Computer-implemented methods for the simulation of at least a part of a spine

Abstract

The invention relates to a computer-implemented method for the simulation of at least a part of a spine, comprising the steps: executing of an image segmentation on at least one image, particularly from medical sectional imaging such as a CT and / or an MR image, of at least a part of the spine, for obtaining a segmentation mask; deriving of one or more vertebral body geometr(y / ies) and / or intervertebral disc geometr(y / ies) as a surface mesh from the segmentation mask; processing, in particular smoothing, of the surface mesh of the vertebral body geometry and / or the intervertebral disc geometry; filling of a volume being enveloped by the surface mesh; and generating of a finite element method model, also referred to as FEM model, from the volume; wherein, prior to smoothing, extracting of contact nodes is conducted, wherein the contact nodes are nodes of the surface mesh, which are adjacent to or in contact with nodes of a further surface mesh of another adjacent element of the part of the spine, in particular of an adjacent intervertebral disc and / or an adjacent vertebral body, for the modeling of contact points of the vertebral body geometry and / or the intervertebral disc geometry.

Description

[0001] fl HOEFER & PARTNER TUM251201PCT 19.12.2025

[0002] Applicant:

[0003] Technische Universitat Munchen, in Vertretung des Freistaates Bayern

[0004] Arcisstr. 21

[0005] 80333 Munchen

[0006] Computer-Implemented Methods for the Simulation of at Least a Part of a Spine

[0007] Field of the Invention

[0008] The invention relates to computer-implemented methods for the simulation of at least a part of a spine.

[0009] Background of the Invention

[0010] Till today, the reasons for back pain are understood only to a limited extent. The plurality of factors of influence and the inter-individual biological variability complicate epidemiological investigations of pain and degenerative changes of the spine. Besides psychological or social factors, it is assumed that biomechanical factors contribute to the patient's pain situation. These factors, among others, include the weight of the upper part of the body or the curvature of the spine, along with the loads on various structures of the spine resulting from these factors. So, for example, the mechanisms of the degeneration and ruptures of intervertebral discs, as they occur in the case of herniated vertebral discs, as a subfield of biomechanics, are still not fully understood. Here, experimental studies under laboratory conditions provide valuable insights. In vitro studies help us to understand the passive properties of biological structures; however, they cannot illustrate the conditions in the living object. In vivo studies allow such an insight, but, however, due to their invasive character, they cannot be used for large cohorts. Computer simulations allow a non-invasive insight into the biomechanical situation of the spine. Here, concretely, two methods can be distinguished: the multibody simulation (MBS) and the finite element method (FEM). In the first case, mechanical systems, such as the spine, are represented and investigated by concatenating rigid bodies through joints. In this way, on a macroscopic level, for example, the forces in the joints of the spine can be calculated, and also the effects of individual boundary conditions, such as, for example, concrete kinematics, on the occurring loading can be analyzed. In these models, flexible elements such as intervertebral discs are only considered as bodiless force elements, which consider the effects on the mechanics of the total system, but do not allow a statement about local deformationsand inner stress conditions within these elements. For such analyses, normally, FEM is used, in which flexible bodies are represented in detail as volume models, but it is restricted to the analysis of single components rather than the holistic perspective of an MBS analysis. The combination of MBS and FEM enables the analysis of mechanisms with respect to wear, through to the failure of biological structures, considering the mechanics of the total system. Scientific studies show that individual characteristics of the spine, such as anatomy or bone density, are crucial in computer simulations, and their integration into the respective models is indispensable. For identifying relationships between pathologies and pains, a large amount of data is required. As of late, the German National Cohort provides this opportunity.

[0011] Recent developments in the field of artificial intelligence enable the automated segmentation of CT and MRI scans - a crucial factor in analyzing large cohorts. For finding out correlations between biomechanical factors and pains, and pathologies, respectively, also in the field of computer simulation of MBS and FEM models, a certain degree of automation has to be achieved.

[0012] The different technologies that are used in the field of spine operations or for the analysis of back pains include, for example, Stryker SpineMap, SurgiCase, MedCAD, Brainlab, and Vuze. These tools either use biomechanical simulations or are merely based on 3D models from segmentations.

[0013] Stryker SpineMap is focused on preoperative planning and intraoperative navigation. Here, the system primarily utilizes 3D models derived from image segmentations to display anatomical structures and plan screw positionings or implants. Here, biomechanical simulations are not so important because the main target is the precise positioning on the basis of the anatomical data. SurgiCase from Materialise also provides 3D models from segmentations, which are used for the individual planning of operations. Although SurgiCase provides patient-specific models and adjusted implants, it focuses primarily on the geometry and adjustment of surgical tools, and only to a lesser extent on simulating biomechanical forces or reactions. MedCAD, a specialized tool for custom-tailored implants and surgical guides, primarily works with 3D models derived from segmentations. Here, the top priority is the exact reproduction of anatomical structures and the adjustment of implants. Here, biomechanical simulations are not normally used; the emphasis is, in fact, on the geometrical fit. Brainlab, however, may use biomechanical simulations to a certain extent, since the system processes complex intraoperative image data and provides detailed anatomical visualizations. While the main focus is on imaging and navigation, the system may consider biomechanical aspects, for e.g., assessing the stability of screw positionings or implants. Nevertheless, the main focus is primarily on the exact imaging and only to a lesser extent on the simulation of biomechanical interactions. Vuze, as an augmented reality platform, primarily utilizes 3D models derived fromsegmentations to project real-time anatomical structures during operations. Here, the focus is clearly on the visualization and the improvement of the surgical precision, while biomechanical simulations do not play an important role. In summary, it can be said that in most of these tools, primarily 3D models on the basis of segmentations are used. Biomechanical simulations are used, if at all, only to a very small extent, and primarily they are used for a better geometrical adjustment or for supporting the navigation.

[0014] Agada Medical, as an upcoming company, provides products and services for improving the surgical planning and conduct of spine operations. This includes highly sophisticated imaging software for preoperative planning, surgical planning tools for the individual adjustment to the anatomical conditions of the patients, and simulation technologies analyzing the effects of different treatment approaches. In addition, they develop individualized implants that are optimally adapted to the biomechanics of the spine, and they research the diagnosis and treatment of spine diseases.

[0015] Existing software for the modeling and simulation of multibody models comprises, inter alia, commercial software such as Anybody, ADAMS, or Simpack. In the context of scientific work, the open-source software OpenSim is in wide use and provides a large repertoire of freely available generic models that can be scaled in a patient-specific manner. Normally, these models are based on the data set of a single individual, and they are not directly derived from image data. So, the individualization is only based on a few predefined parameters. Thus, characteristics apart from these parameters (such as individual geometries of the vertebrae or the intervertebral disc) are not considered. For the modeling and simulation of biomechanical models with the FEM, scientists often use commercial software such as Abaqus and Ansys, or open-source software such as FEBio. In the case of co-simulations, which combine MBS and FEM commercial solutions, such as Abaqus / Simpack, ArtiSynth serves as an open-source alternative.

[0016] There are various scientific papers about the automated segmentation and / or analysis of MR data of the spine [1, 2], However, in these papers, the processing of image data into numerical models is not described, and therefore, they are not suitable for analyzing individual spine biomechanics.

[0017] In the year 2021, Caprara et al. published a paper about a pipeline for the automated generation of FE models of a movement segment of the spine based on CT data [3], One year later, our research group has published a similar paper, however, with a focus on the automated generation of highly individualized multibody models of the torso based on CT data [4], A few months ago, Munoz-Moya et al. published a paper about the automated generation of patient-specific FE models of intervertebral discs by means of morphing [5],Recently, comprehensive reviews on the current state of research have been published by Knapik et al. [6], Lerchl et al. [7], and Nispel et al. [8], Nothing has been published relating to the completely automated generation and simulation of patient-specific MBS and FE models of the spine that are suitable for coupling based on segmentation masks from medical imaging.

[0018] Summary

[0019] The object of the invention is to provide a computer-implemented method for the simulation of at least a part of a spine, which is able to model and / or simulate spines of different individuals with high accuracy in a particularly simple and fully automated manner. It is, in particular, the object of the invention to analyze for potential users the possibility of macroscopic loading patterns (MBS) and detailed stress conditions (FEM), wherein both are supported by the respective other one, and thus, a more comprehensive picture of the individual spinal mechanics is provided.

[0020] These objects are solved by the features of the independent claims. The dependent claims concern advantageous embodiments of the invention.

[0021] In the following, embodiments of the invention according to the claims are explained in detail: In the present sense, the term “processing of the surface mesh” comprises, in particular, “smoothing” such as described below. In an alternative or in addition to “smoothing” for “processing”, in the present sense, Al-based super-resolution techniques can be used, or other filters can be used, which compensate image-specific parameters such as, e.g., a limited resolution and / or noise.

[0022] Further details, advantages, and features of the preferred embodiments of the present invention are described in detail with reference to the figures. Therein:

[0023] Brief Description of the Drawings

[0024] Fig. 1 shows a data flowchart according to an embodiment of the present invention.

[0025] Fig. 2 shows pictures of A) MRI scan, B) Automatically generated segmentation of one image plane of the MRI scan, C) 3D model from the segmentations of the single bodies, D) MBS model of the spine, based on the segmentation data, E) Combined MBS & FEM model for the detailed simulation of the patient-specific spine biomechanics according to an embodiment of the present invention;

[0026] Fig. 3 shows pictures of the Process of smoothing of vertebral bodies and intervertebral discs (left and middle), including FEM simulation result (right), according to an embodiment of the present invention;Fig. 4 shows visualized processing steps in the presented pipeline according to an embodiment of the present invention.

[0027] Fig. 5 shows pictures of (A) Solid vertebra and adjacent intervertebral disc displayed as a grid mesh, and (B) with respective, selected interface nodes of the intervertebral disc model highlighted according to an embodiment of the present invention;

[0028] Fig. 6 shows mesh statistics for the generated vertebrae (A) and intervertebral disc FEM meshes (B) according to an embodiment of the present invention.

[0029] Fig. 7 shows statistical evaluation of the duration for the different parts of the pipeline when processing a single subject, displayed in a box plot, according to an embodiment of the present invention.

[0030] Fig. 8 shows pictures of CT (left) vs. MRI (right) scan of the same subject, wherein characteristic bone structures are represented in the CT;

[0031] Fig. 9 shows pictures of an exemplary smoothing process of an intervertebral disc mesh, wherein from left to right: Raw, preprocessed, adaptively smoothed, and postprocessed mesh, and wherein interface vertices of the intervertebral disc are marked in black in the preprocessed mesh, according to an embodiment of the present invention;

[0032] Fig. 10 shows pictures of mean curvature calculated with the quadric fitting method according to an embodiment of the present invention;

[0033] Fig. 11 shows pictures of the shared-nodes contact surface of an exemplary vertebra, and intervertebral disc, wherein intervertebral disc nodes are represented as turquoise squares, and vertebra nodes are represented as green dots, according to an embodiment of the present invention;

[0034] Fig. 12 shows pictures of comparison of selective smoothing results (top row in green) and conventional smoothing, represented by 10 iterations of HC Laplace (bottom row in red), wherein the wireframe views display the unsmoothed version, while the face views display the differentially smoothed versions, according to an embodiment of the present invention;

[0035] Fig. 13 pictures of notch stress in FEM models derived from a conventional smoothing algorithm (10 iterations HC Laplace) and our selective smoothing pipeline, wherein starting from a raw mesh, smoothed meshes are created and converted into FEM models using an automated pipeline, and a section view on the right visualizes the stress in the respective models, wherein it is noted that the stress scale limit has been adapted for this view due to visualization reasons;

[0036] Fig. 14 shows pictures of a morphing process according to an embodiment of the present invention, wherein top: structured FEM mesh incl. validated material parameters (= sourcemesh), middle: affine deformation of the source mesh, and Bottom: surface mesh of the intervertebral disc originating from the MRI of the patient;

[0037] Fig. 15 shows a data flowchart according to an embodiment of the present invention.

[0038] Fig. 16 shows pictures of results from a pipeline based on the embodiment of Fig. 15 showing details of the morphing pipeline used to create individualized FEM models with surface mesh derived point clouds shown on the top line and volume mesh derived point clouds shown on the bottom, wherein (a) Point clouds of TM (blue) and SM (yellow) with an initial, large distance in space; (b) Rigid registration result of TM and SM point clouds; (c) Affine registered TM point cloud (orange) and (d) non-rigidly registered point cloud using the CPD algorithm (red); (e) SM point cloud split into surface points and inner volume points, (f) Affine-transformed SM nodes using the transformation matrix from the respective surface mesh registration step; (g) Arrows indicate the displacement necessary for each node to achieve the TM shape; Vectors were calculated from the step (c-d);

[0039] Fig. 17 shows an overview of the methodology used to create patient-specific intervertebral disc models according to the embodiment of Figs. 15 and 16, wherein (a) Segmentation as SPINEPS creates it [2] and (b) afterthe inclusion of endplates into the intervertebral disc labels; (c) Raw surface mesh of an exemplary intervertebral disc, derived by the marching cubes algorithm; (d) Smoothed surface mesh using our smoothing approach (embodiment of Figs. 8 - 13), advanced by an additional segmentation smoothing step, this stage serves as a target mesh (TM) for the morphing; (e) Final, individualized FEM intervertebral disc model, which was created by morphing the (f) calibrated, hyperelastic HGO source mesh (SM)

[0024] into the TM’s; Individualized models were simulated with four load cases to derive a displacement distribution; and

[0040] Fig. 18 shows example models of a modification of the embodiment of Figs. 15 - 17, showing example models for degeneration grades 1 (a), 3 (b), and 5 (c).

[0041] Description of the Embodiments

[0042] Mode of operation and structure of the invention:

[0043] The invention implements a method for the generation of highly individualized MBS & FEM models, being suitable for coupling based on segmentation masks from medical imaging (figures 1 & 2).

