Automatic Modelling of Human Musculoskeletal Ligaments -- Framework Overview and Model Quality Evaluation
Noura Hamze, Lukas Nocker, Nikolaus Rauch, Markus Walzthöni, Fabio Carrillo, Philipp Fürnstahl, Matthias Harders
NNoname manuscript No. (will be inserted by the editor)
Automatic Modelling of Human MusculoskeletalLigaments – Framework Overview and Model QualityEvaluation
Noura Hamze · Lukas Nocker · NikolausRauch · Markus Walzth¨oni · FabioCarrillo · Philipp F¨urnstahl · MatthiasHarders Received: date / Accepted: date
Abstract
Accurate segmentation of connective soft tissues is still a challengingtask, which hinders the generation of corresponding geometric models for bio-mechanical computations. Alternatively, one could predict ligament insertion sitesand then approximate the shapes, based on anatomical knowledge and morpho-logical studies. Here, we describe a corresponding integrated framework for theautomatic modelling of human musculoskeletal ligaments. We combine statisti-cal shape modelling with geometric algorithms to automatically identify insertionsites, based on which geometric surface and volume meshes are created. For demon-strating a clinical use case, the framework has been applied to generate modelsof the interosseous membrane in the forearm. For the adoption to the forearmanatomy, ligament insertion sites in the statistical model were defined accord-ing to anatomical predictions following an approach proposed in prior work. Forevaluation we compared the generated sites, as well as the ligament shapes, todata obtained from a cadaveric study, involving five forearms with a total of 15ligaments. Our framework permitted the creation of 3D models approximating lig-aments’ shapes with good fidelity. However, we found that the statistical modeltrained with the state-of-the-art prediction of the insertion sites was not alwaysreliable. Using that model, average mean square errors as well as Hausdorff dis-tances of the meshes increased by more than one order of magnitude, as comparedto employing the known insertion locations of the cadaveric study. Using the lat-ter an average mean square error of 0.59 mm and an average Hausdorff distanceof less than 7 mm resulted, for the complete set of ligaments. In conclusion, thepresented approach for generating ligament shapes from insertion points appearsto be feasible but the detection of the insertion sites with a SSM is too inaccurate.For this part, another more patient-specific approach should be followed. Keywords
Musculoskeletal Ligaments · Gaussian Process Morphable Model · Geometric Modelling · Interosseous Membrane Interactive Graphics and Simulation Group, University of Innsbruck, Austria. Computer Assisted Research and Development Group, Balgrist University Hospital, Univer-sity of Zurich, Switzerland.CONTACT Noura Hamze. Email: [email protected], Matthias Harders. Email:[email protected] a r X i v : . [ c s . G R ] M a r Noura Hamze et al. In orthopedic surgery, an accurate diagnosis and the subsequent preoperative plan-ning of the surgical steps are crucial for the successful restoration of a patient’sanatomy. High precision in the preoperative planning and the surgical executionare mandatory for ensuring satisfactory clinical outcomes (e.g. [1, 2]). Three-dimensional, computer-assisted approaches have become the established optionas they contribute to a more comprehensive planning. Providing dynamic biome-chanical simulations allows for the analysis of complex pathologies, as well as anevaluation of a larger range of possible intervention strategies. Nevertheless, mostpreoperative methods are currently limited to simple bone-based models, not tak-ing into account the influence of soft tissue.For the correct diagnosis of soft tissue influence in case of impairment of thepatient function, a simulation framework also integrating the influence of rele-vant soft tissue structures is required. As an example, the kinematics of forearmpro-supination, and the resulting range of motion, is highly influenced by the in-terosseous membrane (IOM). The latter is the strongest ligament structure in theforearm, connecting radius and ulna bones [3, 4]. Previous studies have demon-strated that it is the main stabilizing element during forearm motion [3, 4, 5, 6],and thus has to be included in respective