Joint surface modeling with thin-plate splines

A novel thin plate spline methodology to model tissue surfaces and quantify tumor cell invasion in organ-on-chip models

Organ-on-chip (OOC) models can be useful tools for cancer drug discovery. Advances in OOC technology have led to the development of more complex assays, yet analysis of these systems does not always account for these advancements, resulting in technical challenges. A challenging task in the analysis of these two-channel microfluidic models is to define the boundary between the channels so objects moving within and between channels can be quantified. We propose a novel imaging-based application of a thin plate spline method - a generalized cubic spline that can be used to model coordinate transformations - to model a tissue boundary and define compartments for quantification of invaded objects, representing the early steps in cancer metastasis. To evaluate its performance, we applied our analytical approach to an adapted OOC developed by Emulate, Inc., utilizing a two-channel system with endothelial cells in the bottom channel and colorectal cancer (CRC) patient-derived organoids (PDOs) in the top channel. Initial application and visualization of this method revealed boundary variations due to microscope stage tilt and ridge and valley-like contours in the endothelial tissue surface. The method was functionalized into a reproducible analytical process and web tool - the Chip Invasion and Contour Analysis (ChICA) - to model the endothelial surface and quantify invading tumor cells across multiple chips. To illustrate applicability of the analytical method, we applied the tool to CRC organoid-chips seeded with two different endothelial cell types and measured distinct variations in endothelial surfaces and tumor cell invasion dynamics. Since ChICA utilizes only positional data output from imaging software, the method is applicable to and agnostic of the imaging tool and image analysis system used. The novel thin plate spline method developed in ChICA can account for variation introduced in OOC manufacturing or during the experimental workflow, can quickly and accurately measure tumor cell invasion, and can be used to explore biological mechanisms in drug discovery.

A novel thin plate spline methodology to model tissue surfaces and quantify tumor cell invasion in organ-on-chip models

Organ-on-chip (OOC) models can be useful tools for cancer drug discovery. Advances in OOC technology have led to the development of more complex assays, yet analysis of these systems does not always account for these advancements, resulting in technical challenges. A challenging task in the analysis of these two-channel microfluidic models is to define the boundary between the channels so objects moving within and between channels can be quantified. We propose a novel imaging-based application of a thin plate spline method - a generalized cubic spline that can be used to model coordinate transformations - to model a tissue boundary and define compartments for quantification of invaded objects, representing the early steps in cancer metastasis. To evaluate its performance, we applied our analytical approach to an adapted OOC developed by Emulate, Inc., utilizing a two-channel system with endothelial cells in the bottom channel and colorectal cancer (CRC) patient-derived organoids (PDOs) in the top channel. Initial application and visualization of this method revealed boundary variations due to microscope stage tilt and ridge and valley-like contours in the endothelial tissue surface. The method was functionalized into a reproducible analytical process and web tool - the Chip Invasion and Contour Analysis (ChICA) - to model the endothelial surface and quantify invading tumor cells across multiple chips. To illustrate applicability of the analytical method, we applied the tool to CRC organoid-chips seeded with two different endothelial cell types and measured distinct variations in endothelial surfaces and tumor cell invasion dynamics. Since ChICA utilizes only positional data output from imaging software, the method is applicable to and agnostic of the imaging tool and image analysis system used. The novel thin plate spline method developed in ChICA can account for variation introduced in OOC manufacturing or during the experimental workflow, can quickly and accurately measure tumor cell invasion, and can be used to explore biological mechanisms in drug discovery.

Empirical joint contact mechanics: A comprehensive review

Empirical joint contact mechanics measurement (EJCM; e.g. contact area or force, surface velocities) enables critical investigations of the relationship between changing joint mechanics and the impact on surface-to-surface interactions. In orthopedic biomechanics, understanding the changes to cartilage contact mechanics following joint pathology or aging is critical due to its suggested role in the increased risk of osteoarthritis (OA), which might be due to changed kinematics and kinetics that alter the contact patterns within a joint. This article reviews and discusses EJCM approaches that have been applied to articulating joints such that readers across different disciplines will be informed of the various measurement and analysis techniques used in this field. The approaches reviewed include classical measurement approaches (radiographic and sectioning, dye staining, casting, surface proximity, and pressure measurement), stereophotogrammetry/motion analysis, computed tomography (CT), magnetic resonance imaging (MRI), and high-speed videoradiography. Perspectives on approaches to advance this field of EJCM are provided, including the value of considering relative velocity in joints, tractional stress, quantification of joint contact area shape, consideration of normalization techniques, net response (superposition) of multiple input variables, and establishing linkages to regional cartilage health status. EJCM measures continue to provide insights to advance our understanding of cartilage health and degeneration and provide avenues to assess the efficacy and guide future directions of developing interventions (e.g. surgical, biological, rehabilitative) to optimize joint's health and function long term.