[0044] See Figure 1, which shows a data flowchart. From the MRI segmentation mask (left), both functioning FEM models of the intervertebral disc and the vertebral bodies ( top) and finished MBS models (bottom) are generated. The combination of elements of both simulation modelsis realized in the form of a co-simulation (bottom, right) from which again statistical correlations between pathologies and pains, therapies, or operation techniques can be derived.

[0045] See figure 2, which shows:

[0046] A) MRI scan. B) Automatically generated segmentation of one image plane of the MRI scan. C) 3D model from the segmentations of the single bodies. Data of this kind are used, inter alia, by Stryker SpineMap, SurgiCase, and MedCAD. D) MBS model of the spine, based on the segmentation data. E) Combined MBS & FEM model for the detailed simulation of the patientspecific spine biomechanics.

[0047] Embodiments of the invention comprise:

[0048] 1. Automated MBS modeling (figure 2D). The individualization degree can be adjusted according to the requirements, and it depends on the present segmentation masks. Here, missing bodies are automatically replaced by generic bodies, which are scaled respectively. For this:

[0049] a. Deriving the vertebral body geometries as a surface mesh from the segmentation masks (figure 2B-C).

[0050] b. Generating the kinematic chain based on defined coordinates for intervertebral joints. Missing bodies can be replaced by generic bodies, which are scaled to the dimensions in the present case.

[0051] c. Modeling of the weight of the torso via user-defined segment masses with respective gravity centers per spinal level, with rigid connection to the respective vertebra.

[0052] d. Adding of passive components (intervertebral discs, ligaments) as non-linear viscoelastic force elements based on literature data.

[0053] e. Adding detailed back musculature based on literature data.

[0054] 2. MBS simulation (Figure 2D): Determining the muscle activity and the resulting spinal loadings for the biomechanical analysis of the torso in view of factors of influence and risk for potential overloading, as well as for the definition of the required boundary conditions for FEM simulations, involving patient-specific mechanics of the whole torso. For this:

[0055] a. Determining the muscle activity by a combination of inverse dynamics and static optimization. In the case of inverse-dynamical simulations, the kinematics of the system is preset, and a back calculation to the underlying forces and moments is conducted. Musculoskeletal systems, however, are overdetermined, thus have more control elements(muscles) than degrees of freedom, which makes it impossible to unambiguously determine the required forces. For this reason, normally, such approaches are combined with optimization algorithms. This mathematical process determines from an infinitely large solution space the optimum solution for a specific problem in compliance with defined criteria and boundary conditions. In the context of biomechanical models in everyday scenarios, an often-used criterion is the minimization of the cubic muscle tension, which punishes high muscle tension and prefers low muscle tension, and thus supports an activation pattern that is designed for stamina. According to the simulated case of load, the selection of alternative optimization criteria (for example, metabolic energy consumption) is possible.

[0056] b. Determining the resulting occurring forces and moments in intervertebral joints as well as in ligaments and intervertebral discs.

[0057] See figure 3, which shows:

[0058] Process of the smoothing of vertebral bodies and intervertebral discs (left and middle), including FEM simulation result (right). On the top right, figure 3 shows a vertebral body, and on the bottom right, figure 3 shows an intervertebral disc.

[0059] 3. Automated FEM modeling of the vertebral bodies and intervertebral discs. For this: a. Deriving the geometries of the vertebral bodies and intervertebral discs as a triangulated surface mesh from the segmentation.

[0060] b. Smoothing of the vertebral bodies (figure 3). For maintaining the edges and specific characteristics of the vertebral bodies in spite of smoothing, a proprietary smoothing process has been developed. This algorithm calculates the contact area from the scan to adjacent intervertebral discs and selectively smoothens this area. In this way, biofidelic models can be generated, also from scans with low resolution, and, at the same time, a homogeneous distribution of the contact force on the whole end plate can be guaranteed.

[0061] c. Adaptive smoothing of the intervertebral disc models. In this step, a special focus is on the modeling of the contact areas, which is relevant due to two reasons: On the one hand, the modeling of the contact area is a challenge for FEM, and, on the other hand, the coincidence of the nodes of the adjacent surface meshes is an advantage for later coupled simulations of MBS and FEM. Our software guarantees the coincidence of the node points of the meshes of the vertebral bodies and intervertebral discs, apart from a little tolerance.

[0062] d. Converting the surface meshes into volume. We use FreeCAD, a classical open-source CAD software with a Python interface, for the generation of solids from surface meshes. Thebasis for this approach is the area reconstruction. The volume models of the intervertebral discs and vertebral bodies are stored in the step format for each.

[0063] e. Interlinking of the volume models. Classical FEM models consist of nodes and elements connecting these nodes. The step files generated in the step above are imported into an FEM software, and there they are adopted with tetrahedron elements unchanged as parts of the tetrahedron. As a result, FEM bodies consisting of nodes and elements are created, which can be used in all relevant software. Owing to the equivalent node positions between surface and volume meshes, the contact nodes are defined in step b. between the vertebral body and the intervertebral disc are integrated as a node set in the FEM model. In addition, a reference node at the upper and lower end plates of the intervertebral disc is defined, which allows the later definition of constraints in a simple and automated manner.

[0064] 4. FEM simulation for determining local deformation and stress conditions in vertebrae and intervertebral discs. For this:

[0065] a. Definition of the simulation parameters. As a further step, the FEM bodies are supplemented with simulation-specific parameters such as load, boundary conditions, constraints, and material. The basis for this is a specifically developed proprietary code that reads and adapts the FEM files. The loading is directly extracted from the corresponding MBS model (Figure 2D), and, therefore, it represents a realistic total load.

[0066] b. Executing the simulations (Figure 2E). By means of a batch file created during the process, it is possible to transfer the simulation files directly to the FEM software, so that an automated simulation of individual vertebral bodies and intervertebral discs is made possible. See also the right column of Fig. 3, which shows exemplary deformation / stress from FEM simulation similar to what is shown in Fig. 2E.

[0067] The invention according to special embodiments functions with both CT and MR images originating from clinical routine, even with such ones that only contain parts of the spine. Based on our automated segmentation pipeline, it provides an individual numerical model that combines the advantages of the MBS and the FEM.

[0068] In contrast thereto, current solutions of industry leaders such as Stryker or Brainlab are only focused on a better visualization of the classical operation planning, and so, here, they neglect any biomechanical information. Other start-ups such as “Moving Spine” already integrate local FEM in their planning approach. In contrast to our software, no existing approach considers the individual distribution of the body weight and the alignment of the spine, although both parameters have been shown to be important for the success of the operation. For the first time, it is possible to conduct biomechanical analyses of the spine with the help ofsegmentation data from imaging in a completely automated manner. Here, for the first time, the detailed stress conditions in the single components (FEM) in interaction with the total mechanics of the torso (MBS) are calculated.

[0069] - Combination of the patient-specific MBS models with the corresponding FEM models as an automated process

[0070] • on the basis of segmentations

[0071] • for the completely automated calculation of spinal patterns of loading on joints and intervertebral discs (MBS) and

[0072] • for the completely automated calculation of deformation and stress conditions in vertebrae and intervertebral discs (FEM) [drawing MBS & FEM Patrick]

[0073] Advantages and Improvements

[0074] Other approaches for the biomechanical analysis of back pain (I), for planning therapies (II), and for conducting operations (III) often require several days of intensive manual work. Our invention revolutionizes this process by coupling MBS and FEM in one automated cosimulation workflow. So, holistic loading analyses (MBS) are combined with detailed structural investigations (FEM). In contrast to tools such as SurgiCase or Stryker SpineMap, which only provide 3D visualizations without consideration of loadings or deformations, our invention results in a comprehensive biomechanical presentation of the spine. This is even true for MRI or CT images, which only show parts of the spine. While the term “individualized” is often used for the description of personalized approaches, a lot of solutions turn out to be insufficient. For example, MBS models are mostly focused on specific pathologies, such as scoliosis, or they scale generic spine models based on CTs of the patient, wherein the patient-specific bone geometry and body weight distribution are not sufficiently considered. FEM models are often based on standardized intervertebral disc drafts, which, with the help of morphing, are adjusted to images of patients. In such cases, intervertebral disc geometries are only roughly transferred into the underlying patient-specific geometry with the aid of single orientation points. This method is stretched to its limits when complex geometries need to be presented, such as when intervertebral discs are strongly degenerated. Our invention is the only approach that is based directly on the full torso and intervertebral disc segmentationintervertebral disc. In our approach, intervertebral disc models are prepared directly from the segmentation masks, and so, here, all details of the structure are considered for FEM analysis. In addition, our invention allows (II) the simulation of conservative treatment methods as well as (III) the prediction of surgical results, such as stabilization by segment stiffening with MBS. In this way, the risk of possible complications such as subsequent segment degeneration can be estimated andreduced by analyzing alternative treatment strategies. With these improvements, clinicians are provided with valuable findings, and a truly individualized treatment becomes possible, which in turn guarantees better results for patients. We assume that this combination allows a more realistic analysis of the conditions than previous approaches.

[0075] Up to now, there are no FEM models of intervertebral discs or vertebral bodies that are prepared and simulated on the basis of individual segmentation masks and, at the same time, consider patient-specific boundary conditions of the MBS.

[0076] With respect to the methodology, the kind of coupling between MBS and FEM can be realized in two different ways: unidirectional and bidirectional. Unidirectional models only forward the forces that are calculated in the MBS to the FEM model. Bidirectionally coupling models exchange results in each iteration step, thus in each solution step of the solver (MBS & FEM solver). Here, the results are the forces and the deformations. In our invention, we do not define a specific kind of coupling, but we see the content of the coupling as innovation. From the MBS model, a loading by the forces and / or deformation is applied to the FEM model or vice versa. Here, not only forces are exchanged, but also deformations. In particular, always, one simulation is responsible for one part, and then the other simulation is responsible for the other part. Thus, e.g., MBS calculates forces, FEM calculates the deformation with these forces, this is forwarded to the MBS, which then again calculates the updated forces, and so on, and then all of this can also be realized the other way round.

[0077] With regard to content, the coupling in our invention in the first instance means that we examine macroscopic loads (it is better to calculate them with MBS; for this, numerically speaking, an FEM model would be too expensive) with analyses on the level of detail (FEM deformations and stress conditions in the body). Generally, normal FEM models of the intervertebral discs from literature are NOT calculated with patient-specific loads, but with generic loads. By the MBS, we achieve, for example, much more precise, individualized loads on the intervertebral discs.

[0078] In addition, by the derivation of both the MBS and the FEM components from one single segmentation, the anatomically correct contact areas between, for example, the vertebral body and the intervertebral disc can be defined.

[0079] For the first time, our invention allows biomechanical analyses also for persons who do not have relevant experience in the field of modeling and simulation (e.g., medical staff). By the enormous saving of time, when biomechanical simulations of patient-specific data are conducted in an automated manner, for the first time, it is possible to simulate large cohorts. This allows a statistical analysis of correlations between biomechanical parameters and pathologies.

[0080] In summary, the invention compared to other solutions is:• highly individualizable, including bone and intervertebral disc geometries, spinal alignment, body mass distribution, and individual anatomy.

[0081] • a completely automated solution for users without any expert knowledge in calculation and mechanics, which can be operated easily.

[0082] • a holistic presentation of loading and alignment with a detailed analysis of deformation and loading by coupling of MBS and FEM simulations.

[0083] • based on large cohort studies, which consider statistical relationships between pathologies and simulation results.

[0084] • interpretable by a readily understandable visualization of spine forces and resultant probabilities for pain and implant failure.

[0085] • adjustable by the use of existing input values of standard MR and CT images, wherein data are generically completed, when images are only partially available.

[0086] • reproducible in its result, and thus, a reduction of distortions due to subjective interpretations.

[0087] Uses

[0088] The invention allows the individual analysis of the spine biomechanics in research and in daily clinical routine.

[0089] The relationship between back pain and biomechanical parameters from numerical simulations of large data sets results in a better understanding of back pain.

[0090] Furthermore, our patient-specific models provide the basis for the design of individual implants. By variations in the design, it is possible to adjust mechanical parameters such as, for example, stiffnesses of the implant, to comply with the specific situation of the patient. An exact replication of the biomechanical starting situation by an implant can avoid subsequent degeneration and can considerably increase the function as well as the service life of the implant.

[0091] Further details and examples of the invention are described with reference to an embodiment of Figs. 4 to 7 as follows:

[0092] Introduction: Biomechanical simulations can enhance our understanding of spinal disorders. Applied to large cohorts, they can reveal complex mechanisms beyond conventional imaging. Therefore, automating the patient-specific modeling process is essential.Methods: We developed an automated and robust pipeline that generates and simulates biofidelic vertebrae and intervertebral disc finite element method (FEM) models based on automated magnetic resonance imaging (MRI) segmentations. In a first step, anatomically constrained smoothing approaches were implemented to ensure seamless contact surfaces between vertebrae and discs with shared nodes. Subsequently, surface meshes were filled isotropically with tetrahedral elements. Lastly, simulations were executed. The performance of our pipeline was evaluated using a set of 30 patients from an in-house dataset that comprised an overall of 637 vertebrae and 600 intervertebral discs. We rated mesh quality metrics and processing times.

[0093] Results: With an average number of 21 vertebrae and 20 intervertebral discs per subject, the average processing time was 4.4 min for a vertebra and 31s for an intervertebral disc. The average percentage of poor quality elements stayed below 2% in all generated FEM models, measured by their aspect ratio. Ten vertebrae and seven intervertebral disc FE simulations failed to converge.