simulations. However, creating a geomet-ric simulation model of such soft tissue structures is a challenging task, becauseof the high inter-subject variation in their shapes and insertion sites. Further, thesegmentation of ligaments in medical images is hardly possible in a reliable way,due to low contrast to neighboring anatomy.Regarding biomechanical simulations, some prior works have modelled liga-ments from patient-specific segmentations. For instance, models of the anteriorcruciate ligament of the knee have been generated using morphological operationscombined with active contours [7] or graph cuts with shape constraints [8], appliedto MR images. However, processing MR data acquired with clinical protocols isoften not possible due to poor resolution and data heterogeneity. Other works haverelied on surrogate modeling methods, based on prior knowledge of the ligaments’shapes and locations. A common approach here is to employ single or multipleline segments connecting bones (see e.g. for the knee [9, 10], forearm [11], or el-bow [12]). In these models, the line segments are considered as linear springs; this isstraightforward, but has several limitations, such as the inability to describe com-plex geometry or to predict nonuniform stresses and strains. As a more accuratealternative, the use of 3D finite element models for simulations has been proposed(e.g. for analyzing the knee [13, 14], ankle [15], shoulder [16] or wrist [17]). Fi-nally, statistical shape models have also been explored in this context, e.g. forACL reconstruction [18] or for the planning of corrective orthopedic surgeries ofmalunited forearm bones [19].We strongly believe that one reason for the limited clinical translation of func-tional preoperative planning, which is based on range of motion simulation in the forearm [20, 21, 22, 23, 24], is associated with the difficulty of obtaining reliablepatient-specific 3D models of the IOM ligaments. Motivated by these limitations,we aimed to develop a novel framework capable of generating 3D ligament modelsin an automatic fashion based on statistical shape models and geometric meshingalgorithms. The work will contribute to improve the accuracy of patient-specific itle Suppressed Due to Excessive Length 3 motion simulations in the forearm. Our approach was evaluated by comparingligaments segmented from a cadaver study against models of our framework. band on the ulna is labeled as AB U, while the proximal insertion point on thecentral band on the radius is specified as CBP R.Regarding anatomical locations of insertion points, one of the most completeanatomical studies of the IOM was performed by Noda et al. [27], incorporating 30cadaver forearm specimens. They specified the 3D locations of IOM ligament origin
Noura Hamze et al. and insertion as distance percentages, given as the ratio of the distance from thedistal part of the corresponding bone to its total length. In addition, they providedwidths and thicknesses of the structures. This state-of-the-art study will serve as aguide for the construction of the statistical shape model of our framework. Below,in Section 2.2 we first detail the setup of the statistical model in a pre-processingstep. Note that there will be four different submodels, one each for radius andulna, left and right side. Thereafter, in Section 2.3 we outline the use of the shapemodel to generate new ligament meshes in a patient-specific fashion.2.2 Pre-Processing – Statistical Shape Modelling Statistical shape models (SSMs) are a well established approach to describe thevariability of a class of similar shapes (see e.g. [28] for an overview). In SSMs, akey step is to determine variability across a set of constitutive samples, as well asthe mean shape. With this information, the SSM permits to approximate any newcandidate shape from the same class. A key step for SSMs is to establish point-to-point correspondences between input samples. To this end, we make use of aGaussian Process Morphable model (GPMM), as outlined in [29], which extendsSSMs and permits incorporating expressive shape priors; in our case landmarks ofligaments on forearm bones. In GPMMs, shape deformations are represented as aGaussian process, also permitting combination of multiple levels of deformations.Next, we describe the medical datasets from which the SSMs were built.
