

  Manual extraction of the mean HU value from a lumbar vertebra. Images courtesy of?Mahadevan (2018); Zou et?al. (2019)

  Imaging Medical imaging evaluates the status of the different tissues and pathological damage evolution; to this end, CT images are widely used (Bibb et?al. 2014). Usually, the tissue density in the image is indicated by shades of grey. The Hounsfield scale is a quantitative scale for describing radio density in medical CT, which means that voxels (three-dimensional pixels) grey levels of CT images are expressed in Hounsfield units (HU)?(DenOtter and Schubert 2022). In the Hounsfield scale, the air is represented by a value of?1000 HU (black on the greyscale) and bone between?700 (cancellous bone) and? HU (dense bone) (white on the greyscale). Bones stand out clearly in CT images since they are much denser than soft tissues. Different studies evaluated HU values in CT for the analysis of the physio-pathological status of the subject to help in disease diagnosis?(Loffler et?al. 2020; Zou et?al. 2019); other works identified a correlation between HU values and bone mineral densities?(Kim et?al. 2019).

  Fig. 3figure 3

  Description of the structure of the framework with its input data and its output results. Information on the data set used for this work can be found in?Sekuboyina et?al. (2021); Loffler et?al. (2020a)

  The DXA-based (dual-energy X-ray absorptiometry) T-score is used to measure and evaluate bone mineral density and diagnose osteoporosis. Moreover, it has been demonstrated that there is a correlation between the T values of the DXA measurement and the HU of the same vertebral body. Thus, the significant correlation of HU values with DXA T-scores means that patients’ HU values can indicate the presence of osteoporosis?(Lee et?al. 2013). This correlation is crucial since it allows the use of CT HU values for evaluating quantitative information, avoiding other types of invasive images, and reducing the overall amount of ionising radiation for the patient. In clinical practice, as well as in different studies, the evaluation of the HU values is usually conducted on a 2D slice and in the region of interest (ROI) manually identified by experts?(Lee et?al. 2013; Zou et?al. 2019; Kim et?al. 2019). This practice is time-consuming, error-prone, and user-dependent and does not take advantage of the modern 3D imaging techniques available (Fig.?2).

  3D modelling Further works focused on realising 3D models to study the spine properties, considering the whole spine or the single vertebra. These models are mainly built for finite element analysis?(Barron 2007; Aroeira et?al. 2017; Salsabili et?al. 2019; Campbell and Petrella 2016; Anitha et?al. 2020). Usually, they are not patient-specific, since to assign material tissue properties, these works rely on the state-of-the-art instead of on the single subject situation. Standard techniques for the development of vertebral models include statistical shape (Castro-Mateos et?al. 2015; Campbell and Petrella 2016) or parametric models?(Stern et?al. 2011), which are patient-specific within a certain level of accuracy but usually require the construction of a prior reference model. For a deeper evaluation of the spine biomechanics, various studies focused on alignment analysis?(Laouissat et?al. 2018; Yeh et?al. 2021; Roussouly and Pinheiro-Franco 2011) and the analysis of the vertebral spine or single vertebra morphology?(Keller et?al. 2005; Lois?Zlolniski et?al. 2019; Casciaro and Massoptier 2007; Shaw et?al. 2015). Their main drawback is using 2D images, which provide a limited visualisation of the spine.

  Even though rendering techniques are available, the common practice still considers individual slices. Recent studies have shown that the 3D information of the vertebral spine can make a difference in early diagnosis or subject evaluation?(Labelle et?al. 2011). In contrast to 2D image analysis, 3D information allows the inclusion of asymmetries in the evaluations?(Barron 2007), improves the estimation of curvatures?(Lois?Zlolniski et?al. 2019), and encodes information on the vertebral disc status?(Fazzalari et?al. 2001; Lois?Zlolniski et?al. 2019). Most of these studies start from CT images, which have the advantage of maintaining the distance between vertebral bodies and the real curvature information?(Barron 2007). However, 3D modelling and imaging usually concentrate only on a specific region or motion segment, not on the complete vertebral spine?(Barron 2007), as in?Lois?Zlolniski et?al. (2019).

