Malunion deformity of the forearm: Three‐dimensional length variation of interosseous membrane and bone collision

It remains unclear to what extent the interosseous membrane (IOM) is affected through the whole range of motion (ROM) in posttraumatic deformities of the forearm. The purpose of this study is to describe the ligament‐ and bone‐related factors involved in rotational deficit of the forearm. Through three‐dimensional (3D) kinematic simulations on one cadaveric forearm, angular deformities of 5° in four directions (flexion, extension, valgus, varus) were produced at two locations of the radius and the ulna (proximal and distal third). The occurrence of bone collision in pronation and the linear length variation of six parts of the IOM through the whole ROM were compared between the 32 types of forearm deformities. Similar patterns could be observed among four groups: 12 types of deformity presented increased bone collision in pronation, 8 presented an improvement of bone collision with an increase of the mean linear lengthening of the IOM in neutral rotation, 6 had an increased linear lengthening of the IOM in supination with nearly unchanged bone collision in pronation and 6 types presented nearly unchanged bone collision in pronation with a shortening of the mean linear length of IOM in supination or neutral rotation. This kinematic analysis provides a better understanding of the ligament‐ and bone‐related factors expected to cause rotational deficit in forearm deformity and may help to refine the surgical indications of patient‐specific corrective osteotomy.

experience in the operating room also showed occasionally a tension of the soft tissues after the osteotomy, which required intraoperatively a partial release of the interosseous membrane (IOM). In these complex cases, a clear understanding of ligament isometry during preoperative planning is therefore mandatory.
Authors advocated that with a larger deformity, regardless of its direction, the ROM will subsequently be smaller. 7 Although tension between the IOM or a bone collision is logically supposed to be the cause, 8,9 there is in the literature no detailed description of factors that influence either the loss of pronation or supination for specific deformities.
The purpose of this study is to describe what are the factors which may lead to a deficit of rotational ROM in terms of ligament linear lengthening of the IOM or bone collision.

| MATERIALS AND METHODS
This study was performed on a computer tomography-based 3D model of one left cadaveric forearm. The 3D surface models were produced during a previous study from our institution, which are publicly available and licensed under the Creative Commons Attribution 4.0 International. 10 The specimen was acquired through a donor platform (Science Care) and is from a healthy Caucasian donor. The simulations were performed with an in-house developed planning software (Balgrist CARD AG). 2. As previously described, the motion of the radius around the ulna can be described through a single rotation axis without considering the humerus as reference, 11 and be simplified as a line passing from the center of the radial head to the ulnar fovea. Manual adjustment of the rotation axis on the ulnar head was performed from one single investigator while aiming to maintain a stable distance between the sigmoid notch and the articular surface of the ulnar head through the whole ROM, and maintain a suitable sphericity of the radial head.

3.
A pronation or supination of 90°was defined as a parallelism of the humero-ulnar lines and the palmar ridge of the distal radius.

| Simulation of bone deformities
1. With the forearm in 90°supination, the reference line of the humero-ulnar joint was distally transposed on the radius and ulna at 33.3% and 66.6% of the total bone length in the center of the shaft while preserving the same coordinate axis, allowing thus to define a rotation axis for the angular deformities ( Figure 2A).
2. Angular deformities of 5°in four directions (flexion, extension, varus, valgus) at the two locations of the ulna and the radius (33.3% and 66.6% of total bone length) were simulated, producing thus proximal or distal third deformities ( Figure 2B).
3. To achieve a constant congruency of the distal radio-ulnar joint motion, the distal part of each simulated radius or ulna were repositioned while the proximal radio-ulnar joint was maintained fixed ( Figure 2C). The reposition was manually performed until an overlapping of the 3D surface of the sigmoid notch between the native and deformed radius could be reached, and until an overlapping of the 3D surface of the articular ulnar head surface between the native and deformed ulna could be reached. This reposition was performed for each deformity allowing all models to fit on the same rotational axis ( Figure 2D). 2. The distance (D) between the radial and ulnar insertion points was calculated using the Euclidean distance in 3D space following the formula: Where the insertion point on the radius is 3. The length of the six components of the IOM were measured throughout the seven forearm positions for all bone deformities.
The rotation in 3D space of the ligament insertion points in the radius along the rotation axis at a given rotation position allowed to obtain the spatial coordinates of the rotated insertion points following the formula: where the initial ligament insertion points is  F I G U R E 1 Simulation of pronation and supination on a single axis model simulation of pronation and supination with native forearm in 90°, 60°, 30°supination, neutral position, 30°, 60°, and 90°pronation. Dark gray cylinder: humero-ulnar joint. x: line along humero-ulnar joint. A parallelism of the palmar ridge with the x axis defines a 90°pronation or 90°supination. Gray line: rotation axis of pronation/supination passing from the radial head to ulnar head. Red circle: bone collision on the native forearm occurring at 67°pronation on the palmar ridge of the proximal third of the ulna and palmar ridge of the proximal third of the radius.   (Figures 6 and 7).

| DISCUSSION
Our results describe the potential origins of rotational deficit in forearm deformity and highlight results reported in previous biomechanical studies. 7  3. Defining the pro/supination axis through the ulnar head and obtaining an optimal kinematic simulation may be challenging.
The distal location of this axis has been described as passing through the ulnar fovea 16 or near the center of the ulnar head, 17 and the ulnar fovea has been defined as the center of curvature of the ulnar head. 18 However, as shown by Katoaka and colleagues anatomic variation with flat-or concave-type of fovea may respectively lateralize or medialize this axis 19 In this  Review. Andreas Schweizer: conceptualization; supervision; review.