Training data were obtained from CT scans of 18 healthy forearms, acquired usinga Somatom Edge Plus scanner (Siemens Medical Systems, Erlangen, Germany);with 1 mm slice thickness, at 120 kV . 3D meshes of the radii and ulnae boneswere segmented via intensity thresholding and region growing (Mimics Medical,Version 19.0, Materialise 2016, Leuven, 195 Belgium), followed by 3D marchingcube reconstruction [30]. The average number of vertices in a bone mesh was12K, which was further reduced to 3K using mesh decimation methods providedby ParaView [31]. Thereafter, six 3D coordinates for the ligaments’ landmarkswere manually identified on each bone, guided by Noda’s prescribed percentages.The manual labelling was performed by an orthopedic resident at the BalgristUniversity Hospital Zurich, with the Medical Imaging ToolKit MITK [32]. Thesedetails of ligament locations are consistently propagated through the subsequentpipeline.Next, to be able to create a SSM, consistency has to be ensured across thecontributing shapes by aligning them into the same coordinate system, enforc-ing the same number of vertices in all meshes, and establishing point-to-point correspondence between the vertices. In a first step, all bone meshes are rigidlytransformed, starting with a coarse alignment of all bones according to the mainaxis of the longest one, followed by a fine alignment via the iterative closest point(ICP) registration [33], implemented in the Insight Segmentation and Registra-tion Toolkit (ITK) [34]. For the resulting aligned four sets of input meshes X (one itle Suppressed Due to Excessive Length 5 each for radius and ulna, left and right side), we next set up GPMMs to facilitateobtaining the correspondences [29]. The setup starts with the selection of a reference bone mesh; a typical choice beingthe average bone shape or one of the aligned input meshes. For each representativebone, denoted by Γ m ∈ X , we assign a Gaussian process GP ( µ, k ) over the shapedomain Ω . Here, function µ : Ω → R encodes the mean deformation (i.e. shapevariation) between instances in X ; the latter being expressed as the mean squaredistance between points of two shape surfaces. Further, the Gaussian process kernel k : Ω × Ω → R × is a covariance matrix function, expressing the spread ofdeformations inside X . Note that a key advantage of using GPMMs is the optionto use multi-scale kernel Gaussian processes k ms . We employ a smooth kernel k g for the landmarks as well as a larger scale one k h for the bones, leading to anexpression via a sum of two functions: k ms ( x, y ) = k g ( x, y ) + k h ( x, y ) . This permits to conveniently include the ligaments’ landmarks with constraintposition variations into the model, thus ensuring that these details are includedin the shape-prior for the following registration. For setup of the GPMM we em-ploy the open source shape modelling libraries Scalismo [35] and Statismo [36].Following [29], we then make use of the GPMMs for establishing point-to-pointcorrespondence between the training samples in X . The problem of finding correspondences is formulated as a non-rigid registrationbetween a target shape surface Γ i represented by a set of 3D points, and a binaryreference image I m , constructed from the Gaussian process reference mesh Γ m .In the registration, a transformation function is sought that minimizes the meansquared distance from the reference image to the closest target point in currentshape Γ i . Applying this transformation to all sample shapes in X yields mesheswith the desired properties – i.e., all meshes have the same number of vertice withestablished point-to-point correspondences, in the same coordinate system. Thewhole process is carried out again using ITK implementations. For the optimizationin ITK, the Limited Memory Broyden Fletcher Goldfarb Shannon minimizationwith simple bounds (LBFGSB) [37] is employed. Note that the insertion locationsare maintained according to the GPMM formulation. In the final phase, a PrincipalComponent Analysis (PCA)-model is built from the generated intermediate bonemeshes with correspondences. Following the PCA scheme, we create the final statistical model. Reference shapes Γ R with insertion landmarks can be obtained, as linear combination of the meanshape and the most important Eigen-shapes. Note that knowledge about the land-marks’ positions is implicitly embedded into the model through a restriction in Noura Hamze et al.(a) PCA-model construction from a setof shapes in correspondence after fitting,landmarks indicated as red circles. (b) Comparison in 3D of generatedlandmarks (red) to manually anno-tated ones (green). Fig. 2: Statistical shape model of forearm bones.variation in the intermediate input data. The restriction can be regarded as geo-metric constraints fixing parts of the bone at the ligament connection sites. Fig-ure 2a illustrates the PCA-model resulting from a set of meshes in correspondencewith landmarks. In order to assess the accuracy of the shape model, we carriedout a cross-validation study with leave-one-out testing. We found a mean error of3 mm in the landmarks’ locations across all data samples. Figure 2b also qualita-tively compares landmarks obtained with our framework with manually annotatedones.2.3 Patient-Specific Ligament Model Generation The target of the model generation process is the automatic creation of ligamentmeshes, based on the known bone geometry of a specific patient, but without anyknowledge about the ligaments. To predict the ligament insertion sites, we relyon the SSMs described in Section 2.2.5. In the first step, landmarks of ligamentinsertions are automatically transferred to the 3D patient-specific bone mesheswhich can be obtained by segmentation of medical image data. In the second step, 3D surface models represented by triangles or, if needed, volumetric meshesrepresented by tetrahedra are generated, approximating the shapes of the liga-ments. The modelling is based on the identified landmarks as well as on additionalanatomical parameters. The key steps in the modelling pipeline are overviewed inFigure 3. itle Suppressed Due to Excessive Length 7(a) Alignment oftarget Γ T (yellow;shown before andafter) to reference Γ R (green). (b) Fitting processvia establishingcorrespondences. (c) Projection oflandmarks. (d) Creation ofligament meshes(with an instanceshown for twoinsertion points). Fig. 3: Overview of the modelling pipeline.