Estimating motion between avian vertebrae by contact modeling of joint surfaces

Estimating the motion between two bones is crucial for understanding their biomechanical function. The vertebral column is particularly challenging because the vertebrae articulate at more than one surface. This paper proposes a method to estimate 3D motion between two avian vertebrae, by bones surface reconstruction and contact modeling. The neck of birds was selected as a case study because it is a functionally highly versatile structure combining dexterity and strength. As such, it has great potential to serve as a source for bioinspired design, for robotic manipulators for instance. First, 3D models of the vertebrae are obtained by computed tomography (CT). Next, joint surfaces of contact are approximated with polynomial surfaces, and a system of equations derived from contact modeling between surfaces is established. A constrained optimization problem is defined in order to find the best position of the vertebrae for a set of given orientations in space. As a result, the possible intervertebral range of motion is estimated.

Three dimensionality of gleno-humeral deformities in obstetrical brachial plexus palsy

The primary objective of this study was to test the hypothesis that gleno-humeral deformity in children and adolescent with obstetrical brachial plexus palsy is three-dimensional (3D). The study also compared the metrological properties of typical two-dimensional gleno-humeral measures to the newly developed 3D measures. Thirteen individuals (age = 11.8 ± 3.3 years) with obstetrical brachial plexus palsy participated in this IRB-approved study. 3D axial magnetic resonance images were acquired for both shoulders. Glenoid and humeral models were created in order to quantify 3D glenoid version, humeral head migration, and glenoid concavity. Two-dimensional (2D) measures were acquired as recommended in the literature. All measures were completed by two observers in this observer-blind study. Compared to the non-involved side, the glenoid was more retroverted (7.91°, p = 0.003) and inferiorly oriented (7.28°, p = 0.009). The humeral head was migrated more posteriorly (5.54 mm, p = 0.007), inferiorly (-3.96 mm, p = 0.013), and medially (-3.63 mm,p = 0.002). Eleven of the 13 glenoids were concave, based on the 3D glenoid models. The concurrent validity between three- and 2D measures were highly dependent of the parameter measured, the slice level used for the 2D analysis, and the presence/absence of pathology (0.63 < r < 0.91). The standard error of measurement for the 2D anterior-posterior version (>3°) was larger than that for the 3D measure of version (<1°) on the involved side. This study clearly demonstrated that the gleno-humeral deformation in obstetrical brachial plexus palsy is 3D, emphasizing the need for 3D subject specific gleno-humeral shape analysis for follow-up and treatment plans in children with obstetrical brachial plexus palsy.

A new measure of tibiofemoral subchondral bone interactions that correlates with early cartilage damage in injured sheep

We have demonstrated previously that chondral damage is associated with increased knee surface velocities following ligament and meniscus injuries in sheep. We tested the hypothesis that cartilage damage scores would correlate with a new bone surface interaction measure that captures complex changes in tibiofemoral alignment, "proximity disturbance" (PD). Six sheep underwent combined anterior cruciate and medial collateral ligament transection (ACL/MCLx), five complete lateral meniscectomy (Mx), and four sham arthrotomy (Sham). Tibiofemoral subchondral bone surfaces were modeled, and the post-operative changes in relative separation of the surfaces (i.e., "proximity") were derived from subject-specific in vivo 3D stifle kinematics. Surface areas of regions of near contact were determined, and PD was calculated as the range of change in tibiofemoral proximity, divided by normalized overlapping proximity surface areas between baseline and post-operative time points. Cartilage morphology was graded at dissection. ACL/MCLx PD was significantly elevated relative to Mx and Shams, and correlated with cartilage damage (r(2)  = 0.88-0.98). Although not statistically significant, Mx PD values tended to be higher than those of Shams, and correlated with cartilage damage. Results from both injury models suggest that increasing change in tibiofemoral surface alignment may be increasingly deleterious to long-term cartilage health in sheep.