[0094] Discussion: The main goal of our work was to automate the modeling and FEM simulation of both patient-specific vertebrae and intervertebral discs with shared-node surfaces directly from MRI segmentations. The biofidelity, robustness, and time-efficacy of our pipeline mark an important step towards investigating large patient cohorts for statistically relevant, biomechanical insight.

[0095] Fig. 1 shows the f chart of the developed pipeline, starting at the MRI scan (not shown), in particular, an MRI segmentation mask from image segmentation of the MRI scan, and resulting in FEM models (intervertebral disc FEM model and Vert FEM model) of the patients’ intervertebral discs and vertebrae. In between, the following substeps are carried out: two distinct smoothing algorithms, surface mesh filling, volume meshing, and the inclusion of interface nodes in implementing an FEM model of the vertebra and intervertebral disc, respectively.

[0096] Addressing the need for automated approaches to realize large dataset investigations, the following presents the first pipeline to create and simulate patient-specific FEM models of vertebrae and intervertebral discs with shared-node contact surfaces from MRI segmentations in a completely automated manner. Note that the focus here is on methodological development, particularly in automating model creation. As such, complex material models or biologically related parameters, such as varying loading conditions or patient-specific weights, are deliberately excluded herein. The FEM simulation presented here serves solely to verify that the pipeline produces models capable of converging under simplified conditions, laying the groundwork for future biological model validation.Methods

[0097] We implemented an automated pipeline that takes segmented MRI images of the spine as input and provides FEM simulation results as output (Figure 1, MRI Segmentation Mask to intervertebral disc FEM model & Vert FEM model). All steps were automated using Python as a baseline programming language. We used an in-house dataset that included 30 patients. The data contains MRI images of a 1 x 1 mm resolution in the sagittal plane and a 2.5-3.5 mm slice thickness. The implemented pipeline can broadly be divided into the following substeps: Generation of surface meshes from MRI segmentations, smoothing, mesh filling, volume meshing, FEM modeling, and FEM simulation (Figure 4). FE models can be used in a plug-and-play manner to simulate either single bodies, functional spinal units (FSU), or complete spine models. To demonstrate the functionality of the FEM models, we included the automated execution of FEM simulations as the final substep. Therefore, we defined an exemplary load and material model. Note that this work focused on the automation aspect, and the resulting FEM stresses and displacements were not interpreted biomechanically. Given that a manual approach would not significantly affect the key pipeline steps - mesh smoothing, volume body creation, or FEM meshing - and that the manual process is highly user-dependent, making precise time comparisons challenging, we chose not to include a traditional manual control group in this study. In what follows, we present a detailed description of the substeps.

[0098] MRI to surface mesh

[0099] The MRI image segmentation masks were created using SPIN EPS, an open-source deep learning approach. Refer to Moeller et al. for details on the segmentation approach (Moeller et al., 2024)

[0038] , In brief, the network segments 14 spinal structures, including vertebrae and intervertebral discs, with a dice score above 0.9, respectively. The resulting segmentation masks are visualized in Figures 2B, C. The masks were subsequently edited by removing partial volume segmentations, which were classified by a threshold number of four linked voxels. Segmented partial volumes often lead to sharp edges in the derived surface meshes during smoothing. In vertebrae and intervertebral discs, they were identified by their voxel volume and subsequently removed.

[0100] To convert the segmented geometries into a surface mesh, we applied the marching cubes algorithm (van der Walt et al., 2014)

[0053] with an ascending gradient direction and a step size of 1. Note that for the scope herein, we considered the segmented endplates to be part of the intervertebral discs by combining their labels during the application of the marching cubes algorithm. As a result, we gained a triangulated mesh of each vertebra and intervertebral disc. The resulting meshes of two vertebrae and one intervertebral disc (FSU T10-T11) areexemplary shown from the transverse and sagittal view, as well as in an isoparametric angle in Figure 4.

[0101] Figure 4 shows the visualized processing steps in the presented pipeline. (A) Exemplary MRI scan. (B) Segmentation derived from the SPINEPS network (Moeller et al., 2024). (C) 3D representation of the segmentation, including a highlighted FSU to demonstrate the initial surface mesh result (D), the smoothed surface meshes (E), and the FEM results of the vertebra (F) and intervertebral disc (G).

[0102] Smoothing

[0103] To eliminate inaccuracies such as stair steps, we applied anatomically constrained smoothing algorithms to the surface meshes of vertebrae and intervertebral discs. Vertebrae were smoothed with a focus on preserving anatomical edges and geometrical characteristics like osteophytes. Shared-node contact surfaces of adjacent vertebrae and intervertebral discs were realized by adaptively smoothing intervertebral discs in a subsequent step. However, both approaches can be divided into three parts: preprocessing, main smoothing, and postprocessing.

[0104] For vertebrae, preprocessing consisted of mesh repairing steps such as closing holes and concatenating nodes, which were executed using the trimesh Python package. Those steps were required due to inaccuracies in the marching cubes algorithm.

[0105] For the selective smoothing step, the mesh vertices of the vertebra were compared to the mesh vertices of the two adjacent intervertebral discs to determine those located on the contact surface, which we here refer to as interface vertices. Contact was assumed for distances below a certain threshold, which was iteratively defined by optical observation. Thresholds ranged between 0.6 and 0.8, depending on the spinal level.

[0106] Subsequently, selected interface vertices of the vertebra mesh were smoothed separately using the Laplacian smoothing algorithm (Sorkine, 2005)

[0050] , The smoothed selected vertices are returned to the vertebra mesh before the Taubin smoothing algorithm (Taubin, 1995)

[0052] was applied to the whole vertebra mesh in a post-processing step using PyMeshLab (Cignoni et al., 2008)

[0016] , Refer to the next embodiment and Figs. 8 to 13 for detailed information on the development process and the performance of the smoothing protocol.

[0107] For the intervertebral discs, preprocessing included Taubin smoothing, Laplace smoothing, and mesh repairing steps, which were equal to the ones applied to the vertebrae meshes mentioned above. A final dilation step was included to compensate for the volume loss that typically occurs when using Laplace smoothing filters. The subsequent adaptive smoothing process was aimed at positioning the vertices of the intervertebral disc contact surface equivalently to the vertebrae vertices of the contact surface. Simultaneously with the selectivesmoothing, interface vertices of the intervertebral disc were determined using the smoothed, adjacent vertebrae meshes and the above-mentioned distance thresholds. Each interface vertex in the intervertebral disc mesh was then replaced with the respective nearest vertex of the adjacent vertebra mesh. Arisen edges at the borders of the contact area were smoothed in a postprocessing step, which consisted of a Taubin filter and mesh repairing functions. Figure 4E visualizes the final smoothing results for the exemplary FSU.

[0108] Note that through this approach, the selected interface vertices represented the anatomical contact surfaces in both intervertebral discs and vertebrae (Figure 5).

[0109] Mesh filling

[0110] To convert the surface meshes into solid volumes, we applied a surface reconstruction algorithm that transformed the vertices and faces of the triangulated mesh to a continuous surface using the FreeCAD Python interface (Riegel et al., 2024)

[0047] , During this step, a CAD file was created from the meshes. Subsequently, reconstructed surfaces were converted into solid models. In this solid representation, the coordinates of the surface mesh vertices were retained. This step was carried out equivalently for vertebrae and intervertebral discs.

[0111] Figure 5 shows (A) a Gray, solid vertebra and adjacent intervertebral disc displayed as a (turquoise) grid mesh. (B) The respective selected interface nodes of the intervertebral disc model are highlighted. A section without interface points at the left side of the intervertebral disc indicates that the adjacent vertebra is not in contact with the disc in this area. The remaining stair-step artifacts are still included in the non-contact areas of the model due to the limited spatial resolution of the MR image dataset in the left-right direction.

[0112] Volume meshing

[0113] The resulting solid CAD geometries were subsequently processed using the ABAQLIS Python interface. Two equal subprocesses, one for the vertebrae and one for the intervertebral discs, were carried out. The subprocesses primarily involved the consecutive, homogeneous meshing of the generated CAD geometries. We used tetrahedral elements (C3D10), as they are able to represent the vertex positions of the initial surface mesh. Geometries were seeded with a global seed size of 1 mm, along with a deviation factor and a minimum element size, both set to 0.1 mm. The created, meshed part was stored in an ABAQLIS input file, including the name of the respective vertebra or intervertebral disc.

[0114] Volume mesh to FEM model

[0115] To accurately represent the anatomical loading situation within a simulation framework, the load should be distributed only among the nodes that are in contact with the adjacent body. To realize this, we included the definition of node sets in the generation of the FEM models. Eachpart, vertebra or intervertebral disc, therefore contained two node sets, one for the superior surface and one for the inferior surface, respectively. To define the node sets for the vertebrae, we first parsed the volume nodes that were generated in the volume meshing step. Note that the indices of the vertices changed during the conversion of the surface mesh to the volume mesh. Iterating through the interface nodes defined in the smoothing step allowed us to find the respective nodes in the volume mesh by a comparison of their rounded coordinates. The corresponding volume node indices were appended to the respective node set.

[0116] For both vertebrae and intervertebral discs, we additionally included two node sets containing one superior and one inferior reference node, respectively. The reference node was defined by averaging all surface nodes and determining the closest node to the resulting average. To finalize the simulation definition of the FEM parts, we implemented an automatic inclusion of the remaining simulation parameters, namely material parameters, boundary conditions, loading, and constraints.

[0117] For each standalone FEM model of either a vertebra or an intervertebral disc, a kinematic coupling constraint was implemented to create a rigid body at the superior surface. The coupled surface was defined using the superior surface node set, which represented the biological contact area of the vertebra or intervertebral disc and its respective adjacent intervertebral disc or vertebra. The reference node was taken from the previously defined reference node set. For all vertebrae and intervertebral discs, we simulated a flexion moment of 7.5 Nm (Dreischarf et al., 2014)

[0018] , The moment was applied to the reference node of the superior endplate surface. As a boundary condition, the inferior node set was restrained in all six degrees of freedom (DoF).

[0118] For this work, linear elastic, isotropic material parameters were calculated based on the literature, both for vertebrae (Bouzakis et al., 2004 [9]; Zhou et al., 2000

[0055] ; Bruno et al., 2014

[0010] and intervertebral discs (El Bojairami et al., 2020)

[0019] ,

[0119] To finalize the FEM simulations, we defined a static analysis and appended the simulation files as separate entities to a batch file for automatic execution. Simulation results were visually inspected.

[0120] Results and Advantages

[0121] We implemented a pipeline that is able to automatically calculate FEM results of vertebrae and intervertebral discs in large cohorts. The pipeline is based on an automated segmentation of vertebrae and intervertebral discs in MRI images (Moeller et al., 2024)

[0038] , From this, surface meshes were derived and selectively smoothed to mimic the biological endplate shapes, compensating for image resolution inaccuracies. Hereby, we take advantage of the MRIsegmentations by including both bone and soft tissue. Smoothed surface meshes were then automatically transformed to FEM volume meshes, which contain individual node sets of the superior and inferior contact surface to the adjacent vertebra or intervertebral disc, respectively. FEM models were available as a combination of nodes and elements. In our study, these models were supplemented with boundary conditions, loading, and material definition to create and simulate FEM models. Using this pipeline, we processed all 30 patient MRI scans, resulting in a total of 637 vertebrae FEM simulations and 600 intervertebral disc FEM simulations.

[0122] Mesh quality

[0123] Vertebrae and intervertebral disc meshes differed significantly in their numbers of nodes and elements (Table 1). On average, vertebrae meshes contained approximately 229.500 elements, 4.5 times more than the average intervertebral disc mesh.

[0124] TABLE 1 Number of nodes and elements for all intervertebral disc and vertebra FEM meshes generated by the pipeline.

[0125]

[0126] Across all created FEM models, both vertebrae and intervertebral discs, the average percentage of poor quality elements remained below 2%, well within the 10% guideline defining a good quality mesh (Figure 5). Evaluations were conducted label-wise across the entire dataset, with each label corresponding to a specific spine level. Consequently, vertebra labels ranged from 4 to 25, while intervertebral disc labels ranged from 4-5 to 24-25.

[0127] Specifically for vertebrae meshes (Figure 6A), 98.6% of models contained even fewer than 5% elements of poor quality. The highest proportion of poor quality elements, reaching 13%, was observed in a label 5 vertebra (C5). It is represented as the highest outlier in Figure 5A.

[0128] Figure 6 shows mesh statistics for the generated vertebrae (A) and intervertebral disc FEM meshes (B). Black points represent the percentage of poor quality elements in single FEM models, with poor quality being defined as an aspect ratio >5. The blue beams indicate the average percentage of poor-quality elements in all models of the specific label. Failed vertebrae models were excluded from the plot. For vertebrae meshes (A), the maximum share of poor-quality elements was 13% in the C5 vertebrae. The average percentage of poor qualityelements was never below 2% in both vertebrae and intervertebral discs. For intervertebral discs (B), the average percentage of poor quality elements was never even below 0.5%. The lowest mesh quality was generated in the cervical spine.

[0129] Figure 7 shows a statistical evaluation of the duration needed for the different parts of the pipeline when processing a single subject, displayed in a box plot. Whisker boundaries are drawn at 1.5 times the interquartile range (IQR). Outliers are marked by single points. Each part’s duration is given for the vertebrae and the intervertebral discs, respectively.

[0130] Regarding intervertebral discs (Figure 6B), the average percentage of poor quality elements never dropped below 0.5%. This indicates a good mesh quality, well within the defined guideline for mesh quality (10%). In the whole dataset, six intervertebral disc labels even contained no elements with poor quality, which were 5-6, 8-9, 10-11, 14-15, 15-16, and 24-25. For another six labels, namely 9-10, 11-12, 16-17, 17-18, 18-19, and 19-20, only one intervertebral disc model was generated, which contained elements of poor quality.