  Goals The aim of the work is the 3D characterisation of the human spine from a patient-specific and subject-specific perspective, to support the diagnosis of possible pathologies and to improve the visualisation of the district when planning surgical interventions. Our framework (Fig.?3, Sect.?2) is composed of 4 sub-parts: (i) extraction of patient-specific 3D models of the whole spine by combining 3D images and 3D geometry analysis (Sect.?2.1). This evaluation can be extended to a follow-up analysis to compare the subject’s evolution in time or different acquisitions. Then, we address the (ii) segmentation of the 3D model in the three main functional parts that constitute the vertebral bones, performing a shape segmentation on the 3D patient-specific model and including a characterisation of the tissue status in the neighbourhood of the vertebral surface (Sect.?2.2). This segmentation allows the (iii) extraction of the intervertebral space leveraging the information retrievable from the previous analysis (Sect.?2.3). Finally, we discuss the (iv) quantitative evaluation of the tissue inside the vertebral body through the computation of HU parameters in an automatic and patient-specific way (Sect.?2.4).

  The framework is implemented in Matlab and grouped into five macro-functions corresponding to the flowchart elements (Fig.?3). In every macro-function, the methods described are applied for each vertebra separately to maintain the highest generality. The first macro-functions involve extracting the 3D model and the consequent shape segmentation. It is mandatory to place these functions first since all the others depend on them. The order for the other macro-function is up to the user, and they relate to the tissue status evaluation on the surface with the relative parameters computation, the intervertebral space extraction with parameters computation, and the 3D ROI growing with parameters computation.

  The framework’s input is a segmented spine data set composed of 3D segmented images, where each vertebra is labelled with a value. For more information on the data set used in this study, we refer the reader to Sect.?3.1. Starting from the segmented image, we develop a 3D grid, where each element has the same dimension as the voxel in the image, and we obtain the 3D coordinates of the voxels. Then, the next step is extracting the 3D model of each vertebra and its relation with the other vertebrae composing the spine from the segmented volume image. The single vertebra is localised in the image space, searching for the voxels with that vertebra’s specific label value. The centroid coordinates of the vertebral bodies are provided in voxels in the image space. To obtain the 3D model of a single vertebra, we apply the?-shape technique?(Edelsbrunner and Harer 2010), built on the image voxel centroids and the data structure described in?Paccini et?al. (2020).

  To build the 3D model through the?-shape technique, the only points required are the ones belonging to the vertebra to be reconstructed, which correspond to the centroids of the voxels belonging to the vertebra (Fig.?4). The?-shape technique is applied to accurately represent the vertebra’s external surface, closed, without cavities or tunnels, and empty inside. For this reason, all the voxel’s centroid belonging to the vertebra are used as an input set for the ?-shape, and the smallest? that produces an?-shape enclosing all points is considered. The extraction of the boundary facets of the?-shape simplifies the resulting triangulation, obtaining only the representation of the external surface of the vertebra. Matlab presents a built-in function for extracting ?-shapes and their boundary from point clouds. once the?-shape has been extracted, the vertebra’s surface is represented as a triangle mesh, corresponding to the external surface of the volume occupied by the interested vertebra in the volume image. Basic geometric information (e.g., volume and area) are extracted from the 3D model of each vertebra.

  Fig. 4figure 4

  3D vertebral surfaces: a input points, b vertebral?-shape extracted with the points in a, and c final 3D vertebral surface

  Fig. 5figure 5

  Distance distribution of a vertebral bone. Each vertex is associated with the value of its distance from the vertebral body centroid. For visualisation purposes, the distance values are mapped into a colour map where blue indicates the smaller distance value, while yellow indicates the vertices farther from the centroid. The unit measure of the colour map is millimetres

  The segmentation of the vertebral bones shows each vertebra’s three main functional components (i.e., vertebral body, vertebral arch, and transverse processes).