In order to transfer a set of landmarks P to a patient target bone shape Γ T , thelatter is first aligned to the reference shape Γ R of each bone-specific SSM, via theICP algorithm. Next, the target shape is fitted to Γ R , following the same processused before for establishing point-to-point correspondences (see Section 2.2.4).Finally, the set of landmarks found on the SSM are projected onto the targetpatient bone shape. For each landmark in the reference shape the closest vertexon the aligned and fitted target shape Γ T is found and labeled as that respectiveligament landmark. The output of this phase is a patient-specific bone mesh withall ligament insertion points.
3D meshes of ligaments are generated based on the patient-specific bone meshesand associated landmarks of the previous step. As additional information, thick-ness of ligaments, and potentially also their width has to be supplied. The processis again outlined for the test scenario of the IOM, but transfers directly to anyother anatomy.The process is carried out in several substeps. First, four vertices are identi-fied – the proximal and distal ends of a ligament on each bone. Next, pairs ofthese are connected, yielding four line segments forming a quadrilateral surface.The line segments are then regularly discretized, yielding a set of vertices on thequadrilateral boundary; some vertices are further projected onto bones surfaces for a better fit. Based on all boundary vertices, new vertices are then generatedwithin the quadrilateral. A triangle mesh is finally generated from all vertices andperpendicularly extruded. Figure 4 indicates the vertices generated in this process,in case of the CB. In the following, the individual shape modelling substeps willbe addressed with more detail.
Noura Hamze et al. Fig. 4: Vertices generated for building the initial ligament surface triangle mesh(in order of creation; orange : ligament endpoints, red : sampled traversal segments, grey : sampled bone-aligned segments, black : projected samples, green : sampledligament sheet).The objective is to model a 3D surface of a ligament connecting two bonesurfaces. As mentioned above, the starting points are four vertices located at theproximal and distal ends of a ligament on the radius and ulna meshes (orangevertices). According to the setup of the SSMs, in case of the CB these vertices aredirectly given by the four landmarks; i.e. vertices p CBP R , p CBD R , p CBP U , p CBD U ,which in addition also yield the widths of a ligament along a bone directly on thesurface. For the remaining ligaments (DOB, AB, DOAC, POC), only a mid-pointlandmark is available from the SSMs. In this case the four vertices at the ligamentends are found via the bone main axes direction vectors d R or d U (pointing fromproximal to distal end), and associated ligament widths per bone w R or w U . Theformer can be computed from the bone meshes, the latter have to be user-defined.This also results in four vertices; for instance, for AB we determine as one vertex p ABD R = p AB R + 0 . · w R · d R .Next, forming pairs of some of the four vertices – i.e. on each bone (magentaline segments), as well as traversally between the proximal and distal ends (stip-pled black line segments) – yields a quadrilateral surface. Note that the former linesegments may intersect the bone meshes or the endpoints may not directly touchthe bone surfaces. Subsequently, the line segments are regularly subdivided yield-ing additional vertices. The sampling is controlled via user-supplied parameters,indicating the intra-(along the bone) and inter-bone number of samples per liga-ment; in our experiments intra- and inter-bone sampling were, for instance in thecase of CB, set to 10 and 12, respectively. The resulting 3D vertices are depictedas grey and red circles on the line segments.As previously indicated, the line segment along each bone (magenta), and thusthe sampled vertices (grey), will likely not be located directly on the bone mesh.Thus, in an additional step, these vertices are first projected onto the nearest bone mesh triangle along its normal whereafter the nearest existing vertex on the bonesurface is finally found (black vertices). The reason for using existing vertices is theeasier handling of boundary conditions in a potential subsequent biomechanicalsimulation, e.g. using finite element meshes. Overall, this results in a piecewiselinear approximation of the ligament contact on the bone surface (blue). itle Suppressed Due to Excessive Length 9 Based on the vertices – i.e. those on the transversal segments (red) and the pro-jected ones (black) – additional 3D vertices are then generated at regular locations(green), via linear interpolation of positions. Next, using the incremental builderfunctionality of the Computational Geometry Algorithms library CGAL [38], apolygonal (triangle) surface is constructed from all vertices. Note that we employa halfedge data structure to maintain incidence information of vertices, edges,and faces, using the CGAL Halfedge package [39]. An example of such a result-ing triangle mesh is illustrated in Figure 5a. Finally, to incorporate the ligamentthickness, the mesh is extruded into normal direction, via the Linear Extrusionfilter of ParaView [31]. A parameter for the thickness also has to be supplied; inour experiments we employed values in the range of 1 to 4 mm . The overall resultis a 3D piecewise linear mesh, approximating the surface of a single ligament.As an additional step, the surface triangle mesh of a ligament can be fur-ther transformed into a volumetric tetrahedral mesh. This is carried out with theConstrained Delaunay-based quality tetrahedral mesh generator TetGen [40]. InTetGen, the mesh quality can be controlled either by enforcing a maximum volumeor a minimum radius value for each element. As an example, we have used radii ina range of 0.6 to 1 mm . Steiner points are added inside the ligament mesh volumeto satisfy the imposed constraint. An example mesh is visualized in Figure 5b. (a) Generated intermediate trianglemesh. (b) Visualizations of tetrahedral 3D volume meshcreated in two steps.