[0131] For both vertebra and intervertebral disc models, the lowest mesh quality was consistently found in the cervical spine. The best results, considering mesh quality, were achieved in the higher labels, namely the lumbar spine.

[0132] Calculation times

[0133] With an average number of 21 vertebrae and 20 intervertebral discs per subject, the average processing time was 4.4 min for a vertebra and 31s for an intervertebral disc. For one subject, the average duration to process and simulate all vertebrae was 93.3 min. For all intervertebral discs, the average calculation time per subject was 10.4 min.

[0134] With significant distance, vertebrae smoothing, and their FEM simulation make up the most costly parts of the pipeline, considering processing times (Figure 7). Note that, especially for the smoothing process, the selective smoothing of vertebrae takes an average time of 35 minutes per subject, while the adaptive intervertebral disc smoothing algorithm takes less than a minute (Table 2 below). With approximately 13 min per subject, meshing the vertebrae volumes is still among the most time-consuming parts of the pipeline. Note that the MRI to surface mesh process includes the complete processing and segmentation of the MRI file, as well as alignment and the determination of points of interest.

[0135] Finally, the developed pipeline is automated to a point where only the MRI image paths of the patients and the FEM simulation parameters need to be defined as input. The latter includes loading and material parameters. As output, an ABAQLIS output database is created, containing deformation and stress values as requested. No manual steps were required.

[0136] Discussion637 vertebrae and 600 intervertebral discs were modeled and simulated using our automated pipeline, with an average duration of 4.4 min per vertebra and 31s per intervertebral disc. We evaluated the quality and performance of the pipeline by investigating the quality of generated meshes, failed attempts, and processing times.

[0137] With the predefined mesh quality criteria, more than 98% of the generated models achieved good quality.

[0138] TABLE 2 Quantitative statistical values for the durations of different pipeline parts. The averages refer to the duration needed to process one subject.

[0139] > > >

[0140] > >

[0141] > >

[0142]

[0143] The processing time for the FEM simulation of vertebrae was approximately tenfold higher compared to that for intervertebral discs. It is worth noting that meshing and smoothing times are directly proportional to the number of elements in the mesh, which is roughly 4.5 times greater in vertebrae models than in intervertebral disc models.

[0144] Manual processes typically involve segmentation software for surface mesh derivation, followed by volumetric model generation and FEM simulations using separate tools, a process that can take up to several days

[0013] , In contrast, our automated pipeline drastically reduces this timeframe. With no user interaction and reliance solely on an MRI image, our method achieves biomechanical analysis of a vertebra of intervertebral disc within just about 4.3 min or 27 s, respectively. In addition, it is insusceptible to variability due to manual steps.

[0145] Summary and Advantages

[0146] The goal of this work was to advance the automated generation of patient-specific FEM models derived directly from MRI segmentations. In comparison to recent approaches, our approach is based on the MRI image itself and does not rely on templates like SSMs. The process ofmorphing a mesh is thereby obsolete, which constitutes the advantage of having fewer processing steps and higher flexibility in representing geometries that do not fit into statistical norms, like osteophytes, strongly deformed vertebrae, or extreme bulges in intervertebral discs.

[0147] By realizing surfaces with shared nodes and elements for adjacent vertebrae and intervertebral discs, we spare the time-consuming and unstable process of implementing penalties during contact modeling. In addition, shared interface nodes are advantageous in the framework of exchanging load and displacement data in coupled MBS and FEM simulations.

[0148] Manual implementations of full spine models may be subject to automation efforts in the future. Constitutive models of the intervertebral disc and vertebrae can be advanced by including locally varying, individualized MRI- or CT-derived material parameters. To include both detailed bone geometries with, e.g., osteophytes and intervertebral disc deformities such as bulges, a co-registration of MRI and available CT data could be beneficial.

[0149] For the intervertebral disc, a differentiation between nucleus pulposus and annulus fibrosus, together with a fiber- re info reed or biphasic implementation, could be beneficial in answering specific research questions. Vertebrae might benefit from a differentiation between the cortical shell and trabecular bone. Prospectively, combining our pipeline with validated models, as demonstrated in our group’s recent work

[0024] , will enable large cohort studies to gain insight into the causes of spinal disorders such as degeneration or back pain.

[0150] Further details and examples of the invention are described with reference to an embodiment of the figures 8 to 13 as follows:

[0151] Ensuring Anatomical Integrity and Shared Contact Surfaces in Vertebra and Disc Models: A Segmentation-based Smoothing Approach

[0152] Summary

[0153] Due to limited MRI resolution, patient-specific simulation models derived from medical images often lack bio-fidelity. To address this, we present a smoothing pipeline for generating high-fidelity meshes of vertebrae and intervertebral discs from medical images, which serve as a base for biomechanical simulations. Using a diverse array of vertebrae smoothing algorithms, including Laplace, HC Laplace, Taubin, and Two Step, alongside surface subdivision methods such as Tri-to-Quad by 4-8, Loop, LS3-Loop, Catmull-Clark, and Butterfly, we systematically explored 136 combinations across six protocols to determine an optimal smoothing pipeline. Subsequently, an adaptive smoothing algorithm was developed for intervertebral disc meshes. By adjusting vertex locations to those of the vertebra mesh, we ensured seamless alignmentof contact surfaces, including shared nodes. Evaluation of our pipeline against conventional smoothing methods demonstrates superior edge preservation and reduced stair-step effects, enhancing the fidelity of the generated meshes. Finite Element Method simulations further confirmed the accuracy of our selective smoothing pipeline, showing increased notch stress. Our results demonstrate the significance of a designated smoothing algorithm for vertebrae and disc models. Validated on a diverse dataset, our automated smoothing pipeline generates patient-specific models with enhanced biomechanical fidelity, enabling large-scale studies and deeper insights into spine biomechanics and pathology.

[0154] Introduction

[0155] Spinal pathologies encompass a range of conditions affecting the spine, including, e.g., low back pain, neck pain, scoliosis, spinal stenosis, and degenerative disc disease

[0056] , In addition, traumatic injuries such as wedge fractures of vertebrae occur with increasing degeneration

[0057] , These conditions have significant implications for patients’ quality of life and often require long-term support and treatment, including surgery

[0058] ,

[0156] Numerous studies investigated degenerative changes in vertebrae [59; 60] and intervertebral discs intervertebral discs [61; 62; 63] using either MBS [58; 64] or FEM [65; 66], Fewer studies have used patient-specific models in their studies[67; 68; 69; 70; 62], despite considerable proof of unique model characteristics leading to more diverse results [71 ; 72; 64], Most patientspecific modeling approaches apply mesh morphing methods, which are based on landmark extraction from medical images and subsequent deformation of a predefined mesh, often referred to as a reference or source mesh [67; 69; 73], Once the target geometry gets more complex, larger deformations have to be performed during the morphing process, which can lead to decreasing mesh quality

[0074] , Deriving meshes directly from a medical scan using the marching cubes algorithm

[0075] and a subsequent volume meshing method can be advantageous, as it recreates segmented bodies directly based on the physiological reality

[0076] , However, resolutions of common MRI and CT images are limited, leading to low-resolution artifacts in the derived surface meshes, which are the basis for the FEM models

[0058] , These artifacts alter the body’s geometry, which is, in turn, commonly known to impact FEM results. In vertebrae specifically, artifacts like the stair-step effects are known to significantly impact the accuracy of FEM results

[0077] , To prevent artifacts from being propagated into the final FEM model, the implementation of surface mesh smoothing is inevitable for accurate biomechanical simulations.

[0157] Previous studies have addressed the need for smoothing processes [78; 77], but few have provided comprehensive descriptions of the applied smoothing protocols [69; 73; 65; 66], Commonly, low-resolution-caused artifacts like stair-steps are compensated using overallvertebra smoothing

[0078] , This approach may result in features like vertebra edges or osteophytes being smoothed to the point of disappearance, which likely affects respective simulation results in later stages.

[0158] In comparison, vertebrae are more complex in shape and thus pose a greater challenge for smoothing protocols, whereas intervertebral discs seem less of a challenge. However, distinctly smoothing them would result in non-coherent contact surfaces. In turn, computational efficiency in the FEM simulation decreases, potentially leading to convergence problems and less accurate results [79; 80], Further, the absence of coherent contact surfaces, or more specifically, shared contact nodes, can be disadvantageous for coupled MBS and FEM simulations

[0081] ,

[0159] In this context, the primary objectives of this study include achieving smooth endplate (EP) surfaces on vertebrae meshes, ensuring precise coherence with intervertebral disc surfaces while preserving characteristic bone structures such as osteophytes and sharp edges. Additionally, we investigate an adaptive smoothing algorithm to seamlessly integrate intervertebral disc meshes into the overall spine model. By addressing these challenges, our work aims to enhance the accuracy and reliability of patient-specific biomechanical models, ultimately facilitating the translation of biomechanical simulations into routine clinical practice to offer personalized treatment options.

[0160] Methods

[0161] A subset of an internal dataset containing 31 MRI scans with a resolution of 1 mm x 1 mm in the sagittal plane and a slice thickness of 2.5 mm to 3.5 mm was used to develop and evaluate the smoothing pipeline, here referred to as the primary dataset. Vertebrae with labels 5 - 23 and the respective associated intervertebral discs were segmented using the automated approach SPIN EPS

[0082] , Since CT segmentations are more adequate in capturing characteristic bone structures that deviate from the norm (Fig. 8), we used a second dataset to investigate the pipeline performance regarding stair-step smoothing and edge maintenance in those extreme cases. Fig. 8 shows a CT (left) vs. an MRI (right) scan of the same subject. Characteristic bone structures are represented in the CT. The dataset was a retrospective, internal dataset containing rigidly, point-registered CT and MRI images

[0083] , and is here referred to as the point-registered dataset. CT segmentations were created using SpineR, an automated algorithm by Sekuboyina et al.

[0084] , and MRI segmentations again using SPINEPS

[0082] , The segmented intervertebral disc and EP masks were subsequently transferred to the CT image segmentation. For both datasets, segmented vertebrae and intervertebral discs were converted to triangulated surface meshes using the marching cubes algorithm. EPs were considered part of the intervertebral disc. The ethics committee of the Technical University Munich approved our German-law-compliant studies (593 / 21 S-NP).We first developed a smoothing pipeline for vertebra meshes and subsequently accounted for the seamless integration of the intervertebral disc meshes by implementing an adaptive smoothing step. The development process was based on the primary dataset, including MRI-segmented vertebrae. The point-registered dataset served as subsequent validation data. Vertebrae Smoothing Algorithm Development using the Primary Dataset

[0162] Using the primary dataset, we implemented and combined a range of mesh processing methods for vertebrae (Table 1). Broadly, methods can be divided into basic mesh smoothing algorithms (BSA) and surface subdivision methods (SSM). Implemented BSA, including Laplace

[0085] , HC Laplace

[0086] , Taubin

[0087] , and the Two Step algorithm

[0088] , As SSM, we investigated Tri-to-Quad by 4-8 subdivision

[0089] , Loop, LS3-Loop

[0090] , Catmull-Clark, and the Butterfly approach. Besides varying these algorithms and approaches in their parameters and orders, we distinguished between applying them either to the complete meshes or to selected parts. In the latter case, we further differentiated the parameters used to select the specific parts of the mesh, namely the normal vectors of elements or the distance of nodes to the adjacent intervertebral disc mesh. In total, we implemented seven different smoothing protocols, here referred to as the seven different approaches. Each of them consisted of a different combination of the above-mentioned mesh processing methods.

[0163] Present Approach: Selective Smoothing based on Intervertebral Disc Distance

[0164] Three different approaches were applied that made use of the adjacent intervertebral disc meshes of the vertebrae, which resulted from the comprehensive segmentation mask. We herein selected the EP contact surfaces based on distance thresholds ranging from 0.6 mm to 0.8 mm. In an approach 3c) according to the present embodiment, no distinct submeshes were generated. Initially, EP surfaces were smoothed using Laplace filtering with parameters 0.05 < A < 0.3 and 40-90 iterations. Subsequently, the entire vertebra underwent Taubin smoothing (20-50 iterations, 0.5 < A < 0.7 and p = -A + 0.03).

[0165] Adaptive Intervertebral Disc Smoothing

[0166] Based on the vertebrae smoothing, the adaptive intervertebral disc smoothing algorithm was implemented (Fig. 9), which shows the exemplary smoothing process of an intervertebral disc mesh. From left to right: Raw, preprocessed, adaptively smoothed, and postprocessed mesh. Interface vertices of the intervertebral disc are marked in black in the preprocessed mesh. A Taubin filter (A = 0.5, p = -0.53) and 5% dilation to account for the potential volume loss after the vertebra smoothing was applied. We then identified the interface vertices of the intervertebral discs using smoothed adjacent vertebrae meshes and the previously determined distance thresholds. A nearest neighbor function was employed to identify the closest vertexon the adjacent vertebra mesh for each interface vertex in the intervertebral disc mesh. Correspondence between interface vertices was established by replacing the intervertebral disc vertex locations with those of the vertebra mesh, facilitating seamless alignment. Taubin filtering (A = 0.5, . = -0.53) ensured mesh quality in a postprocessing step.

[0167] Algorithm Performance Validation

[0168] We evaluated all smoothing algorithms based on their ability to (I) produce a smooth EP surface, (II) create a coherent contact surface between intervertebral disc and vertebra, and (III) preserve characteristic bone shapes in the case of vertebrae.