  Distance distribution For the identification of the three functional components of each vertebra, the first step is the computation of the distance distribution of each vertex composing the vertebral surface from the centroid of the vertebral body. The idea is to grow a sphere centred in the centroid and to assign to each vertex of the vertebral surface a value of distance equal to the radius of the first sphere containing it. For efficiency, the sphere growth is executed by computing the Euclidean distance of each vertex? from the vertebral body centroid? (Fig.?5).

  Fig. 6figure 6

  Probability density curve of a vertebra and resulting segmentation associated with the inflexion points. Distances from the centroid values (x-axis) and probability density value (y-axis). The distance values corresponding to an inflexion point on the curve are considered thresholds for the vertebral shape segmentation:?t1 and?t2 create the distinction between the three functional parts, where?t1 is considered the reference value of distance for the vertebral body,?t2 for the vertebral arch, and?t3 for the spinous and transverse processes region

  Probability density Extracting probability density estimates from the distribution of distances associated with the vertices of each vertebra, the 3D information, consisting of the vertex’s distance from the vertebral body centroid, becomes 1D information. In different subjects, the same vertebra presents a similar behaviour of the probability density curve. Thus, the inflexion points of such curves function as thresholds to identify the different regions of the vertebral bones. Indeed, the vertex with a distance lower than the first inflexion point is considered a part of the vertebral body. The vertex whose distance belongs to the range between the first and the second inflexion point is considered a part of the vertebral arch. All the vertices with a distance higher than the second inflexion point are classified as part of the transverse or spinous processes (Fig.?6). once the vertebral bone has been segmented and labelled in its functional sub-parts, each region can be geometrically evaluated for further analysis, considering the distance values corresponding to the inflexion points for each vertebra as geometrical parameters.

  Fig. 7figure 7

  a Nearest neighbour localisation on consecutive vertebrae and b selection of the vertex belonging exclusively to the vertebral body. c 3D surface triangulation of the inter-vertebral space and d inter-vertebral surface model in a moving spine segment

  Combined grey-level and geometric analysis Until now, all the analysis and shape segmentation have been based on 3D surface models. Since those 3D surfaces have been obtained from a segmented image, the information related to the tissues is lost in the image segmentation. The original CT image is applied to enhance the shape segmentation and geometrical information with the volume and tissue information in a neighbourhood of the surface. To retrieve the information of the original volume, we apply the grey-levels mapping method proposed in?Paccini et?al. (2020).

  The result of the grey-level mapping is a textured surface, where each vertex coordinate is associated with its specific colour, representing the information in the image. In particular, in the Euclidean mapping, the surface vertex? gets the grey level of the voxel closest to? in terms of the Euclidean distance. In the internal mapping, the closest voxels are searched only inside the surface, that is, inside the object’s volume. In the external mapping, the closest voxels are searched only outside the surface, outside the object’s volume.

  The geometric information related to the segmentation of the 3D surface into the three functional parts is linked with the texture information obtained with the texture mapping method. In particular, the geometric thresholds localising the vertebral region (i.e., the distance thresholds corresponding to the inflexion point on the probability distribution curve:?t1,?t2, and?t3 in Fig.?6) are correlated with the mean grey value (HU) of the region in all three mapping method criteria. This correlation helps the characterisation of the spinal district considering both tissue and geometric information and evaluating which mapping criteria is best suited for this characterisation.