Fig. 5: Examples of generated ligament 3D surface and volume models (in thiscase, for the CB of dataset DS ). In a first study, we examined the accuracy of the landmarks that were automati-cally generated with our presented framework. To do so, we obtained ground truthdata via a cadaveric study (see also [41]). In the latter, radial and ulnar insertionlocations of the ligaments were visually identified on five forearm specimens (twofemale, three male); associated datasets are denoted below as DS to DS . Theindividual ligaments of the IOM were marked by a surgeon with titanium ligation et al. clips, via a clip applicator tool (Ethicon endo-surgery, LLC, USA). Note that thePOC could not be labeled in any of the samples. Moreover, in the specimens ei-ther the DOAC or the DOB was present, but not both; the former was found infour cases, the latter only in one. This finding is in line with current anatomicalknowledge about variation in forearm ligaments (see e.g. [4, 27]).For annotation of DOB, AB, and CB four clips were employed, at the proximaland distal insertion locations of the ligament attachments on both bones, respec-tively. Further, due to its narrow width, the DOAC was annotated using only onemetal clip per bone. The markers were placed at the centers of the attachmentsof its main fiber bundle. An example image of an annotated specimen is shownin Figure 6. Thereafter, Micro-CT as well as CT images were obtained from theannotated cadaveric arms. In the resulting image data, all IOM insertion locationswere then manually segmented; the latter subsequently serving as ground truthfor the comparison.Fig. 6: Annotation of ligaments with metallic clips in cadaver forearms; DS shownas example.Next, using our proposed framework, we automatically obtained an additionalset of landmarks via our SSM. As outlined, the input to the process was the bonesurface meshes created from segmentations of the CT scans of the five cadaverarms. The output was the estimated landmarks of the IOM ligaments, matchingthe input geometries.For further processing, in both the SSM-predicted and ground truth datasets,we computed for the wider ligaments (i.e. those with four marked locations; twoproximal and two distal) the average mid-points. Based on this, we finally deter-mined the (cid:96) -vector norm of the distances between the locations in the groundtruth data and in the framework output. The averages of the distance errors arevisualized per insertion location mid-point in millimeters in Figure 7a. Note thatdue to the presence or absence of ligaments, some values are only based on a singlemeasurement (i.e. the DOB).Excluding the AB, the average errors range between 2.5 mm and 12.0 mm ; i.e. for CB, DOAC, and DOB. In contrast, the AB exhibits considerably largererrors of about 30 mm . This large value is mainly caused by dataset DS , forwhich the respective ligament was exceptionally proximal.Besides the insertion locations, the accuracy of the generated models can beassessed by examining the widths of the ligaments. Figure 7b shows exemplary thewidth of the CB for the five specimens, separately for radius and ulna. An average itle Suppressed Due to Excessive Length 11(a) Mean square error in landmark mid-pointlocations in mm , comparing SSMs landmarkswith those from cadaver study. (b) Error in widths for CB in mm . Fig. 7: Quantitative evaluation of landmarks locations and ligament width.width of about 35 mm was found for this band in the cadaver dataset. Note thatthis differs considerably from the 9.7 mm average reported by Noda et al.3.2 Similarity of Generated Ligament MeshesIn the second experiment, we examined the geometric similarity of ligament sur-face triangle meshes, generated following different strategies. As ground truth weemployed meshes, which were manually segmented by a medical student in thepreviously described cadaveric study. Starting points for these were raw ligamentmeshes which were then cut employing ParaView [31] into three sub-components,according to the provided metallic clip annotations (see Section 3.1) on both ra-dius and ulna. Note that when only the ligament mid-points were known, thenwidths were set according to quantitative measurements of the cadaver study. Theresulting meshes were further improved, e.g. by filling holes. Overall, this resultedin three triangle surface meshes, for the respective ligaments present in the forearmspecimen datasets DS to DS .To this