In vivo patellofemoral contact mechanics during active extension using a novel dynamic MRI-based methodology

OBJECTIVES

To establish an in vivo, normative patellofemoral (PF) cartilage contact mechanics database acquired during voluntary muscle control using a novel, dynamic, magnetic resonance (MR) imaging-based, computational methodology and validate the contact mechanics sensitivity to the known sub-millimeter methodological accuracies.

DESIGN

Dynamic cine phase-contrast and multi-plane cine (MPC) images were acquired while female subjects (n = 20, sample of convenience) performed an open kinetic chain (knee flexion-extension) exercise inside a 3-T MR scanner. Static cartilage models were created from high resolution three-dimensional static MR data and accurately placed in their dynamic pose at each time frame based on the cine-PC (CPC) data. Cartilage contact parameters were calculated based on the surface overlap. Statistical analysis was performed using paired t-test and a one-sample repeated measures ANOVA. The sensitivity of the contact parameters to the known errors in the PF kinematics was determined.

RESULTS

Peak mean PF contact area was 228.7 ± 173.6 mm(2) at 40° knee angle. During extension, contact centroid and peak strain locations tracked medially on the femoral and patellar cartilage and were not significantly different from each other. At 25°, 30°, 35°, and 40° of knee extension, contact area was significantly different. Contact area and centroid locations were insensitive to rotational and translational perturbations.

CONCLUSION

This study is a first step towards unfolding the biomechanical pathways to anterior PF pain and osteoarthritis (OA) using dynamic, in vivo, and accurate methodologies. The database provides crucial data for future studies and for validation of, or as an input to, computational models.

Tibiofemoral centroid velocity correlates more consistently with cartilage damage than does contact path length in two ovine models of stifle injury

Anterior cruciate ligament (ACL) rupture and/or meniscal injury are known risk factors for post-traumatic osteoarthritis. We tested the hypothesis that increasingly abnormal tibiofemoral centroid path lengths and velocities would correlate with the severity of cartilage damage in injured sheep. Six sheep underwent combined ACL/medial collateral ligament transection (ACL/MCLx), five complete lateral meniscectomy (Mx), and four sham arthrotomy (Sham). Weighted centroids were used to estimate in vivo tibiofemoral cartilage contact path length during stance and the velocity of relative motion. Cartilage morphology was graded at dissection. Ligament transection significantly elongated plateau centroid path lengths and velocities, whereas condyle paths and velocities were reduced. Differences between plateau and femoral velocities (relative centroid velocity) were increased up to 10-fold over baseline values in the medial compartment. Reductions in Mx lateral compartment paths were significantly different from ACL/MCLx paths, but not relative to baseline or Sham values. Importantly, only centroid velocities consistently correlated with cartilage damage in either injury model, suggesting that while path length is valuable in detecting changes in the envelope of joint motion, it may average out meaningful peaks in the rate of relative motion that more closely relate to the mechanisms that might be damaging articular cartilage in these models.

Alterated talar and navicular bone morphology is associated with pes planus deformity: a CT-scan study

We compared bone and articular morphology of the talus and navicular in clinically diagnosed flatfeet and evaluated their potential contribution to talo-navicular joint instability. We used CT images to develop 3D models of talus and navicular bones of 10 clinically diagnosed flatfeet and 15 non-flatfeet. We quantified their global bone dimensions, inclination and dimensions of the articular surfaces and their curvatures. Additionally, ratios of six talar and navicular dimensions were calculated. The values for these parameters were then compared between both groups. In flatfeet, the talar head faced more proximal and its width was larger compared to non-flatfeet. Also the navicular cup faced more proximal and its depth was significantly increased. Furthermore, we observed a more protruding talar head compared to the navicular cup in the control group with the articular surface depth being relatively larger for the navicular cups when compared to the talus in flatfeet. The ratio of the talar and navicular articular surface height was decreased in flatfeet, suggesting increased height of navicular cups relative to the articulating talar heads. Our results show that flatfoot deformity is associated with morphological changes of talar and navicular articular surfaces that can favor medial arch collapse and forefoot abduction.