  Fig. 8figure 8

  a Bone mineral density (BMD) behaviour in function of subject age;?x-axis present subject to age,?y-axis BMD values. b Age distribution of training set

  The intervertebral disc is the structure that bonds adjacent vertebral bodies. The discs in the thoracic region are thinner than the ones in the lumbar region. Moreover, the discs help the lumbar part of the vertebral column to assume the pronounced physiological lordosis curve since they are thicker anteriorly and narrow posteriorly. The intervertebral space between two consecutive vertebrae is localised, leveraging the 3D surface models. This information helps in the 3D characterisation of the district other than facilitating the localisation of the intervertebral space in the 3D CT, which does not highlight soft tissue as well as it does with bony structures. The intervertebral space involves only the space between two consecutive vertebral bodies. Two consecutive vertebrae at a time are considered to extract and locate each inter-vertebral space throughout the whole vertebral spine. For each couple of vertebrae, we identify the vertices belonging to one vertebra and nearest to the other vertebra. To this end, we apply a?kd-tree approach (Fig.?7a).

  The same method and thresholds applied to the vertebral surface segmentation (Sect.?2.2) are applied to select only the vertices belonging to the vertebral body. Ideally, the vertices of the intervertebral space are those facing the upper/lower vertebra and included in a sphere centred in the vertebral body centroid, with a ray equal to the first threshold (t1) (Fig.?7b). In this way, the point cloud surrounds the intervertebral space. Computing the ?-shape of the point cloud, we obtain a 3D triangulation of the intervertebral space, thus the 3D surface model that we were looking for (Fig.?7c, d). The 3D triangulation of the intervertebral space allows us to efficiently compute geometrical parameters related to the surface (e.g., the volume of the intervertebral space).

  This section describes the evaluation of the HU values on each vertebra, leveraging the 3D surface model of the spine obtained from the segmented volume image (Sect.?2.1). The input data set?(Sekuboyina et?al. 2021) provides the centroid of the vertebral body of each vertebra that appears in the CT image (Sect.?3.1). To identify a 3D ROI, we grow a sphere centred in the centroid of the vertebral body until it reaches the external 3D surface of the vertebra; thus, the sphere stops growing when it first touches the boundary of the vertebral surface. The sphere, as well as all the other 3D surfaces, is represented as a 3D triangulation. The superimposition of the sphere and the vertebra to the 3D input CT (loaded on the 3D grid described in Sect.?2.1) localises all the voxels that fall inside the sphere.

  Given the radius?r of the maximum sphere? contained in the vertebral body,? a centroid of the voxels belonging to the vertebra and? the centroid of the vertebral body,?, where the distance of each voxel from the vertebral body centroid is?. once all the voxels inside the ROI are identified, it is possible to compute the mean value and the sum of the grey levels (HU values) that those voxels preset. This procedure obtains information on the tissue inside the vertebral volume and geometric information regarding the vertebral body (maximum ray obtained by growing the sphere). Thus, the physician’s evaluation can consider all the possible aspects and leverage all the information retrievable from the data set.

  Abstract

  Introduction

  Methods

  Results

  Discussions

  Conclusions

  Data and code availability

  Materials availability

  References

  Acknowledgements

  Author information

  Ethics declarations

  #####

  This section presents the experimental results of the proposed approach (Sect.?3.2) on benchmarks of the spine district (Sect.?3.1) for the characterisation of the morphology and pathologies of the spine.

  Table 1 Details on patients and their characteristics in the data considered for the study, i.e., the training set?(Loffler et?al. 2020a)Fig. 9figure 9

  a Single vertebra distance distribution from the centroid. b Single vertebra shape segmentation

  Fig. 10figure 10

  Spine segmentation results in a an healthy subject and b a pathological subject

  The CT data are a sub-part of the Large Scale Vertebrae Segmentation challenge(VerSe)?(Sekuboyina et?al. 2021), which provides a standard benchmark for spine-processing algorithms?(Sekuboyina et?al. 2021). It consists of multi-detector spine CT (MDCT) scans with vertebral-level (3D centroids) and voxel-level annotations (segmentation masks). The data are multi-site acquired using multiple CT scanners and present a variety of fields of views (including cervical, thoracolumbar, and cervical-thoracolumbar scans), and a mix of sagittal and isotropic reformations, and cases with vertebral fractures, metallic implants, and foreign materials (Sekuboyina et?al. 2021).