ground truth M GT we then compared two sets of ligament meshesgenerated with our geometric modelling framework. For the first, we obtain inser-tion locations with our newly developed statistical framework. The widths of theligaments were given according to the findings by Noda et al. [27]; i.e. 9.7 mm forCB, 3.2 mm for DOAC, and 4.4 mm for DOB, respectively. Further, in the case ofAB, an experimental value of 7 mm was assigned, since this measurement was notprovided in their study. Similarly, thickness was set according either to their data,or to the values of our cadaver study. For the second set of meshes, the generationprocess was repeated, however, this time using the ground truth locations of themetallic clips as insertion points. Moreover, widths and thicknesses were set asmeasured in [41]. Overall, this resulted in two additional sets of meshes M sta and M clp , which were compared against the ground truth. To illustrate the resultingtriangle mesh surfaces, Figure 8 depicts these exemplary for dataset DS . Meshesare rendered for the ligaments DOAC, CB, and AB, showing the ground truth(beige) against the modelled ligament meshes (red). Ligaments generated withinsertions from the statistical framework are shown on top, those using the anno- et al. tated clips instead on the bottom. Note that in the latter case the visual similarityis higher, since the same insertion locations and widths were employed. (a) Modelling with landmarks from our statistical model.(b) Modelling with landmarks given via clip annotation. Fig. 8: Comparison of modelled ligament meshes (red) against ground truth (beige) for example dataset DS (in this case comprising AB, CB, DOAC).In order to quantify the similarity between a modelled triangle surface mesh( M ) and the ground truth ( GT ), we computed four standard shape similaritymetrics:1. the mean Euclidean distance d ME – for all vertices in M to their nearestneighbor vertices in GT ;2. the average symmetric surface distance d AS – averaging all distances, fromvertices in M to nearest neighbors in GT and vice versa;3. the root mean square distance d RMS – given as square root of the average ofall square distances from vertices in M to nearest neighbors in GT and viceversa;4. the common Hausdorff distance d HD between two points sets (see e.g. [42]).The latter is given as the largest of all distances from a vertex in one mesh tothe closest point in the other mesh. Applying these metrics, we obtain similaritymeasurements for both sets of modelled ligaments, in comparison to the groundtruth. The data are compiled in Table 1. For each of the five forearm specimensthe similarity metrics are provided (in mm ) per ligament and modelling approach.Also, the average over all values is specified.As can be seen, surface meshes modelled using statistical prediction of inser-tion locations ( M sta ) exhibit larger errors compared to using the exact insertion locations ( M clp ). This is expected, since in the latter case the error to the groundtruth is only due to differences in shape of the surfaces. In contrast, in the formercase it is also resulting from differences in the ligament attachments and widths.Clear outliers (in bold) are the d ME metrics for the AB in DS and DS . Themain reasons is the identification of the AB ligaments in those cadaver specimens itle Suppressed Due to Excessive Length 13 on the proximal instead of the distal portion of the bones. Such a case was notincluded in the SSM training data. This underlines the high morphological varia-tion in the forearm ligament anatomy. The relatively low errors for M clp indicatethat the ligament mesh modelling process can provide reasonable results, giveninsertion locations and widths of sufficient accuracy.Table 1: Similarity errors in mm between ground truth and ligament meshesmodelled with our pipeline, assuming different insertion locations and widths;compiled for three ligaments in five cadaver specimens (note DOAC vs. DOB);outliers are shown in bold. Data- Liga- d HD d ME d AS d RMS set ment M sta M clp M sta M clp M sta M clp M sta M clp DS AB 22.14 5.74 8.97 0.24 5.92 0.73 7.875 1.161CB 31.64 7.48 0.33 0.28 5.45 0.99 7.73 1.38DOAC 13.40 7.20 4.55 0.49 3.11 1.50 3.87 1.93 DS AB 24.90 7.70 2.91 0.38 7.01 1.45 8.85 2.23CB 13.82 9.61 0.62 0.84 4.06 1.74 4.81 2.37DOAC 20.17 3.83 2.89 0.65 5.00 1.37 6.91 1.65 DS AB 95.98 3.13 DS AB 75.41 2.23 DS AB 46.22 9.47 59.77 0.60 19.53 1.48 22.12 2.04CB 27.71 6.81 13.75 0.75 5.18 1.19 7.54 1.45