[0169] (I) The bio-fidelity of the EP surfaces was evaluated by visual inspection, focusing on the absence of stair-step effects. We additionally calculated the curvature of the vertebra meshes using the quadric fitting method, which approximates mesh nodes and associated normals by a quadratic surface. (II) The coherence of the vertebra and intervertebral disc contact surface was evaluated by the distance of their interface nodes. (Ill) Increased EP smoothness correlates with decreased edge sharpness for smoothing filters applied to the whole mesh, which was considered during the result evaluation. To evaluate edge preservation in severe cases like osteophytes or fractures, we used the point-registered dataset. Conventionally smoothed meshes were compared to selectively smoothed meshes visually. In an additional FEM simulation, notch stress was analyzed for conventional vs. selective smoothing. Simplified linear material parameters were assumed, and a flexion moment within a physiologically plausible range was applied to the nodes that represented the intervertebral disc contact region. FEM models were generated and simulated using an automated pipeline

[0076] ,

[0170] Results

[0171] We developed a smoothing pipeline for vertebra and intervertebral disc smoothing, which achieves smooth EP surfaces, ensuring precise coherence of vertebra and intervertebral disc surfaces while preserving characteristic bone structures such as osteophytes and sharp edges.

[0172] Smooth EP surfaces

[0173] In Approach 3c), the entire vertebra was smoothed before selectively smoothing the EP contact surfaces. The approach involved selecting and smoothing the EP contact surfaces separately while maintaining their connection to the vertebrae. Considering selection distance thresholds, adjustment based on vertebrae labels was found most effective: labels 5-7 were selected with a 0.6 mm threshold, 8-16 with a 0.7 mm threshold, and 17-23 with a 0.8 mm threshold. 80iterations were found to deliver visually good results. As the Laplace filter was able to remove the stair-step effect before, we used 80 iterations for smoothing the EP surface. No shrinkage problems were observed as smoothing was applied to a surface only. The Taubin filter provided volume retention, maintained edges more appropriately, and allowed precise adjustments without over-smoothing. Final smoothing parameters are summarized in Table 3 below.

[0174] Applying a curvature representation to vertebrae smoothed with the selective smoothing pipeline (Approach 3c) showed negligible signs of stair-step artifacts on the EP surface for all different samples (Fig. 10), wherein Fig. 10 shows mean curvature calculated with the quadric fitting method. Color mapping is based on a 10% scale. The strongest convex curvatures are indicated by the color blue, while green indicates a low curvature and red indicates the strongest concave curvature.

[0175] Coherent Interface between Vertebra and Intervertebral Disc

[0176] Adaptive intervertebral disc smoothing was applied using the selective smoothing of Approach c, which proved superior to other methods. The contact areas of the vertebra and intervertebral disc surfaces were well-aligned and non-intersecting, with shared node locations between the intervertebral disc and vertebrae (Fig. 11), wherein Fig. 11 shows the shared-nodes contact surface of an exemplary vertebra and intervertebral disc, intervertebral disc nodes are represented as turquoise squares, and vertebra nodes are represented as green dots.

[0177] Table 3: Final parameters for the selective smoothing pipeline, including the distance thresholds for contact surface determination and EP surface smoothing parameters.

[0178] Parameter

[0179] Distance thresholds (mm) Labels 5-7: 0.6 Labels 8-16: 0.7 Labels 17-23:

[0180] 0.8

[0181] Laplace Smoothing Parameters Labels 5 - 15: Labels 16 - 21: Labels 22 - 23: (EP) 0.2 w. 80 0.15 w. 80 0.2 w. 80 iterations iterations iterations Taubin Smoothing Parameters Labels 5 - 14: Labels 15 - 23: A (entire vertebra) = 0.5, p = -0.53, A = 0.6, p = -0.63,

[0182] 30 iterations 30 iterations

[0183] Edge Preservation

[0184] For more complex vertebrae from the point-registered dataset (CT segmented bones), the selective smoothing pipeline showed significantly better edge preservation for characteristic bone structures compared to the conventional approach, represented by 10 iterations of the HC Laplace algorithm (Fig. 12), wherein Fig. 12 shows a comparison of selective smoothing results (top row in green) and conventional smoothing, represented by 10 iterations of HCLaplace (bottom row in red). The wireframe views display the unsmoothed version, while the face views display the differentially smoothed versions. The shape of the selectively smoothed mesh closely followed the raw version, containing the fundamental bone structure. In contrast, detail was lost during the conventional smoothing approach. FEM simulation results showed an increased notch stress for the models resulting from the selective smoothing pipeline compared to a conventional one (Fig. 13), wherein Fig. 13 shows notch stress in FEM models derived from a conventional smoothing algorithm (10 iterations HC Laplace) and our selective smoothing pipeline. Starting from a raw mesh, smoothed meshes are created and converted into FEM models using the automated pipeline of the foregoing embodiments (MRI to FEM-pipeline, see for example Figs. 1 - 7). A section view on the right visualizes the stress in the respective models. Note that the stress scale limit has been adapted for this view due to visualization reasons.

[0185] Discussion

[0186] The objective of this study was to develop an automated smoothing pipeline for vertebra and intervertebral disc meshes that removes resolution artifacts and maintains patient-specific details, which was achieved by using the settings of Approach 3c), here referred to as our approach or the selective smoothing pipeline.

[0187] As the developed pipeline is based on a single Python script, the process can be described as automated. In comparison with other Pipelines

[0073] , it is not necessary to further adjust the file by, for example, cropping the image.

[0188] Being able to automatically detect the biological EP contact surfaces with the help of the segmented and labeled intervertebral disc data represents a novel advancement, to the best of our knowledge.

[0189] Conclusion

[0190] Smoothing processes for the vertebrae and intervertebral discs have been given little attention yet. Therefore, we created an innovative, completely automated smoothing pipeline for vertebrae and intervertebral discs based on segmentation data, which resolves artifacts on EP surfaces and retains characteristic bone structures of vertebrae, all while realizing a shared-node contact surface. We expect our pipeline to aid in the automation of patient-specific modeling processes while simultaneously improving the results of sole FEM simulations and co-simulations of MBS and FEM.

[0191] Future investigations could involve comprehensive FEM mesh generation integrating biological material parameters derived from bone densitometry measurements in point-registered MRI and CT datasets

[0021] , with further refinements involving advanced technologies like machine learning.Further details and examples of the invention are described with reference to an embodiment of Fig. 14 as follows:

[0192] Morphing of the Intervertebral Disc

[0193] In the MRI to FEM pipeline of the above explanation, the FEM models were generated as unstructured meshes using tetrahedral elements. The intervertebral disc itself is structured and heterogeneous. The gold standard of intervertebral disc FEM modeling thus contains heterogeneous, structured meshes (Fig. 14 left, top). Fig. 14 shows a morphing process, which generates such structured intervertebral disc meshes, according to an embodiment of the present invention. Left, top: structured FEM mesh incl. validated material parameters (= source mesh). Left, middle: affine deformation of the source mesh. Left, bottom: surface mesh of the intervertebral disc originating from the MRI of the patient. Progressing from left, middle to right, middle: Finalizing the morphing process towards a patient-specific, structured intervertebral disc FEM mesh.

[0194] In the morphing process, the structured FEM mesh of Fig. 14 left, top is deformed such that it takes on the outer geometry of the surface mesh originating from the MRI (Fig. 14, left bottom). The process is preferably as depicted in a flow chart in Fig. 15.

[0195] The following steps are contained in the process:

[0196] 1. Extraction of the surface nodes from the source mesh. When the one mesh is a volume mesh, and the other mesh is a surface mesh, this step allows to register the point clouds. 2. Calculating the registrations (used in informatics) of the clouds of points from the I) source mesh and the II) target mesh.

[0197] a. Rigid registration parameters. Calculation of the rigid body movement from the surface mesh of the source mesh to the target mesh. (Not the deformation, only the translatory and rotatory movement to the position of the target mesh).

[0198] b. Affine registration parameters. Here, we calculate a matrix that scales and distorts the source mesh.

[0199] c. Non-rigid. Here, for every single node, the residual translation between the affinely deformed source mesh surface point cloud and target mesh point cloud is calculated to achieve the form of the target cloud of points.

[0200] 3. Applying the registration parameters of 2a) and 2b) to the volume source mesh. The registration is calculated with the surface mesh point clouds (Fig. 16, top), but the calculated parameters are applied to the volume mesh point clouds. (Fig. 16, bottom).4. The remaining key challenge is to deform the surface nodes of the volume mesh into the final shape of the target mesh, while the inner nodes of the volume mesh follow this deformation. To solve this, we use a dummy FEM simulation. In this simulation, for the affine deformed volume mesh (Fig. 14, left, middle), we define a dummy material and apply the displacements of the surface points ^translation between affinely transformed surface mesh and non-rigidly deformed surface mesh, for every single point) as a respective boundary conditions in the FEM.

[0201] The exact translational displacements were calculated as the difference between 2b and 2c for each point.

[0202] The stresses resulting from the deformation in the FEM model (the part which is normally the reason for running FEM simulations), are discarded, and preferably only the end positions of the nodes of the volume mesh are retained.

[0203] Further details and examples of the invention are described with reference to an embodiment of Figs. 15 to 18 as follows:

[0204] The present embodiment concerns “femReg” as an exemplary preferable embodiment of Morphing. Preferably, the present embodiment is combinable with the foregoing embodiment referring to Fig. 14, and with one or more embodiments referring to Figs. 1 to 13.

[0205] Fig. 15 shows a data flowchart according to an embodiment of the present invention. Details of the steps in the functional boxes thereof can be taken from Fig. 16.

[0206] Fig. 16 shows pictures of results from a pipeline based on the embodiment of Fig. 15 showing details of the morphing pipeline used to create individualized FEM models with surface mesh derived point clouds shown on the top line and volume mesh derived point clouds shown on the bottom.

[0207] Therein: (a) Point clouds of TM (blue) and SM (yellow) with an initial, large distance in space, (b) Rigid registration result of TM and SM point clouds, (c) Affine registered TM point cloud (orange) and (d) non-rigidly registered point cloud using the CPD algorithm (red), (e) SM point cloud split into surface points and inner volume points, (f) Affine-transformed SM nodes using the transformation matrix from the respective surface mesh registration step, (g) Arrows indicate the displacement necessary for each node to achieve the TM shape. Vectors were calculated from the step (c-d).

[0208] An overview thereof is given by Fig. 17. Fig. 17 shows an overview of the methodology used to create patient-specific intervertebral disc models according to the embodiment of Figs. 15 and 16.Therein: (a) Segmentation as SPINEPS creates it [2] and (b) after the inclusion of endplates into the intervertebral disc labels, (c) Raw surface mesh of an exemplary intervertebral disc, derived by the marching cubes algorithm, (d) Smoothed surface mesh using our smoothing approach (embodiment of Figs. 8 - 13), advanced by an additional segmentation smoothing step, this stage serves as a target mesh (TM) for the morphing, (e) Final, individualized FEM intervertebral disc model, which was created by morphing the (f) calibrated, hyperelastic HGO source mesh (SM)

[0024] into the TM’s. Individualized models were simulated with four load cases to derive a displacement distribution.

[0209] The present method shown in Figs. 15 and 16 can be summarized by the following steps (with reference to Fig. 16):

[0210] (a) segmentation / smoothing of target mesh (TM).

[0211] (b-c) Rigid and affine registration using Coherent Point Drift.

[0212] (d) Non-rigid registration of surface point clouds (including CPD parameter scope, p-values of 1 < P <15). For example, p = 10, v = 0, E = 70.000 MPa.

[0213] (g) Defining / determining surface translation vectors.

[0214] (g) Dummy-FEM for morphing the inner nodes, respectively, morphing the surface node, and volumetric morphing

[0215] i) Boundary conditions = surface translations of the individual points

[0216] ii) Material = Dummy material based on parameter studies,

[0217] iii) Temperature-dependent material in nucleus pulposus (NP) of the intervertebral disc (temperature gradient causes bulging), definition / determination via parameter studies iv) Transformation of fibers in annulus fibrosus of the intervertebral disc via multiplication with the affine transformation matrix (see Fig. 15, “Apply Transformation matrix A” and “Affine Transformation of Annulus Fibrosus fibers using A”, pointing to “morphed FEM model”).

[0218] (f) Replacing the SM-Nodes with the morphed node positions and applying the original materials.

[0219] (g) Simulating load cases.

[0220] Preferably, the present method determines / calculates a determinant of the affine transformation matrix and, in case the determinant is zero or negative, corrects the transformation matrix to have a positive determinant. In some cases, the affine transformation matrix mirrors the point cloud, which can cause a negative volume of the model, and thepresent method’s preferred correction thereof corrects for this. Subsequently, the method preferably performs a further rigid transformation.

[0221] For instance, the method in such cases preferably carries out: Rigid - Affine (mirrored) - Rigid - Non-Rigid.

[0222] In the foregoing, the method preferably employs a source mesh (SM) based on healthy intervertebral disc data (height = 14 mm, for example) and validates using healthy in vitro data (ROM in Flexion, Extension, Lateral Bending, and Axial Rotation). In some preferable embodiments, the method employs source meshes predetermined with a degree of degeneration (degrees 1 - 5).

[0223] For instance, for degree 5, a source mesh with a height of 8 mm is used and is calibrated with the help of in vitro data.

[0224] Further examples thereof are shown in Fig. 18. Fig. 18 shows example models of a modification of the embodiment of Figs. 15 - 17, showing example models for degeneration grades 1 (a), 3 (b), and 5 (c).

[0225] Thereby, the present embodiment achieves physically consistent volume deformation / volume morphing, higher mesh quality with little or no overlaps, temperature bulging for realistic lamellae in the AF, and the use of structured meshes provides an internal structure with anatomic structures of the nucleus, fiber ring with fibers in the individual model being achieved. Thereby, the present method provides an efficient and highly accurate modelling of patientspecific geometries, which are preferably extracted from medical imaging data. These are preferably, as also discussed in the further embodiments, used for individualized FEM simulations.

[0226] Furthermore, the present method is time-efficient. In particular, prior art simulations commonly take many hours, in some cases even 24 hours, while the present method is achieved within a few, preferably 6 - 7 minutes using common computing architecture.