  The data set is annotated with 3D coordinate locations of the vertebral centroids and voxel-level labels as segmentation masks. Twenty-six vertebrae (C1 to L5 and the transitional T13 and L6) are annotated with labels from 1 to 24, along with labels 25 and 28 for L6 and T13, respectively. This CT data set contains 160 image series of 141 patients, including segmentation masks of 1725 fully visualised vertebrae; it is split into a training data set (80 image series, 862 vertebrae), a public validation data set (40 image series, 434 vertebrae), and a test data set (40 image series, 429 vertebrae)?(Loffler et?al. 2020b). The metadata includes annotation of vertebral fractures obtained through Gentant’s method, the indication of foreign material, and the measurement of lumbar bone mineral density per patient age (Fig.?8a). We used only one type of CT scan in the training set. Figure?8b shows the age distribution of the subjects considered in our work. Table?1 provides further information on the characteristics of the data set considered in the study and provided by?Loffler et?al. (2020a) including relevant information on the patients that participated in the research.

  This section discusses the results obtained with all the methods described in Sect.?2 and all the analyses performed with the geometric and tissue-related parameters. More precisely, the results discussed are the spine segmentation and combined evaluation (Sect.?3.2.1), the intervertebral space extraction (Sect.?3.2.2), and the tissue and bone analysis (Sect.?3.2.3).

  Fig. 11figure 11

  Difference between curve morphology and inflexion point locations in a healthy subjects and b pathological subjects

  Spine segmentation and combined evaluation

  Figure?9 shows the results of the thresholding of the distance distribution that leads to the shape segmentation described in Sect.?2.2. The red part of the surface represents the vertebral body, the blue one the vertebral arch, and the green one the transverse and spinous processes. Applying the segmentation to all the vertebrae represented in the image, we obtain the segmentation of the whole vertebral spine (Fig.?10a). On a pathological subject, the shape and morphology of the vertebra can change drastically due to different processes that damage the tissue. Thus, the 3D surface models highlight such morphological changes. Applying our segmentation to a pathological case that presents a vertebral fracture due to osteoporosis, the fractured vertebra was identified among the others by a clear change in the segmentation result (Fig.?10b). Indeed, a change in the distance from the vertebral centroid distribution, in turn, modifies the vertebra’s probability distribution curve and the position of the inflexion points. Figure?11 shows how the inflexion points’ location on the probability distribution has changed due to the osteoporosis processes that brought the vertebral fracture.

  Applying the grey-level mapping algorithm to the vertebral surface model produces a 3D textured spine representation, where the texture corresponds to the HU values of the original 3D image. Depending on the mapping criteria, we can investigate the tissues inside, across, or outside the vertebral surface (Fig.?12). To combine the geometrical information retrieved from the 3D model and the tissue information given by the grey-level mapping, we evaluate the mean HU values of the vertebra’s functional region according to the distance values of its inflexion point on the probability distribution (t1,?t2, and?t3). In this case, the geometrical information corresponds to the threshold used to segment the vertebral shape model in the three functional parts. In contrast, the tissue information is the mean HU value of the correspondent vertebral functional component. Figure?13 shows the results of comparing geometrical and tissue information. In each different mapping criterion, the graphs show various clusters.

  In the case of healthy subjects, the comparison of heterogeneous information can differentiate the functional components of the vertebra, thus providing insight into the tissue status. Indeed, the distribution of the points in the combined graph could represent the patient-specific insight into the patient’s healthiness from a clinical point of view. Comparing the result with the combined analysis of a pathological subject (Fig.?14), the point in the graph related to the vertebral body of the patient (which is the functional part primarily affected in this case) is an outlier of the results of the healthy subject. The graphs related to the internal and external mapping can differentiate between healthy and pathological subjects; once the osteoporosis processes damage and erodes the bone tissues, the cartilaginous tissues are involved and suffer.