IN-VIVOESTIMATION OF THE TIBIO-FEMORAL CONTACT AREA USING THIN-PLATE SPLINE TOOL

Interaction between articular surfaces at the knee joint allows movement and stability. The knowledge of how this mechanism works in physiological conditions could be very useful for the development of new clinical procedures. The objective of this study was to develop a subject-specific model able to estimate the articular contact area at the tibio-femoral joint avoiding any destructive measurements. Thin plate splines were used to describe articular surfaces and to allow an analytical estimation of the distance between the surfaces. The sensitivity of the model was evaluated and the tibio-femoral contact area was estimated in a living subject. Femoral contact area results were always smaller than the tibial one, whereas tibial contact area results were less repeatable. Increasing the distance threshold, the increase of the contact area was almost linear. High repeatability was obtained sampling each condyle with more than 60 steps. Contact areas, estimated with the loaded knee, were in accordance with physiology and literature showing a good repeatability. The devised model was suitably used to evaluate the articular contact at the knee joint of an healthy living subject and can be a useful clinical tool to suggest procedures aimed at restoring physiological conditions.

BIOMECHANICS OF THE INTACT AND REPLACED HUMAN ANKLE JOINT

The main objective of the study was to develop advanced biomechanical models of the intact human ankle complex. It was also aimed at designing a total ankle replacement which would better reproduce the physiological function of the joint. Passive flexion was analyzed in a number of lower-leg preparations with stereophotogrammetry and radiostereometry. The articular surfaces and fibres within the calcaneofibular and tibiocalcaneal ligaments were observed to prescribe the changing positions of bones, ligaments and instantaneous axis of rotation. Joint motion included rolling as well as sliding. Computer-based models elucidated this kinematics at the intact joint, and how changing positions of the centre of rotation and muscle lines of action affect lever arm length at different flexion angles. The mechanical response of the joint to anterior drawer and talar tilt tests was explained in terms of fibre recruitment. The experimental evidence and the geometrical models gave the basis for the design of a novel ankle replacement. A three-component, convex-tibia prosthesis was developed with articular surface shapes that are compatible with the geometry of the ligaments. The proposed prosthesis based on ligament/shape compatibility is showing encouraging results in initial implantation.

Mathematical reconstruction of human femoral condyles

There is a direct correlation between ligament function and the articulating surface of the normal knee, and changes to any of these structures can affect the other. This is also true for knee replacements, where the articulating surface is greatly changed compared to the natural knee. This study investigated the morphometry of healthy knees and proposes a method to predict original normal knee profiles. A variety of mathematical techniques are compared in terms of the accuracy with which they can represent the original knee joint geometry. Additionally, a method of predicting the irregular femoral condyle geometry for an individual knee is described by making use of the mathematical techniques presented, and the accuracy of this method is also investigated. The mathematical approach using B-splines provides flexibility and can accurately describe the complex geometry of the femoral condyles in both the sagittal and transverse planes. It was further found that the condyles are highly asymmetrical; therefore simpler methods cannot portray the condyles sufficiently and are especially inaccurate in representing the lateral condyle. The study proposes a method for predicting the geometry of the femoral condyles with good accuracy. The B-spline model showed best results.

Articular surface approximation in equivalent spatial parallel mechanism models of the human knee joint: An experiment-based assessment

In-depth comprehension of human joint function requires complex mathematical models, which are particularly necessary in applications of prosthesis design and surgical planning. Kinematic models of the knee joint, based on one-degree-of-freedom equivalent mechanisms, have been proposed to replicate the passive relative motion between the femur and tibia, i.e. the joint motion in virtually unloaded conditions. In the mechanisms analysed in the present work, some fibres within the anterior and posterior cruciate and medial collateral ligaments were taken as isometric during passive motion, and articulating surfaces as rigid. The shapes of these surfaces were described with increasing anatomical accuracy, i.e. from planar to spherical and general geometry, which consequently led to models with increasing complexity. Quantitative comparison of the results obtained from three models, featuring an increasingly accurate approximation of the articulating surfaces, was performed by using experimental measurements of joint motion and anatomical structure geometries of four lower-limb specimens. Corresponding computer simulations of joint motion were obtained from the different models. The results revealed a good replication of the original experimental motion by all models, although the simulations also showed that a limit exists beyond which description of the knee passive motion does not benefit considerably from further approximation of the articular surfaces.