[0227] The total compute time is reduced, the Hausdorff-precision is increased, the mesh quality is robust, and ROM is shown even with degeneration being present.

[0228] The process is preferably fully automated.

[0229] Further details of the present embodiment are herewith described.

[0230] The performance of the morphing algorithms was further evaluated by morphing a large sample of intervertebral discs. Of 241 lumbar patient-specific FE IVD models, 238 completed the morphing and simulation pipeline successfully. A random subset of ten morphed meshesdemonstrated good mesh quality metrics, with an average aspect ratio of 1.65. Of the ten meshes, the worst aspect ratio was between 3.67 and 6.37 - no mesh included aspect ratios >10, and no mesh led to analysis errors. Analysis warnings, as defined by an angle between the isoparametric lines in an element being <45° or >135°, were depicted for 3.2% of the elements, on average. In comparison, the highest aspect ratio in the SM was 4.53, and the average aspect ratio was 2.1, while there were 112 analysis warnings.

[0231] The FE models were validated in terms of their ability to represent degeneration-grade specific in vitro data. Healthy discs were validated against: In vitro ROM of Heuer et al.

[0094] , which was originally used for calibration of the source mesh. Degenerated intervertebral discs were compared to in vitro data of different degeneration grades of lumbar IVDs, which were determined under the same loading conditions as in the study of Heuer et al.

[0094] by evaluating representative ROM data of the lumbar spine for 1 , 2.5, 5, and 7.5 Nm.

[0232] The present embodiment is preferably also described by the following clauses:

[0233] Clause 1. Computer-implemented method for the simulation of an intervertebral disc of a spine, comprising the steps:

[0234] - extracting surface nodes from a volumetric source mesh of the intervertebral disc, also referred to as intervertebral disc, wherein the source mesh is a finite element method model, also referred to as FEM model, of the intervertebral disc;

[0235] - generating a surface target mesh of the intervertebral disc from at least one image, particularly from medical sectional imaging such as a CT and / or an MR image, of the intervertebral disc;

[0236] - morphing the volumetric source mesh into, especially approximately, the target mesh by: - morphing the surface nodes of the source mesh into approximately the surface target mesh; and

[0237] - performing a dummy FEM simulation using a dummy material for morphing inner volumetric nodes of the source mesh based on the morphing of the surface nodes.

[0238] The FEM model of the intervertebral disc is preferably calibrated and validated based on in vitro data.

[0239] The volumetric nodes preferably can be morphed / transformed via below transformation matrices before the FE simulation is performed. Preferably, between morphing the surface nodes and performing a dummy FEM simulation of Clause 1, the method further comprises “morphing the volumetric nodes of the source mesh into, especially approximately, the target geometry”.Preferably, the dummy FEM simulation achieves the exact target mesh, especially via the translation of the last, non-rigid registration, which is then used as a boundary condition for the FEM simulation. In particular, the term “especially approximately” above is preferably in such a case “exactly”.

[0240] Clause 2. Computer-implemented method according to Clause 1 , wherein morphing of the surface nodes comprises defining registration parameters of a point cloud of the surface nodes of the source mesh and of a point cloud of the surface target mesh.

[0241] Clause 3. Computer-implemented method according to Clause 2, wherein the defining of registration parameters comprises defining rigid registration parameters representing rigid body movement, especially translational and / or rotational movement, from the point cloud of the surface nodes of the source mesh to the point cloud of the surface target mesh.

[0242] Clause 4. Computer-implemented method according to Clause 3, wherein the defining of registration parameters further comprises defining affine registration parameters for defining a matrix that scales and deforms the point cloud of the surface nodes of the source mesh to the point cloud of the surface target mesh.

[0243] Clause 5. Computer-implemented method according to Clause 4, wherein the defining of registration parameters further comprises defining non-rigid registration parameters, especially translational parameters, for all surface nodes of the source mesh.

[0244] Clause 6. Computer-implemented method according to any one of Clauses 3 to 5, wherein for the defining of rigid registration parameters and / or affine registration parameters and / or non-rigid registration parameters, coherent point drift, especially Bayesian coherent point drift, is used, especially with a beta value of 1 < p < 15, especially p = 10.

[0245] Clause 7. Computer-implemented method according to any one of Clause 4 to 6, wherein morphing of the volumetric source mesh comprises applying the rigid registration parameters and the affine registration parameters, especially as respective transformation matrices, defined for the point cloud of the surface nodes of the source mesh to the volumetric source mesh.Clause 8. Computer-implemented method according to Clause 7, wherein the registration parameters are defined only for the point cloud of the surface nodes of the source mesh and are applied to the entire volume source mesh.

[0246] Clause 9. Computer-implemented method according to Clause 7 or Clause 8, wherein applying the registration parameters to the volumetric source mesh comprises updating volume node positions of the volumetric source mesh while keeping element connectivity unchanged.

[0247] Clause 10. Computer-implemented method according to Clause 9, wherein the rigid registration parameters and the affine registration parameters, especially the respective transformation matrices, are applied to all FEM nodes of the volumetric source mesh.

[0248] Clause H. Computer-implemented method according to any one of Clauses 5 to 10, wherein morphing of the volumetric source mesh comprises applying the non-rigid registration parameters, especially as a non-rigid transformation matrix, defined for the point cloud of the surface nodes of the source mesh to the volumetric source mesh.

[0249] Clause 12. Computer-implemented method according to Clause 11, wherein applying the non-rigid registration parameters to the volumetric source mesh comprises:

[0250] - defining surface translation vectors, especially for each surface node, as a difference between a state of the surface nodes of the source mesh after applying the affine registration parameters and a state of the surface nodes of the source mesh after applying the non-rigid registration parameters;

[0251] - in performing the dummy FEM simulation, applying the surface translation vectors as a boundary condition of the dummy FEM simulation, especially to propagate surface node translations to the volume, especially inner volume, of the source mesh.

[0252] Clause 13. Computer-implemented method according to Clause 12, wherein performing the dummy FEM simulation comprises defining the dummy material as comprising a temperaturedependent region, especially corresponding to a nucleus pulposus of the intervertebral disc, and applying a temperature gradient to drive outward bulging of the dummy material.Clause 14. Computer-implemented method according to Clause 13, wherein performing the dummy FEM simulation further comprises applying the rigid registration parameters, especially the rigid transformation matrix, and the affine registration parameters, especially the affine transformation matrix, to one or more regions of the FE model, especially corresponding to fibers of an annulus fibrosus of the intervertebral disc.

[0253] Clause 15. Computer-implemented method according to any one of the foregoing Clauses, wherein morphing the volumetric source mesh further comprises replacing volumetric nodes of the source mesh with volumetric nodes of the dummy FEM simulation result and especially subsequently re-applying one or more material properties of the volumetric source mesh.

[0254] Clause 16: Computer-implemented method according to any one of the foregoing Clauses, wherein the volumetric source mesh of the intervertebral disc is a source mesh based on healthy intervertebral disc data, preferably with a height of 14 mm, or is based on data on one or more intervertebral discs comprising a predetermined degree of degeneration, especially a Pfirrmann degree between one and five, with especially corresponding reduced height, preferably 8 mm for degree 5 and especially a linear increase with each degree below five to 14 mm for healthy intervertebral disc.

[0255] Clause 17: Computer-implemented method according to any one of the foregoing Clauses, wherein the volumetric source mesh of the intervertebral disc is a source mesh based on healthy intervertebral disc data, preferably with material parameters calibrated to healthy in vitro data, and / or is based on data of one or more intervertebral discs comprising a predetermined degree of degeneration, especially a Pfirrmann degree between one and five, with especially corresponding altered material parameters derived from calibration to in vitro experiments of especially discs with those degeneration grades one to five.

[0256] The foregoing clauses 1 to 17 are preferably combinable with the embodiments described above. Preferably, the foregoing clauses 1 to 17 are combinable with the present invention according to claim 7, with any one or multiple of the foregoing clauses preferably being the means of morphing of claim 7.

[0257] ReferencesBackground of invention:

[0258] [1] Du, X., et al. Spinenet: Learning scale-permuted backbone for recognition and localization. In Proceedings of the IEEE / CVF conference on computer vision and pattern recognition. 2020.

[0259] [2] Moeller, H., et al., SPINEPS - Automatic Whole Spine Segmentation of T2-weighted MR images using a Two-Phase Approach to Multi-class Semantic and Instance Segmentation. Eur Radiol, 2025. 35(3): p. 1178-1189

[0260] [3] Caprara, S., et al., Automated Pipeline to Generate Anatomically Accurate Patient-Specific Biomechanical Models of Healthy and Pathological FSUs. Front Bioeng Biotechnol, 2021. 9: p. 636953.

[0261] [4] Lerchl, T., et al., Validation of a Patient-Specific Musculoskeletal Model for Lumbar Load Estimation Generated by an Automated Pipeline From Whole Body CT. Front Bioeng Biotechnol, 2022. 10: p. 862804.

[0262] [5] Munoz-Moya, E., etal., Unveiling interactions between intervertebral disc morphologies and mechanical behavior through personalized finite element modeling. Front Bioeng Biotechnol, 2024. 12: p. 1384599.

[0263] [6] Knapik, G.G., et al., Computational lumbar spine models: A literature review. Clinical Biomechanics, 2022. 100: p. 105816.

[0264] [7] Lerchl, T., et al., Multibody Models of the Thoracolumbar Spine: A Review on Applications, Limitations, and Challenges. Bioengineering (Basel), 2023. 10(2).

[0265] [8] Nispel, K., et al., Recent Advances in Coupled MBS and FEM Models of the Spine-A Review. Bioengineering.

[0266] Figures 4 to 7:

[0267] [9] Bouzakis, K. D., Mitsi, S., Michailidis, N., Mirisidis, I., Mesomeris, G., Maliaris, G., et al. (2004). Loading simulation of lumbar spine vertebrae during a compression test using the finite elements method and trabecular bone strength properties, determined by means of nanoindentations. J. Musculoskelet. Neuronal Interact. 4, 152-158.

[0268]

[0010] Bruno, A. G., Broe, K. E., Zhang, X., Samelson, E. J., Meng, C. A., Manoharan, R., et al. (2014). Vertebral size, bone density, and strength in men and women matched for age and areal spine bmd. J. Bone Min. Res. 29, 562-569. doi:10.1002 / jbmr.2067

[0269]

[0011] Campbell, J. Q., Coombs, D. J., Rao, M., Rullkoetter, P. J., and Petrella, A. J. (2016). Automated finite element meshing of the lumbar spine: verification and validation with 18 specimen-specific models. J. Biomechanics 49, doi:10.1016 / j.jbiomech.2016.05.025

[0012] Campbell, J. Q., and Petrella, A. J. (2015). An automated method for landmark identification and finite-element modeling of the lumbar spine, leee Trans. Biomed. Eng. 62, 2709-2716. doi: 10.1109 / tbme.2015.2444811

[0270]

[0013] Caprara, S., Carrillo, F., Snedeker, J. G., Farshad, M., and Senteler, M. (2021). Automated pipeline to generate anatomically accurate patient-specific biomechanical models of healthy and pathological fsus. Front. Bioeng. Biotechnol. 9, 636953. doi:10. 3389 / fbioe.2021.636953

[0014] Castro-Mateos, I., Pozo, J., Lazary, A., and Frangi, A. (2016). Automatic construction of patient-specific finite-element mesh of the spine from intervertebral discs and vertebra segmentations. Proc. SPIE 9788, 97881. doi:10.1117 / 12.2217343

[0271]

[0015] Castro-Mateos, I., Pozo, J. M., Pereahez, M., Lekadir, K., Lazary, A., and Frangi, A. F. (2015). Statistical interspace models (sims): application to robust 3d spine segmentation. IEEE Trans. Med. Imaging 34, 1663-1675. doi:10.1109 / tmi.2015.2443912

[0272]

[0016] Cignoni, P., Callieri, M., Corsini, M., Dellepiane, M., Ganovelli, F., and Ranzuglia, G. (2008). MeshLab: an open-source mesh processing tool. doi: 10.2312 / LocalChapterEvents / ltalChap / ltalianChapConf2008 / 129-136

[0273]

[0017] Clouthier, A. L., Wenghofer, J., Wai, E. K., and Graham, R. B. (2023). Morphable models of the lumbar spine to vary geometry based on pathology, demographics, and anatomical measurements. J. Biomechanics 146, 111421. doi:10.1016 / j.jbiomech.2022.111421

[0274]

[0018] Dreischarf, M., Zander, T., Shirazi-Adl, A., Puttlitz, C. M., Adam, C. J., Chen, C. S., et al. (2014). Comparison of eight published static finite element models of the intact lumbar spine: predictive power of models improves when combined together. J. Biomechanics 47, 1757-1766. doi:10.1016 / j.jbiomech.2014.04.002

[0275]

[0019] El Bojairami, I., El-Monajjed, K., and Driscoll, M. (2020). Development and validation of a timely and representative finite element human spine model for biomechanical simulations. Sci. Rep. 10, 21519. doi: 10.1038 / s41598-020-77469-1

[0276]

[0020] Fasser, M.-R., Kuravi, R., Bulla, M., Snedeker, J. G., Farshad, M., and Widmer, J. (2022). A novel approach for tetrahedral-element-based finite element simulations of anisotropic hyperelastic intervertebral disc behavior. Front. Bioeng. Biotechnol. 10, 1034441. doi: 10.3389 / fbioe.2022.1034441

[0277]

[0021] Fleps, I., and Morgan, E. F. (2022). A review of ct-based fracture risk assessment with finite element modeling and machine learning. Curr. Osteoporos. Rep. 20, 309-319. doi : 10.1007 / s 11914-022-00743-w