  Fig. 12figure 12

  Results of the mapping method applied to the vertebral surface model in the three different criteria: a internal, b Euclidean, and c external. The difference in texture reflects the differences in tissue composition

  Fig. 13figure 13

  Comparison between tissue and geometrical information in the surface neighbourhood. The?x-axis shows the thresholds distance values from the centroid; the?y-axis shows the mean HU values of the relative functional area localised by the thresholding, i.e., red points refer to the vertebral body, blue to vertebral arch, and green to the spinous and transverse process

  Fig. 14figure 14

  Comparison between tissue and geometrical information in the surface neighbourhood in a pathological case. The?x-axis shows the thresholds distance values from the centroid; the?y-axis shows the mean HU values of the relative functional area localised by the thresholding, i.e., red points refer to the vertebral body, blue to vertebral arch, and green to the spinous and transverse process

  Fig. 15figure 15

  a Extraction of the intervertebral space in the whole spine. b Combined visualisation: 3D volume with segmented surfaces

  Fig. 16figure 16

  Legend for the interpretation of the subject comparison graphs in Figs.?17, 18, 19, 20, 21, and 22

  Intervertebral space extraction

  The results (Fig.?15a) of the extraction of the intervertebral space from the 3D surface models (Sect.?2.3) show how the inter-vertebral spaces interact with the vertebral models of the whole spine captured in the image. The advantage of having the inter-vertebral space boundary is the localisation of the different structures in the volume (Fig.?15b). In all the following plots, which include a comparison between healthy and pathological subjects, the reader can refer to the legend in Fig.?16.

  The purely geometrical parameters retrieved from the inter-vertebral space extraction align with what is expected from the anatomy. Figure?17 shows the volume occupied by inter-vertebral spaces of healthy and pathological subjects throughout the whole spine. The volume globally increases from the cervical to the lumbar spine segment. Moreover, the intervertebral volume in function of the distance between the corresponding two vertebrae’s centroids is evaluated. In Fig.?17, the inter-vertebral volume tends to be higher than the healthy inter-vertebral volume in correspondence of the same centroid distance. This result is related to the erosive processes that start in the more external region of the bone, thus allowing the intervertebral region to occupy a larger volume.

  The tissue-related information is the mean HU value presented by the intervertebral space’s voxels and the sum of such HU values. Figure?18 shows the values obtained for each intervertebral space for healthy and pathological subjects. To combine geometrical and tissue information, the mean HU value and the sum of the HU value in the intervertebral space are evaluated in the function of the distance between the centroid of the relative two vertebrae. In Fig.?19, the mean HU value is more significant in distinguishing pathological cases from healthy subjects.

  Tissue and bone analysis

  From the analysis of the inner tissue of the vertebral body (Fig.?20), it can be observed that the patient data are below the healthy subject ones in the graph, especially when considering the sum of the HU values inside the ROI.

  Fig. 17figure 17

  With reference to the legend in Fig.?16, analysis of geometrical parameters of the intervertebral space

  Fig. 18figure 18

  Tissue information evaluation in the intervertebral space

  Fig. 19figure 19

  evaluated tissue information in the inter-vertebral space in relation to geometric information

  Fig. 20figure 20

  Behaviours of the vertebral body tissue

  Fig. 21figure 21

  Vertebral body geometrical parameters behaviour

  Fig. 22figure 22

  Vertebral body geometrical and tissue information

  Figure?21a shows how the ray of the spherical ROI behaves in the different segments of the vertebra, and Fig.?21b shows the whole vertebral volume changes moving from cervical to lumbar vertebrae. Both the ROI radius and the vertebral volume grow from the cervical to the lumbar segment, as expected from anatomical studies?(Mahadevan 2018). The patient data for the ROI ray graph are below the healthy subject’s data, coherent with hypotheses of bone erosion and morphological changes due to the pathology.

