Multibody modelling of ligamentous and bony stabilizers in the human elbow

Abstract

The elbow ligamentous and bony structures play essential roles in the joint stability. Nevertheless, the contribution of different structures to joint stability is not yet clear and a comprehensive experimental investigation into the ligament and osseous constraints changes in relation to joint motions would be uphill and somehow unattainable, due to the impossibility of obtaining all the possible configurations on the same specimen. Therefore, a predictive tool of the joint behavior after the loss of retentive structures would be helpful in designing reconstructive surgeries and in pre-operative planning. In this work, a multibody model consisting of bones and non-linear ligamentous structures is presented and validated through comparison with experimental data. An accurate geometrical model was equipped with non-linear ligaments bundles between optimized origin and insertion points. The joint function was simulated according to maneuvers accomplished in published experimental studies which explored the posteromedial rotatory instability (PMRI) in coronoid and posterior medial collateral ligament (PB) deficient elbows. Moreover, a complete design of experiments (DOE) was explored, investigating the influence of the elbow flexion degree, of the coronoid process and of the medial collateral ligaments (MCL) structures (anterior and posterior bundles) in the elbow joint opening. The implemented computational model accurately predicted the joint behavior with intact and deficient stabilizing structures at each flexion degree, and highlighted the statistically significant influence of the MCL structures (P<0.05) on the elbow stability. The predictive ability of this multibody elbow joint model let foresee that future investigations under different loading scenarios and injured or surgically reconstructed states could be effectively simulated, helping the ligaments reconstruction optimization in terms of bone tunnel localizations and grafts pre-loading.

Level of evidence: V.

Keywords: coronoid process; elbow stability; medial collateral ligaments; multibody model.

Figure 1

Typical load-strain relation for ligaments, as formulated in Equation 1: the initial toe region is characterized by a parabolic trend while, for ɛ>2ɛ_L, the load is linearly related to the strain through the stiffness K.

Figure 2 a–d

Ligaments origin and insertion points on humerus, radius and ulna shown in the medial view (a), lateral view (b), top view (c) and bottom view (d). Uppercase and lowercase letters identify origins and insertions of each bundle as listed in Table I.

Figure 3

Elastic (left) and damping (right) contributes of the impact function (Eq. 2). The grey region is referred to the interpenetration between the bodies from the initial contact (δ=0) to the interpenetration δ=d, where the damping coefficient reaches its maximum value c.

Figure 4

Complete geometrical model composed of humerus, radius and ulna pre-assembled in the extended position. Mimicking the clinician hand, the motion ring (in black) is positioned at the wrist level.

Figure 5 a–d

Loads and displacements applied to the forearm in the dislocation maneuver: a) flexion of the forearm from full extension (0°) to the set angle (30°, 60° or 90°); b) varus motion in the frontal plane from 0° to 5°; c) compression force along the ulnar axis (from 0 to 10 N or 25 N); d) internal rotation torque around the ulnar axis (from 0 to 2.5 Nm).

Figure 6 a,b

Markers placement in the intact model (a) and in a 50% coronoid cut model (b): the M2–M3 distance increment following the maneuver is the distal gap while the M1–M4 distance increment is the proximal gap, used in the model validation.

Figure 7

Distal (left) and proximal (right) joint gap at 30°, 60° and 90° of flexion. In black are represented the intact elbow with intact ligaments results (used as control) while “Coronoid Cut” is the 50% coronoid cut model with intact ligaments. “AB Cut”, “PB Cut” and “MCLC Cut” represent the anterior bundle deactivation, the posterior bundle deactivation and medial collateral ligament complex deactivation (both anterior and posterior bundles) respectively.

Figure 8

Distal (left) and proximal (right) gap increments with respect to the intact elbow following ligaments dissection and coronoid cut: ○ - intact ligaments; □ - Anterior Bundle dissection; × - Posterior Bundle dissection. Dashed lines are referred to the intact elbow while continuous lines are referred to the 50% coronoid cut elbow.