[0022] Galbusera, F., van Rijsbergen, M., Ito, K., Huyghe, J. M., Brayda-Bruno, M., and Wilke, H.-J. (2014). Ageing and degenerative changes of the intervertebral disc and their impact on spinal flexibility. Eur. Spine J. 23, 324-332. doi:10.1007 / s00586-014-3203-4

[0278]

[0023] Graf, R., Schmitt, J., Schlaeger, S., Moller, H. K., Sideri-Lampretsa, V., Sekuboyina, A., et al. (2023). Denoising diffusion-based mri to ct image translation enables automated spinal segmentation. Eur. Radiol. Exp. 7, 70. doi:10.1186 / s41747-023-00385-2

[0279]

[0024] Gruber, G., Nicolini, L. F., Ribeiro, M., Lerchl, T., Wilke, H.-J., Jaramillo, H. E., etal. (2024). Comparative fem study on intervertebral disc modeling: holzapfel-gasser-ogden vs. structural rebars. Front Bioeng. Biotechnol. 12, 1391957. doi:10.3389 / fbioe.2024.1391957

[0280]

[0025] Herzog, R., Elgort, D. R., Flanders, A. E., and Moley, P. J. (2017). Variability in diagnostic error rates of 10 mri centers performing lumbar spine mri examinations on the same patient within a 3-week period. Spine J. 17, 554-561. doi:10.1016 / j.spinee.2016.11.009

[0281]

[0026] latridis, J. C., Setton, L. A., Foster, R. J., Rawlins, B. A., Weidenbaum, M., and Mow, V. (1998). Degeneration affects the anisotropic and nonlinear behaviors of human anulus fibrosus in compression. J. Biomechanics 31, 535-544. doi: 10.1016 / s0021 -9290(98)00046-3

[0282]

[0027] latridis, J. C., Setton, L. A., Weidenbaum, M., and Mow, V. C. (1997). Alterations in the mechanical behavior of the human lumbar nucleus pulposus with degeneration and aging. J. Orthop. Res. 15, 318-322. doi: 10.1002 / jor.1100150224

[0283]

[0028] Imai, K. (2015). Analysis of vertebral bone strength, fracture pattern, and fracture location: a validation study using a computed tomography-based nonlinear finite element analysis. Aging Dis. 6, 180-187. doi:10.14336 / ad.2014.0621

[0284]

[0029] Johannessen, W., and Elliott, D. M. (2005). Effects of degeneration on the biphasic material properties of human nucleus pulposus in confined compression. Spine 30, E724-E729. doi: 10.1097 / 01.brs.0000192236.92867.15

[0285]

[0030] Kettler, A., Rohlmann, F., Ring, C., Mack, C., and Wilke, H. J. (2011). Do early stages of lumbar intervertebral disc degeneration really cause instability? evaluation of an in vitro database. Eur. Spine J. 20, 578-584. doi:10.1007 / s00586-010-1635-z

[0286]

[0031] Knapik, G., Mendel, E., Bourekas, E., and Marras, W. S. (2022). Computational lumbar spine models: a literature review. Clin. Biomech. 100, 105816. doi:10.1016 / j.clinbiomech.2022.105816

[0287]

[0032] Lavecchia, C. E., Espino, D. M., Moerman, K. M., Tse, K. M., Robinson, D., Lee, P. V. S., et al. (2018]^Lumbar model generator: a tool for the automated generation of a parametric scalable model of the lumbar spine. J. R. Soc. Interface 15, 20170829. doi:10.1098. / rsif.2017.0829

[0033] Lerchl, T., El Husseini, M., Bayat, A., Sekuboyina, A., Hermann, L., Nispel, K., etal. (2022). Validation of a patient-specific musculoskeletal model for lumbar load estimation generated by an automated pipeline from whole body ct. Front. Bioeng. Biotechnol. 10, 862804. doi:10.3389 / fbioe.2022.862804

[0288]

[0034] Lerchl, T., Nispel, K., Bodden, J., Sekuboyina, A., El Husseini, M., Frizsche, C., et al. (2024). Musculoskeletal spine modeling in large patient cohorts: how morphological individualization affects lumbar load estimation. Front. Bioeng. Biotechnol. 12, 1363081. doi:10.3389 / fbioe.2024.1363081

[0289]

[0035] Liebsch, C., and Wilke, H.-J. (2022). Even mild intervertebral disc degeneration reduces the flexibility of the thoracic spine: an experimental study on 95 human specimens. Spine J.

[0290] 22, 1913-1921. doi:10.1016 / j.spinee.2022.06.010

[0291]

[0036] Lorensen, W. E., and Cline, H. E. (1987). Marching cubes: a high resolution 3d surface construction algorithm. SIGGRAPH Comput. Graph. 21, 163-169. doi: 10.1145 / 37402.37422

[0037] Malandrino, A., Pozo, J. M., Castro-Mateos, I., Frangi, A. F., van Rijsbergen, M. M., Ito, K., et al. (2015). On the relative relevance of subject-specific geometries and degenerationspecific mechanical properties for the study of cell death in human intervertebral disc models. Front. Bioeng. Biotechnol. 3, 5. doi: 10.3389 / fbioe.2015.00005

[0292]

[0038] Moeller, H., Graf, R., Schmitt, J., Kleinert, B., Atad, M., Sekuboyina, A., et al. (2024). Spineps - automatic whole spine segmentation of t2-weighted mr images using a two-phase approach to multi-class semantic and instance segmentation. Eur. Radiol. doi : 10.1007 / S00330-024- 11155-y

[0293]

[0039] Molinari, L., and Falcinelli, C. (2021). On the human vertebra computational modeling: a literature review. Meccanica 57, 599-622. doi:10.1007 / s11012-021-01452-x

[0294]

[0040] Mdnch T., Adler, S., and Preim, B. (2010). “Staircase-aware smoothing of medical surface meshes,” in Proceedings of the eurographics workshop on visual computing for biomedicine (VCBM), 83-90. doi:10.2312 / VCBM / VCBM10 / 083-090

[0295]

[0041] Mdnch T., Lawonn, K., Kubisch, C., Westermann, R., and Preim, B. (2013). Interactive mesh smoothing for medical applications. Comput. Graph. Forum 32, 110-121. doi:10.1111 / cgf.12165

[0296]

[0042] Neves, L. A., Machado, J. M., Momente, J. C., Donega Zafalon, G. F., Nogueira da Cruz, M., Zanchetta do Nascimento, M., et al. (2018). Exploring mesh generation and quality enhancement with open source codes. J. Comput. Sci. 14, 1000-1028. doi:10.3844 / jcssp.2018.1000.1028

[0043] Nispel K., Lerchl, T., Senner, V., and Kirschke, J. S. (2023). Recent advances in coupled mbs and fem models of the spine-a review. Bioeng. (Basel) 10, 315. doi: 10.3390 / bioengineeringl 0030315

[0297]

[0044] Nispel, K., Scherzberger, A.-M., Lerchl, T., Gruber, G., Moeller, H., Graf, R., etal. (2024). Creating bio-fidelic vertebra and disc models from segmentation with selective smoothing. Comput. Biol. Med.

[0298]

[0045] Papadopoulos, P., and Taylor, R. L. (1992). A mixed formulation for the finite element solution of contact problems. Comput. Methods Appl. Meeh. Eng. 94, 373-389. doi: 10.1016 / 0045-7825(92)90061 -N

[0299]

[0046] Pfirrmann, C. W. A., Metzdorf, A., Zanetti, M., Hodler, J., and Boos, N. (2001). Magnetic resonance classification of lumbar intervertebral disc degeneration. Spine 26, 1873-1878. doi: 10.1097 / 00007632-200109010-00011

[0300]

[0047] Riegel, J., Mayer, W., and van Havre, Y. (2024). Freecad, version 0.21.1.

[0301]

[0048] Sciortino, V., Pasta, S., Ingrassia, T., and Cerniglia, D. (2023). On the finite element modeling of the lumbar spine: a schematic review. Appl. Sei. 13, 958. doi:10.3390 / appl13020958

[0302]

[0049] Sekuboyina, A., Husseini, M. E., Bayat, A., Loffler, M., Liebl, H., Li, H. W., et al. (2021). Verse: a vertebrae labelling and segmentation benchmark for multi-detector ct images. Med. Image Anal. 73, 102166. doi:10.1016 / j.media.2021.102166

[0303]

[0050] Sorkine, O. (2005). Laplacian mesh processing. Netherlands: The Eurographics Association, doi: 10.2312 / egst.20051044

[0304]

[0051] Stadelmann, M. A., Maquer, G., Voumard, B., Grant, A., Hackney, D. B., Vermathen, P., et al. (2018). Integrating mri-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc. J. Meeh. Behav. Biomed. Mater. 85, 37-42. doi:10.1016 / j.jmbbm.2018.05.005

[0305]

[0052] Taubin, G. (1995). “A signal processing approach to fair surface design,” in SIGGRAPH ’95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques (New York, NY: Association for Computing Machinery), 351-358. doi:10.1145 / 218380.218473

[0306]

[0053] van der Walt, S., Schdnberger, J. L., Nunez-Iglesias, J., Boulogne, F., Warner, J. D., Yager, N., et al. (2014). scikit-image: image processing in phython. PeerJ 2, e453. doi: 10.7717 / peerj.453

[0054] Zadpoor, A. A., and Weinans, H. (2015). Patient-specific bone modeling and analysis: the role of integration and automation in clinical adoption. J. Biomech. 48, 750-760. doi:10.1016 / j.jbiomech.2014.12.018

[0307]

[0055] Zhou, S. H., McCarthy, I. D., McGregor, A. H., Coombs, R. R., and Hughes, S. P. (2000). Geometrical dimensions of the lower lumbar vertebrae-analysis of data from digitised ct images. Eur. Spine J. 9, 242-248. doi:10.1007 / s005860000140

[0308] Figures 8 to 13

[0309]

[0056] P. Gruber, T. Boeni, Spinal Disorders: Fundamentals of Diagnosis and Treatment, Springer Berlin Heidelberg, Berlin, Heidelberg, 2008, ch. History of Spinal Disorders, pp.

[0310] 1 -37. doi : 10.1007 / 978-3-540-69091 -7_1.

[0311]

[0057] I. Melton, L. Joseph, S. H. Kan, M. A. Frye, H. W. Wahner, W. M. O’Fallon, B. L. Riggs, Epidemiology of vertebral factures in women, Am. J. Epidemiol. 129 (5) (1989) 1000-1011. doi: 10.1093 / oxfordjournals.aje.a115204.

[0312]

[0058] L. Molinari, C. Falcinelli, On the human vertebra computational modeling: a literature review, Meccanica 57 (2021). doi:10.1007 / s11012-021-01452-x.

[0313]

[0059] K. Imai, Computed tomography-based finite element analysis to assess fracture risk and osteoporosis treatment, World J. Exp. Med. 5 (2015) 182-187. doi:10.5493 / wjem.v5.i3.182.

[0314]

[0060] I. Fleps, E. F. Morgan, A review of ct-based fracture risk assessment with finite element modeling and machine learning, Curr. Osteoporos. Rep. 20 (5) (2022) 309-319. doi : 10.1007 / s 11914-022-00743-w.

[0315]

[0061] W. Ehlers, N. Karajan, B. Markert, An extended biphasic model for charged hydrated tissues with application to the intervertebral disc, Biomech. Model. Meehan. 8 (3) (2009) 233-251. doi: 10.1007 / s10237-008-0129-y.

[0316]

[0062] S. Natarajan, A. Tiulpin, L. Humbert, M. A. G. Ballester, Mri2mesh: Intervertebral disc mesh generation from low resolution mri using graph neural networks with cross level feature fusion, in: IEEE 20th International Symposium on Biomedical Imaging (ISBI), 2023, pp. 1-5. doi: 10.1109 / ISBI53787.2023.10230651.

[0317]

[0063] M. A. Stadelmann, G. Maquer, B. Voumard, A. Grant, D. B. Hackney, P. Vermathen, R.

[0318] N. Alkalay, P. K. Zysset, Integrating mri-based geometry, composition and fiber architecture in a finite element model of the human intervertebral disc, J. Meeh. Behav. Biomed. Mater. 85 (2018) 37-42. doi:10.1016 / j.jmbbm.2018.05.005.

[0064] T. Lerchl, K. Nispel, J. Bodden, A. Sekuboyina, M. El Husseini, C. Fritzsche, V. Senner, J. S. Kirschke, Musculoskeletal spine modeling in large patient cohorts: How morphological individualization affects lumbar load estimation, Front. Bioeng. Biotechnol.

[0319] 12 (2024).

[0320]

[0065] M. Dreischarf, T. Zander, A. Shirazi-Adl, C. M. Puttlitz, C. J. Adam, C. S. Chen, V. K. Goel, A. Kiapour, Y. H. Kim, K. M. Labus, J. P. Little, W. M. Park, Y. H. Wang, H. J. Wilke, A. Rohlmann, H. Schmidt, Comparison of eight published static finite element models of the intact lumbar spine: Predictive power of models improves when combined together, J. Biomech. 47 (8) (2014) 1757-1766. doi:10.1016 / j.jbiomech.2014.04.002.

[0321]

[0066] S. Naoum, A. V. Vasiliadis, C. Koutserimpas, N. Mylonakis, M. Kotsapas, K. Katakalos, Finite element method for the evaluation of the human spine: A literature overview, J. Funct. Biomater. 12 (3) (2021). doi:10.3390 / jfb12030043.

[0322]

[0067] J. Q. Campbell, A. J. Petrella, An automated method for landmark identification and finite- element modeling of the lumbar spine, IEEE Trans. Biomed. Eng. 62 (11) (2015) 2709- 2716. doi:10.1109 / tbme.2015.2444811.

[0323]

[0068] I. Castro-Mateos, J. Pozo, A. Lazary, A. Frangi, Automatic construction of patient-specific finite-element mesh of the spine from intervertebral discs and vertebra segmentations, in: Proceedings of the SPIE, 2016, p. 97881 U. doi:10.1117 / 12.2217343.