Analysis Techniques for Congruence of the Patellofemoral Joint

Quantifying joint congruence may help to understand the relationship between joint function and health. In previous studies, a congruence index (CI) has been used to define subject-specific joint congruence. However, the sensitivity of the CI algorithm to surface representation was unknown. The purpose of this study was to assess the effects of applying five modifications (M1–M5) to the CI algorithm to determine whether the magnitude and variability of the patellofemoral CI is dependent on the surface representation used. The five modifications focused on calculating the CI based on the principal curvature (M1) at the centroid of the contact region, (M2) using an root mean square value for the contact region, (M3) using a mean value for the contact region, (M4) using all digitized points of the patellar surface, and (M5) using all digitized points in contact. The CI found using the contact area (M1, M2, M3, and M5) provides a local measure for congruence, which was shown to increase (decreasing CI) with increasing joint angle. In ten healthy subjects measured with magnetic resonance (MR) images, the patellofemoral joint became significantly more congruent as the knee angle increased from 15 deg to 45 deg using method M5. The magnitude and variability of the patellofemoral CI was dependent on the surface representation used, suggesting that standardization of the surface representation is important to provide a consistent measure. Specifically, M5 provides a local measure of joint congruence, which can account for joint position and orientation. M5 balances the ability to detect differences in congruence between knee angles without introducing high variability.

Smooth surface meshing for automated finite element model generation from 3D image data

Finite element (FE) modelling based on data from three-dimensional high-resolution computed tomography (CT) imaging systems provides a non-invasive method to assess structural mechanics. Automated mesh generation from these voxel based image data can be achieved by direct conversion to hexahedron elements, however these model representations have jagged edges. This paper proposes an automated method to generate smoothed FE meshes from voxel-based image data. Mesh fairing processes are utilized that allow constraints that control the smoothing process, and are computationally efficient. Surfaces of the mesh on the exterior, as well as interfaces between two tissues, can be smoothed by varying fairing parameters and constraint criteria. The method was tested on a variety of real and simulated three-dimensional data sets, resulting in both hexahedron and tetrahedron meshes. It was shown that the fairing process is linearly related to the number of smoothing iterations, and that peak stresses are reduced in FE simulations of the smoothed models. Although developed for micro-CT data sets, this fast and reliable mesh smoothing method could be applied to any three-dimensional image data where node and element connectivity have been defined.

Articular contact at the tibiotalar joint in passive flexion

The knowledge of the contact areas at the tibiotalar articulating surfaces during passive flexion is fundamental for the understanding of ankle joint mobility. Traditional contact area reports are limited by the invasive measuring techniques used and by the complicated loading conditions applied. In the present study, passive flexion tests were performed on three anatomical preparations from lower leg amputation. Roentgen Stereophotogrammetric Analysis was used to accurately reconstruct the position of the tibia and the talus at a number of unconstrained flexion positions. A large number of points was collected on the surface of the tibial mortise and on the trochlea tali by a 3-D digitiser. Articular surfaces were modelled by thin plate splines approximating these points. Relative positions of these surfaces in all the flexion positions were obtained from corresponding bone position data. A distance threshold was chosen to define contact areas. A consistent pattern of contact was found on the articulating surfaces. The area moved anteriorly on both articular surfaces with dorsiflexion. The average position of the contact area centroid along the tibial mortise at maximum plantarflexion and at maximum dorsiflexion was respectively 58% posterior and 40% anterior of the entire antero-posterior length. For increasing dorsiflexion, the contact area moved from medial to lateral in all the specimens.

A new approach for surface fitting method of articular joint surfaces

The application of joint contact mechanics requires a precise configuration of the joint surfaces. B-Spline, and NURBS have been widely used to model joint surfaces, but because these formulations use a structured data set provided by a rectangular net first, then a grid, there is a limit to the accuracy of the models they can produce. However new imaging systems such as 3D laser scanners can provide more realistic unstructured data sets. What is needed is a method to manipulate the unstructured data. We created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces. We applied our polynomial model to unstructured data sets from an artificial joint, and confirmed that our polynomial produced a smoother and more accurate model than the conventional B-spline method. Next, we applied it to a diarthrodial joint surface containing many ripples, and found that our function's noise filtering characteristics smoothed out existing ripples. Since no formulation was found to be optimal for all applications, we used two formulations to model surfaces with ripples. First, we used our polynomial to describe the global shape of the objective surface. Minute undulations were then specifically approximated with a Fourier series function. Finally, both approximated surfaces were superimposed to reproduce the original surface in a complete fashion.