  The final comparison is between the geometrical and tissue information. Figure?22a shows the behaviour of the HU mean in the ROI region for a given ROI ray, while Fig.?22b provides the HU sum in the ROI for a given ROI ray. In this case, the best way to distinguish a patient from a healthy subject is through the HU mean in the function of the ROI ray. Indeed, the ROI extension and the values of the HU mean are lower for healthy subjects.

  The main files produced by all the methods are (i) the vertebral models stored in a structure containing each vertebra separately. (ii) The grey levels mapping consists of a map that associates to each vertex index the relative grey level, separating each vertebra from the other inside the structure. Each mapping criterion has its structure. (iii) The intervertebral space model consists of a structure containing each intervertebral space separately. Table?2 highlights the dimension of each output file.

  Developing Deep Learning and Machine Learning approaches to medical image analysis has improved Computer-Aided Diagnosis, even in vertebral fracture evaluations. However, it is widely known that this method requires a significant amount of data?(Loffler et?al. 2020a). The approaches presented in this work can be applied to a single image without requiring an extensive training data set. They can also be extended directly to other anatomical images, such as MRI. Compared to previous work focused on vertebral fracture identification, where the fracture search was limited to the bodies of the vertebrae?(Burns et?al. 2016), we expect our method to work also on other regions of the vertebra. Indeed, the method for vertebral segmentation focuses on more than just image intensities but also morphological evaluations.

  In the visualisation proposed, the 3D models are extracted directly from the volume image, and the 3D surfaces of the vertebrae will guide the visualisation of the image by localising the boundary of the bones inside the volume. Two-dimension CT slice evaluation gives a partial perspective on the subject, while our 3D patient-specific surface model allows us to observe the vertebral spine in every direction (Fig.?23). During the evaluation of the morphological characteristics of the patient, a complete visual experience is crucial. The possibility to extract every vertebra also helps to focus the analysis on a specific portion of the vertebral spine without loss in the quality of the representation. The augmented visualisation proposed in this work, showing the volume image and the 3D surface models, helps physicians develop accurate patient-specific evaluations. Moreover, it can guide the preoperative planning phase for surgical interventions, primarily when visualising both the vertebral bones and the intervertebral space (Fig.?23c).

  Table 2 Dimension of the main file resulting from the methods considering a subject where 20 vertebrae were scanned from the CT. The dimensions of the files refer to all 20 vertebraeFig. 23figure 23

  a 3D model visualisation from different point of view. b Single 2D slice visualisation. c Volume image visualisation through the superimposition of the 3D patient-specific models. In CT images, soft tissue is harder to distinguish by human eyes. Thus, the presence of the 3D surface model helps the physician in the localisation of the intervertebral space

  Studies focusing on supporting intervention planning are often specific to the procedure, such as?Knez et?al. (2019). Herefore, they do not provide a comprehensive characterisation of the spine but only the portion of the vertebra involved. At the same time, our work could evaluate the whole spine and segment each vertebra. Moreover, the method proposed in?Knez et?al. (2019) obtains an accurate 3D model by adjusting various parameters, while our patient-specific model can be extracted automatically. Our work provides generic measurements and morphological and tissue information for comprehensive and specific evaluation. Having both the 3D surface and the tissue information allows us to tailor further the measurements extracted from the 3D models and the textures to the physician or surgeon’s requirements.

  The results obtained through the combination of texture and geometrical information in the neighbourhood of the surface demonstrate that the tissue changes are highlighted both by exploring the volume inside the surface and by analysing the volume in the region outside the bone surface. Thus, these representations of combined information can highlight pathological cases or vertebrae that differentiate from the classical health distribution, making it a valuable tool for personalised and efficient analysis. In the internal mapping case, the clusters could be related to a varying percentage of cortical bone in the different vertebral components. The vertebral arch and processes have thicker coverings of cortical bone. The clusters identified in the external mapping results can be related to the tissue surrounding the vertebra from the outside. The ligament insertion distribution on the vertebral arch and body can explain the HU values between the Euclidean and external mapping results.