[0324]

[0069] C. E. Lavecchia, D. M. Espino, K. M. Moerman, K. M. Tse, D. Robinson, P. V. S. Lee, D.

[0325] E. T. Shepherd, Lumbar model generator: a tool for the automated generation of a parametric scalable model of the lumbar spine, J. R. Soc. Interface. 15 (138) (2018). doi:10.1098 / rsif.2017.0829.

[0326]

[0070] T. Lerchl, M. El Husseini, A. Bayat, A. Sekuboyina, L. Hermann, K. Nispel, T. Baum, M. T.

[0327] Loffler, V. Senner, J. S. Kirschke, Validation of a patient-specific musculoskeletal model for lumbar load estimation generated by an automated pipeline from whole body ct, Front. Bioeng. Biotechnol. 10 (2022) 862804. doi:10.3389 / fbioe.2022.862804.

[0328]

[0071] L. Meszaros-Beller, M. Hammer, J. M. Riede, P. Pivonka, J. P. Little, S. Schmitt, Effects of geometric individualisation of a human spine model on load sharing: neuro- musculoskeletal simulation reveals significant differences in ligament and muscle contribution, Biomech. Model. Meehan. (2023). doi:10.1007 / s10237-022-01673-3.

[0329]

[0072] M. R. Fasser, M. Jokeit, M. Kalthoff, D. A. Gomez Romero, T. Trache, J. G. Snedeker, M.

[0330] Farshad, J. Widmer, Subject-specific alignment and mass distribution in musculoskeletal models of the lumbar spine, Front. Bioeng. Biotechnol. 9 (2021) 721042. doi:10.3389 / fbioe.2021.721042.

[0073] S. Caprara, F. Carrillo, J. G. Snedeker, M. Farshad, M. Senteler, Automated pipeline to generate anatomically accurate patient-specific biomechanical models of healthy and pathological fsus, Front. Bioeng. Biotechnol. 9 (2021) 636953. doi:10.3389 / fbioe.2021.636953.

[0331]

[0074] A. Malandrino, J. M. Pozo, I. Castro-Mateos, A. F. Frangi, M. M. van Rijsbergen, K. Ito, H.

[0332] J. Wilke, T. T. Dao, M. Tho, J. Noailly, On the relative relevance of subject-specific geometries and degeneration-specific mechanical properties for the study of cell death in human intervertebral disc models, Front. Bioeng. Biotechnol. 3 (2015). doi:10.3389 / fbioe.2015.00005.

[0333]

[0075] W. E. Lorensen, H. E. Cline, Marching cubes: A high resolution 3d surface construction algorithm, SIGGRAPH Comput. Graph. 21 (4) (1987) 163-169. doi:10.1145 / 37402.37422.

[0334]

[0076] K. Nispel, T. Lerchl, G. Gruber, H. Moeller, R. Graf, V. Senner, J. S. Kirschke, From mri to fem: An automated pipeline for biomechanical simulations of vertebrae and intervertebral discs (in review), Front. Bioeng. Biotechnol. (2024).

[0335]

[0077] K. H. Shivanna, B. D. Adams, V. A. Magnotta, N. M. Grosland, Towards automating patient-specific infinite element model development, in: Proceedings of the Computational Biomechanics For Medicine Workshop at MICCAI, 2006, pp. 85-93.

[0336]

[0078] T. Mdnch, S. Adler, B. Preim, Staircase-aware smoothing of medical surface meshes, in:

[0337] Proceedings of the Eurographics Workshop on Visual Computing for Biomedicine (VCBM), 2010, pp. 83-90. doi:10.2312 / VCBM / VCBM10 / 083-090.

[0338]

[0079] P. Papadopoulos, R. L. Taylor, A mixed formulation for the finite element solution of contact problems, Comput. Methods Appl. Meeh. Eng. 94 (3) (1992) 373-389. doi:https: / / doi.org / 10.1016 / 0045-7825(92)90061-N.

[0339]

[0080] I. El Bojairami, K. El-Monajjed, M. Driscoll, Development and validation of a timely and representative finite element human spine model for biomechanical simulations, Sci. Rep.

[0340] 10 (1) (2020) 21519. doi:10.1038 / s41598-020-77469-1.

[0341]

[0081] K. Nispel, T. Lerchl, V. Senner, J. S. Kirschke, Recent advances in coupled mbs and fem models of the spine - a review, Bioengineering (Basel) 10 (3) (2023) 315. doi:10.3390 / bioengineering10030315.

[0342]

[0082] H. Moeller, R. Grad, J. Schmitt, B. Keinert, M. Atad, A. Sekuboyina, F. Streckenbach, H.

[0343] Schoen, F. Kofler, T. Kroencke, S. Bette, S. N. Willich, T. Keil, T. Niendorf, T. Pischon, B. Endemann, B. Menze, D. Rueckert, J. S. Kirschke, Spineps - automatic whole spine segmentation of t2-weighted mr images using a two-phase approach to multi-class semantic and instance segmentation (in review), Eur. Radiol. (2024).

[0083] R. Graf, J. Schmitt, S. Schlaeger, H. K. Moller, V. Sideri-Lampretsa, A. Sekuboyina, S. M. Krieg, B. Wiestler, B. Menze, D. Rueckert, J. S. Kirschke, Denoising diffusion-based mri to ct image translation enables automated spinal segmentation, European Radiol. Exp. 7 (1) (2023) 70. doi:10.1186 / s41747-023-00385-2.

[0344]

[0084] A. Sekuboyina et al., Verse: A vertebrae labelling and segmentation benchmark for multidetector ct images, Med. Image Anal. 73 (2021) 102166. doi:10.1016 / j.media.2021.102166.

[0345]

[0085] O. Sorkine, Laplacian Mesh Processing, in: Y. Chrysanthou, M. Magnor (Eds.), Eurographics 2005 - State of the Art Reports, The Eurographics Association, 2005. doi:10.2312 / egst.20051044.

[0346]

[0086] J. Vollmer, R. Mencl, H. Muller, Improved laplacian smoothing of noisy surface meshes, Computer Graphics Form 18 (3) (1999) 131-138. doi. https: / / doi.Org / 10.1111 / 1467- 8659.00334.

[0347]

[0087] G. Taubin, A signal processing approach to fair surface design, in: Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’95, Association for Computing Machinery, New York, NY, USA, 1995, p. 351-358. doi: 10.1145 / 218380.218473.

[0348]

[0088] A. Belyaev, Y. Ohtake, A comparison of mesh smoothing methods, in: Israel-Korea BiNational Conference on Geometric Modeling and Computer Graphics, Tel Aviv University, 83-87 (2003), 2003.

[0349]

[0089] L. Velho, D. Zorin, 4-8 subdivision, Comput. Aided Geom. Des. 18 (5) (2001) 397-427, subdivision Algorithms. doi:https: / / doi.org / 10.1016 / S0167-8396(01)00039-5.

[0350]

[0090] S. Boye, G. Guennebaud, C. Schlick, Least squares subdivision surfaces, Computer Graphics Forum 29 (7) (2010) 2021-2028. doi:https: / / doi.org / 10.1111 / j.1467- 8659.2010.01788.x.

[0351]

[0091] I. Castro-Mateos, J. M. Pozo, M. Pereahez, K. Lekadir, A. Lazary, A. F. Frangi, Statistical interspace models (sims): Application to robust 3d spine segmentation, IEEE Trans. Med. Imaging 34 (8) (2015) 1663-1675.

[0352]

[0092] G. Pluvinage, On notch fracture mechanics, Ind. Lab. Diagn. Mater. 87 (2021) 56-64.

[0353] doi: 10.26896 / 1028-6861-2021-87-2-56-64.

[0354]

[0093] A. Kanawati, R. J. R. Fernandes, A. Gee, J. Urquhart, F. Siddiqi, K. Gurr, Geometric and volumetric relationship between human lumbar vertebra and ct-based models, Acad. Radiol. 28 (2021) e172-e181. doi:10.1016 / j.acra.2020.05.027.

[0094] F. Heuer, H. Schmidt, Z. Klezl, L. Claes, H.-J. Wilke, Stepwise reduction of functional spinal structures increase range of motion and change lordosis angle, Journal of Biomechanics 40 (2) (2007) 271-280. doi:https: / / doi.org / 10.1016 / j.jbiomech.2006.01.007.

Claims

Claims1. A computer-implemented method for the simulation of at least a part of a spine, comprising the steps:executing of an image segmentation on at least one image, particularly from medical sectional imaging such as a CT and / or an MR image, of at least a part of the spine, for obtaining a segmentation mask;deriving of one or more vertebral body geometr(y / ies) and / or intervertebral disc geometr(y / ies) as a surface mesh from the segmentation mask;processing, in particular smoothing, of the surface mesh of the vertebral body geometry and / or the intervertebral disc geometry;filling of a volume being enveloped by the surface mesh; andgenerating of a finite element method model, also referred to as FEM model, from the volume; wherein,prior to smoothing, extracting of contact nodes is conducted, wherein the contact nodes are nodes of the surface mesh, which are adjacent to or in contact with nodes of a further surface mesh of another adjacent element of the part of the spine, in particular of an adjacent intervertebral disc and / or an adjacent vertebral body, for the modeling of contact points of the vertebral body geometry and / or the intervertebral disc geometry.

2. The computer-implemented method according to claim 1, wherein during the generation of the FEM model the filled volume is interlinked, also referred to as meshing, for generating an FEM model with a volume mesh of nodes and connections between the nodes.

3. The computer-implemented method according to claim 1 or claim 2, wherein the extracted nodes are integrated into the FEM model.

4. The computer-implemented method according to claim 3, wherein, during the extraction of the contact nodes, equivalence positions of the contact nodes are determined, which are equivalent positions of the contact nodes between the surface mesh and the FEM model, in particular between the surface mesh and the volume mesh according to claim 2.

5. The computer-implemented method according to any one of the preceding claims, wherein, prior to the filling of the volume, a reconstructed surface, in particular in a computer-aided design format, is prepared from the surface mesh, and in particular after the filling of the volume a solid body model, in particular in a CAD format, is output as volume for the FEM model, in particular as STEP data.

6. The computer-implemented method according to any one of the preceding claims, wherein, during the generation of the FEM model, simulation-specific parameters, in particular load, boundary conditions, constraints and / or material, in particular with the help of the contact nodes as implementation aid, are supplemented.

7. The computer-implemented method according to one of the preceding claims, wherein, by means of morphing, a more realistic representation of an intervertebral disc is adjusted to an intervertebral disc geometry, in particular to an individualized intervertebral disc geometry.

8. The computer-implemented method according to claim 7, wherein morphing comprises: extracting surface nodes from a volumetric source mesh of the intervertebral disc, wherein the source mesh is a finite element method model, also referred to as FEM model, of the intervertebral disc;generating a surface target mesh of the intervertebral disc from at least one image, particularly from medical sectional imaging such as a CT and / or an MR image, of the intervertebral disc; morphing the volumetric source mesh into, especially approximately, the target mesh by: morphing the surface nodes of the source mesh into approximately the surface target mesh; andperforming a dummy FEM simulation using a dummy material for morphing inner volumetric nodes of the source mesh based on the morphing of the surface nodes.

9. The computer-implemented method according to claim 8, wherein performing the dummy FEM simulation comprises defining the dummy material as comprising a temperaturedependent region, especially corresponding to a nucleus pulposus of the intervertebral disc, and applying a temperature gradient to drive outward bulging of the dummy material.

10. The computer-implemented method according to claim 8 or claim 9, wherein performing the dummy FEM simulation further comprises applying rigid registration parameters, especially a rigid transformation matrix, and affine registration parameters, especially an affine transformation matrix, to one or more regions of the FE model dummy material, especially corresponding to fibers of an annulus fibrosus of the intervertebral disc.

11. The computer-implemented method according to any one of the preceding claims, the method further comprising:conducting of a multibody simulation modeling, also referred to as MBS modeling, for the generation of an MBS model for forces acting on the spine and / or in the spine, in particular from the segmentation mask; andcombining of the MBS model with the FEM model.

12. The computer-implemented method according to claim 11, wherein during the generation of the MBS model at least one vertebral body geometry is derived from the segmentation mask as a surface mesh and a kinematic chain based on predefined coordinates for joints, in particular intervertebral joints, of the spine is prepared, wherein in particular missing bodies are replaced by pre-created or generic body models.

13. The computer-implemented method according to claim 12, wherein for the preparation of the kinematic chain body- and / or spine-specific parameters, in particular torso weight, in particular via segment masses from the segmentation mask or from predefined segment masses with respective gravity centers per spinal level with rigid connection to the respective vertebral body;and / or passive components such as intervertebral discs and / or ligaments as non-linear viscoelastic force elements, in particular from the segmentation mask or from predefined data; and / or musculature, in particular back musculature, based on predefined geometries and / or data, in particular from the segmentation mask or from predefined data, are added.

14. The computer-implemented method according to any one of claims 11 to 13, wherein from the MBS model a load by the forces and / or deformations on the FEM model or vice versa is applied.

15. A computer-implemented method for the simulation of at least a part of a spine, comprising the steps:executing of an image segmentation on at least one image, particularly from medical sectional imaging such as a CT and / or an MR image, of at least a part of the spine, for obtaining a segmentation mask;deriving of one or more vertebral body geometr(y / ies) and / or an intervertebral disc geometr(y / ies) as a surface mesh from the segmentation mask;generating of a finite element method model, also referred to as FEM model, from the surface mesh;conducting of a multibody simulation modeling, also referred to as MBS modeling, for the generation of an MBS model for forces acting on the spine and / or in the spine, in particular from the segmentation mask; andcombining of the MBS model with the FEM model.

Images