DOB
Average
We have outlined an automatic framework for patient-specific musculoskeletal liga-ment modelling. To this end, we combined statistical shape models with landmarktransfer and mesh generation algorithms. As a proof of concept we applied thegeneric framework to the test scenario of the interosseous membrane of the fore-arm. For this, a statistical shape model was created based on forearm image dataof 18 healthy subjects. Our framework was then evaluated using an additionaldataset of five annotated cadaver forearm specimens. Ligament insertion locationsand shapes based on our framework have been compared to the reference speci-mens.The landmark transfer algorithm is capable of automatically generating land-marks for any ligament based on a statistical anatomical shape model. Regarding the latter, for our test scenario the training dataset was still relatively small, withonly 18 samples. Nevertheless, increasing the number of samples on the same orderof magnitude may not directly lead to a large accuracy improvement, due to thehigh anatomical variation of the IOM ligaments and insertion locations amonghumans. Our study indicates that using distance ratios on average bone shapes, et al. as proposed in previous work such as Noda et al. may not be of sufficient precisionfor a reliable clinical application. Another source of inaccuracy may arise fromthe labeling process, both for the SSM training samples as well as the cadavericstudy; this step was performed by only a single person, which may also introducedeviations from the exact locations. Further, the number of samples in the ex-vivoexperiment was low and may have to be increased to allow for an improved quan-titative assessment. Finally, the separation of the segmented IOM complex intoseparate bands likely also has suffered from inaccuracies.As outlined in our study, errors were still found between ligaments modelledaccording to SSM generated insertion points and corresponding segmentations ofground truth data. Nevertheless, given accurate ligament attachments and widths,our modelling framework can generate shapes with reasonable accuracy. Still,smaller error is introduced according to the anatomical distribution of thicknessand width of the ligaments, which are irregular across axial and medial direction[41, 43]. Another source of possible inaccuracy in our modelling algorithm canbe the ligament-bone connection boundaries. These were defined by line segmentsalong the bone surface, between two given vertices. Modelling these as spline curvesinstead may increase accuracy.Nevertheless, to the best of our knowledge, our study is the first to providequantitative comparisons of automatically modelled interosseous membrane liga-ment shapes with meshes based on ex-vivo data. Moreover, we have presented aframework for automatic ligament mesh generation; it is generic and can easilybe applied to the modelling of other ligaments in the human body. It remains tobe seen, which effect errors in the geometric shapes of ligaments will have on theoverall forearm motion behavior in biomechanical simulations.Overall, the described development is part of a larger research project focusingon improving the quality of preoperative planning in upper extremities. The in-troduced framework constitutes one step towards a more accurate representationof ligaments for simulations of forearm motion. The inclusion of soft tissues intothe preoperative planning is generally a challenging task, which requires sufficientquality of the geometric models of the anatomy. Further, ligament simulation istime-consuming and highly dependent on the morphological data. Nevertheless,mere anatomical information of soft tissue attachments along forearm bones couldalready improve the preoperative pipeline. For example, better implant positionscould be chosen, when taking into account the presence of soft tissue. Also, timeduring surgery could be saved and healing times be improved, by generating lessinvasive intraoperative interventions. Still, in future work we will focus on using themeshes in biomechanical simulations in the context of computer-assisted forearmsurgery planning. Acknowledgements
This work was supported by the Swiss National Science Foundation,under grant number 325230L 163308, and the Austrian Science Fund FWF, under grant num-ber I 2545-N31.
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