Prediction of internal spine configuration from external measurements using a multi-body model of the spine

Predicting cervico-thoraco-lumbar vertebra positions from cutaneous markers: Combining local frame and postural predictors improves robustness to posture

Predictions of vertebra positions from external data are required in many fields like motion analysis or for clinical applications. Existing predictions mainly cover the thoraco-lumbar spine, in one posture. The objective of this study was to develop a method offering robust vertebra position predictions in different postures for the whole spine, in the sagittal plane. EOS radiographs were taken in three postures: slouched, erect, and subject's usual sitting posture, using 21 healthy participants pre-equipped with opaque cutaneous markers. Local curvilinear Frenet frames were built on a spline fitted to spinous processes' cutaneous markers. Vertebra positions were expressed as polar coordinates in these frames, defining an angle (α) and distance (d). Multilinear regressions were fitted to explain α and d from anthropometric predictors and predictors presumed to be linked to spinal posture, the predictors' effects being considered both locally and remotely. Anthropometric predictors were the main predictors for d distances, and postural predictors for α angles, with postural predictors still showing a marked influence on d distances for the cervical spine. Vertebra positions were then predicted by cross-validation. The average RMSE on vertebra positions was 11.0 ± 3.7 mm across the entire spine, 13.4 ± 4.1 mm across the cervical spine and 10.1 ± 3.1 mm across the thoraco-lumbar spine for all participants and postures, performances similar to previous models designed for a single posture. Our simple geometrical and statistical model thus appears promising for predicting vertebra positions from external data in several spinal postures and for the whole spine.

Modeling the Human Tibiofemoral Joint Using Ex Vivo Determined Compliance Matrices

Several approaches have been used to devise a model of the human tibiofemoral joint for embedment in lower limb musculoskeletal models. However, no study has considered the use of cadaveric 6 × 6 compliance (or stiffness) matrices to model the tibiofemoral joint under normal or pathological conditions. The aim of this paper is to present a method to determine the compliance matrix of an ex vivo tibiofemoral joint for any given equilibrium pose. Experiments were carried out on a single ex vivo knee, first intact and, then, with the anterior cruciate ligament (ACL) transected. Controlled linear and angular displacements were imposed in single degree-of-freedom (DoF) tests to the specimen, and the resulting forces and moments were measured using an instrumented robotic arm. This was done starting from seven equilibrium poses characterized by the following flexion angles: 0 deg, 15 deg, 30 deg, 45 deg, 60 deg, 75 deg, and 90 deg. A compliance matrix for each of the selected equilibrium poses and for both the intact and ACL-deficient specimen was calculated. The matrix, embedding the experimental load-displacement relationship of the examined DoFs, was calculated using a linear least squares inversion based on a QR decomposition, assuming symmetric and positive-defined matrices. Single compliance matrix terms were in agreement with the literature. Results showed an overall increase of the compliance matrix terms due to the ACL transection (2.6 ratio for rotational terms at full extension) confirming its role in the joint stabilization. Validation experiments were carried out by performing a Lachman test (the tibia is pulled forward) under load control on both the intact and ACL-deficient knee and assessing the difference (error) between measured linear and angular displacements and those estimated using the appropriate compliance matrix. This error increased nonlinearly with respect to the values of the load. In particular, when an incremental posterior-anterior force up to 6 N was applied to the tibia of the intact specimen, the errors on the estimated linear and angular displacements were up to 0.6 mm and 1.5 deg, while for a force up to 18 N, the errors were 1.5 mm and 10.5 deg, respectively. In conclusion, the method used in this study may be a viable alternative to characterize the tibiofemoral load-dependent behavior in several applications.

Knee Kinematics Estimation Using Multi-Body Optimisation Embedding a Knee Joint Stiffness Matrix: A Feasibility Study

The use of multi-body optimisation (MBO) to estimate joint kinematics from stereophotogrammetric data while compensating for soft tissue artefact is still open to debate. Presently used joint models embedded in MBO, such as mechanical linkages, constitute a considerable simplification of joint function, preventing a detailed understanding of it. The present study proposes a knee joint model where femur and tibia are represented as rigid bodies connected through an elastic element the behaviour of which is described by a single stiffness matrix. The deformation energy, computed from the stiffness matrix and joint angles and displacements, is minimised within the MBO. Implemented as a "soft" constraint using a penalty-based method, this elastic joint description challenges the strictness of "hard" constraints. In this study, estimates of knee kinematics obtained using MBO embedding four different knee joint models (i.e., no constraints, spherical joint, parallel mechanism, and elastic joint) were compared against reference kinematics measured using bi-planar fluoroscopy on two healthy subjects ascending stairs. Bland-Altman analysis and sensitivity analysis investigating the influence of variations in the stiffness matrix terms on the estimated kinematics substantiate the conclusions. The difference between the reference knee joint angles and displacements and the corresponding estimates obtained using MBO embedding the stiffness matrix showed an average bias and standard deviation for kinematics of 0.9±3.2° and 1.6±2.3 mm. These values were lower than when no joint constraints (1.1±3.8°, 2.4±4.1 mm) or a parallel mechanism (7.7±3.6°, 1.6±1.7 mm) were used and were comparable to the values obtained with a spherical joint (1.0±3.2°, 1.3±1.9 mm). The study demonstrated the feasibility of substituting an elastic joint for more classic joint constraints in MBO.