Estimating joint contact areas and ligament lengths from bone kinematics and surfaces

We present a novel method for modeling contact areas and ligament lengths in articulations. Our approach uses volume images generated by computed tomography and allows the in vivo and noninvasive study of articulations. In our method, bones are modeled both implicitly (scalar distance fields) and parametrically (manifold surfaces). Using this double representation, we compute interbone distances and estimate joint contact areas. Using the same types of representation, we model ligament paths; in our model, the ligaments are approximated by the shortest paths in a three-dimensional space with bone obstacles. We demonstrate the method by applying our contact area and ligament model to the distal radioulnar joints of a volunteer diagnosed with malunited distal radius fracture in one forearm. Our approach highlights focal changes in the articulation at the distal radioulnar joint (location and area of bone contact) and potential soft-tissue constraints (increased "length" of the distal ligaments and ligament-bone impingement in the injured forearm). Results suggest that the method could be useful in the study of normal and injured anatomy and kinematics of complex joints.

Three-dimensional morphometry of the femoral condyles

OBJECTIVE

The present study describes the geometry of the three-dimensional articular surfaces of the human femoral condyles based on measurements of surface coordinates.

DESIGN

The purpose was not to obtain a complex representation of one single condyle, but to describe the femoral condyles using simple geometric parameters based on measurements using a number of specimens.

BACKGROUND

In joint modeling, a representative knee joint geometry is often desired which requires an approximation of the irregular joint geometry while taking into account interspecimen variations.

METHODS

An optical device was used to measure the condylar articular surfaces of 12 human femurs in the femorotibial contact region. The sagittal profiles were reconstructed by means of two circular arcs and the radial profiles by means of one circular arc.

RESULTS

The results provide the geometric parameters necessary for the three-dimensional reconstruction of the articular surfaces of the femoral condyles. The results indicate that the medial and lateral condyles of the distal femur are significantly asymmetric in a number of morphological features.

CONCLUSION

The primary application of the results is expected to be in the formulation of finite element models of the knee joint for static contact problems.

RELEVANCE

Numerical models of the knee joint are being widely used to study the mechanics of the joint. However, formulation of such models demands a prior knowledge of the complex three-dimensional geometry of the articular surfaces of the natural joint to establish the input parameters of the model.

A global method based on thin-plate splines for correction of geometric distortion: an application to fluoroscopic images

Quantitative analysis of biomedical images needs a careful correction of geometric distortion. To avoid the discontinuities of the local correction techniques and achieve good accuracy in the presence of global and local distortion, a novel global correction technique based on thin-plate splines is proposed. The technique approximates the grid points by a thin plate minimizing the weighted sum of the bending energy and the mean squared residual errors. The method proposed is compared with three traditional correction techniques: two local and one global. One local technique is linear and takes into account translation, rotation, and scaling, the other is nonlinear and includes skewing. The global technique is based on a two-dimensional polynomial model. Computer-based simulations and experimental tests on fluoroscopic images were carried out. The local techniques were sensitive to both sigmoidal and radial distortion. The polynomial and thin-plate splines global techniques were found sensitive only to sigmoidal distortion and to radial distortion, respectively. The two global techniques showed better performances with respect to any local on synthetic and real images. Where the distortion is predominantly radial or high computational efficiency is required, the polynomial global correction technique should be preferred. Where the distortion has a local nature or is predominantly sigmoidal, the thin-plate splines global correction technique should be chosen.

Fitting manifold surfaces to three-dimensional point clouds

We present a technique for fitting a smooth, locally parameterized surface model (called the manifold surface model) to unevenly scattered data describing an anatomical structure. These data are acquired from medical imaging modalities such as CT scans or MRI. The manifold surface is useful for problems which require analyzable or parametric surfaces fitted to data acquired from surfaces of arbitrary topology (e.g., entire bones). This surface modeling work is part of a larger project to model and analyze skeletal joints, in particular the complex of small bones within the wrist and hand. To demonstrate the suitability of this model we fit to several different bones in the hand, and to the same bone from multiple people.