  The advantage of this approach is the use of both geometrical and texture information in a single analysis, contrary to what is applied in the literature where different works focus either on tissues?(Burns et?al. 2017) or geometrical analysis?(Anitha et?al. 2020; Laouissat et?al. 2018). According to the experimental validation, the geometrical and tissue analyses are coherent with what is expected from the anatomy and can help in the distinction between healthy and pathological subjects. Indeed, they could support physicians in evaluating the subject’s status. All the data representations proposed showed the potential to distinguish between healthy and pathological subjects from different perspectives. Instead of focusing on a particular segment of the spine such as in previous work?(Baum et?al. 2014), our approach is general enough to consider the whole spine or the single segment or even the single vertebra since it does not require any previous shape models templates. The evaluation of the tissues inside the vertebral body is commonly performed by considering a manually selected ROI on a 2D CT slice and computing the average HU value?(Lee et?al. 2013; Zou et?al. 2019; Kim et?al. 2019). The method proposed, instead, improves this practice since it considers a 3D ROI automatically computed and centred in the barycentre of the vertebral body.

  Commercially available tools for visualising and quantifying spine morphology exist. However, our work differentiates from them in a few ways. As an example, the syngo.via?bone reading provides a tool for labelling vertebrae but does not allow further segmentation of each vertebra in the main functional part or a comparison between morphological and tissue parameters. It also provides an interactive visualisation, but the images are shown as single 2D slices without superimposition of volume images and surfaces. The Mimics Innovation Suite from Materilise has great visualisation features and allows different measurements but requires the identification of landmarks. Our frameworks can extract geometric quantities without the user needing landmark identification.

  The main limitation of this work is the need for a segmented 3D image since the 3D model required for the development of the framework is extracted from the segmented 3D image. However, by leveraging deep learning methods, the segmentation can be obtained automatically with good accuracy and reviewed by experts, thus drastically reducing the time required by this operation. A partial limitation is the assumption of the subject’s posture. In our study, the CT images show the patient in a supine position with an effect of gravity lower than the standing posture. The 2D images used in clinical practice have the advantage of capturing the standing patient; thus, they show the spine behaviour under different loads. However, all the proposed methods are general enough to be applied to different imaging modalities and further characterise the subjects’ standing modality.

  The framework for the patient-specific characterisation of the vertebral spine works on 3D surface models. It permits the evaluation of each patient’s health status by analysing the spine in terms of anatomical components, functional regions, and tissue status. In this way, the visualisation of the single bone and the whole district is improved. The quantitative analysis relies on the information collected considering every direction in space, which is impossible with 2D images. The framework brings and elaborates information based on the analysis of geometrical features, such as the volume of each vertebra or the radius of the ROI contained in the vertebral body and the tissue information retrieved from the original CT image of the single patient. This information is obtained by navigating the volume of the image and taking as references the surface of the vertebral models and the barycentre of the vertebral body. The framework has the potential to be applied in different fields of clinical practice, from computer-aided diagnosis to surgical intervention support and planning. Indeed, both the structure and the methods avoid the focus on a single application but are meant for multi-purpose analysis and support. The generality of the methods and the absence of parameter settings or landmark identification make the framework customisable for further geometrical or tissue-related measurements.

  Future work will be focused on (i) the improvement of the spine characterisations while keeping a clinical application perspective and (ii) the localisation of posture landmarks, such as spinous processes, and their visualisation on the skin, which could provide an external reference point for physicians and surgeons during their posture evaluations. Visualising the landmarks on the patient’s skin could also lead to integration with 3D sensors’ data for posture analysis and rehabilitation applications. To further extend the geometric and tissue evaluation, the analysis of the vertebral foramina could be improved with other geometrical parameters and image pre-processing or enhancement techniques.

  ccDownload:/content/pdf/10.1007/s42600-023-00300-z.pdf

 
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