Analysis of the coaptation role of the deltoid in reverse shoulder arthroplasty. A preliminary biomechanical study.

BACKGROUND: Lateralization of the glenoid implant improves functional outcomes in Reverse Shoulder Arthroplasty. Lateralization does not appear to impact the Deltoid's Moment Arm. Therefore, the stabilizing effect described in the literature would not be the result of an increase this moment arm. A static biomechanical model, derived from Magnetic Resonance Imaging, can be used to assess the coaptation effect of the Middle Deltoid. The objective of this study was to analyze the impact of increasing amounts of glenoid lateralization on the moment arm but also on its coaptation effect.
METHODS: Eight patients (72.6 ± 6.5 years) operated for Reverse Shoulder Arthroplasty were included in the study. Three-dimensional models of each shoulder were created based on imaging taken at 6 months postoperative. A least square sphere representing the prosthetic implant was added to each 3D models. A static biomechanical model was then applied to different planar portions of the Middle Deltoid (from 3D models), first without lateralization and then with simulated lateralization of 6, 9 and 12mm. This static model enables to compute a Coaptation/Elevation Ratio and to measure the Deltoid's Moment Arm. The inter- and intra-rater agreement of the 3D models was evaluated.
RESULTS: One patient was excluded due to motion during imaging. The inter- and intra-rater agreement was over 0.99. The ratio increased starting at 6 mm of lateralization (p<0.05), compared to the initial position. The moment arm was not affected by lateralization (p<0.05), except in two slices starting at 9 mm (S1 p<0.05 and S2 p<0.05).
CONCLUSION: Our hypothesis that the Middle Deltoid's coaptation role would be greater with glenosphere lateralization was confirmed. This trend was not found in the moment arm, which showed little sensitivity to lateralization. The stabilizing effect therefore appears to stem from the coaptation role of the Middle Deltoid.

1. Introduction

The Reverse Shoulder Arthroplasty (RSA) technique developed by Grammont aimed to lower and medialize the glenohumeral joint’s center of rotation and increase the Deltoid’s Moment Arm (DMA) [1-3]. Scapular notching remains a common complication of RSA [1-12]. Hettrich et al. [4] define scapular notching as the result of a mechanical conflict between the medial part of the metaglene against the lateral edge of the scapula during adduction movements. Notching is therefore responsible for progressive osteolysis of the glenoid as well as premature wear of the metaglene, making the implant unstable. This is the major complication of this type of arthroplasty. According to Rugg et al. [3], scapular notching is thought to be present in nearly 2/3 of RSA 2 years postoperatively. Hettrich et al. [4] even estimate that notching occurs in 31% to 97% of patients undergoing RSA. Clinically, notching is evidenced by loss of muscle strength, pain, deterioration of active mobility of the shoulder in flexion and abduction [3]. Hoenecke et al. [13] believe that optimal implant positioning is a trade-off between this potential complication and deltoid efficacy. Lateralization can help minimize medialization, which causes notching, using either the glenoid or humeral implant, or a glenoid bone graft [11, 14, 15]. For Boileau et al. [8-12], lateralization is a key element to achieve adequate passive range of motion while minimizing the risk of notching. Tightening of the deltoid through lateralization would help increase joint stability [10-12]. Although lateralization is widely studied, the ideal amount required to improve shoulder mobility, stability and strength—while simultaneously decreasing notching—has yet to be determined. Studies report lateralization between 1 mm and 13 mm [1-13]. For Boileau et al., graft thickness should be 10 mm [9, 11, 16]. However, lateralization does not seem to impact the DMA [14]. Therefore, it is impossible to explain the stabilizing effect described by Boileau et al. [10-12] by changes in this DMA. Li et al. [17] and Smith et al. [18] showed that the Middle Deltoid (MD) has key role after RSA with an increase of EMG activity after surgery. Thus, a specific focus on this part of the deltoid muscle is clinically relevant.

A more in-depth mechanical study of the MD will help define its stabilizing role. Gagey et al. [19], Billuart et al. [20] and Hereter Gregory et al. [21] have developed a model based on Magnetic Resonance Imaging (MRI) studies to characterize the coaptation and elevator role of each portion of the MD using a Coaptation/Elevation Ratio (CER). This ratio is computed between the "elevating" force (which raises the humeral head and “destabilizes” the shoulder) and "lowering" force (which stabilizes the humeral head) using angle measurements and force estimation. This ratio thus makes it possible to characterize the main action of the middle deltoid on the glenohumeral joint in a static and plane condition. This model, applied to patients suffering from shoulder osteoarthritis, showed that the MD played an important role as an elevator muscle but that it had a coaptation component as well, stabilizing the shoulder [19].

Therefore, the primary objective of this preliminary study was to analyze the impact of an increase in glenosphere lateralization on the DMA, but also on the coaptation role of MD. By comparing the initial position of the glenosphere with simulated lateralizations, our hypothesis is that lateralization will increase the coaptation role of the MD without impacting its DMA. Assessing the reliability of the 3D models was the study’s secondary objective.

2. Materials & methods

The Ethics Committee of the Groupe Hospitalier du Havre (GHH) approved and deemed the protocol of this study to comply with the ethics rules on clinical research on January 15th, 2021. Experimental work including human subjects within the framework of this study can be implemented. Each patient was informed of the study via a newsletter. Then, each patient gave their consent to participate in the study by signing a consent letter informing them that their data will be used for the current study. Patient data has been anonymized.

2.1 Patients

Eight RSA patients were included at the beginning of the study, from March 8th to March 12th 2021 (Table 1). The inclusion criteria were RSA performed less than 6 months prior and an indication of cuff tear arthropathy diagnosed with imaging. Exclusion criteria were a history of surgery or trauma to the affected shoulder, the presence of complications, such as dislocation or surgical site infection and other severe medical conditions (neurological, cardiovascular, oncological). The exclusion criteria were screened for on MRI. Finally, movements of the patient (voluntary or not) during the MRI examination, rendering the images uninterpretable was the last exclusion criterion (thus one patient was excluded after imaging). All the patients were treated by the same surgeon between February 1st 2021 and February 5th 2021, using the deltoid-splitting approach without lateralization of the glenoid implant.

Table 1

Patient characteristics.

Patients	Sex	Age	OS	Implant used	Glenosphere (mm)
P1	F	67	L	Aequalis Ascend Flex, Wright-Tornier™	36
P2	F	67	R	Delta XTEND, DePuy-Synthes™	38
P3	M	78	R	Delta XTEND, DePuy-Synthes™	38
P4	F	79	R	Delta XTEND, DePuy-Synthes™	38
P5	F	82	L	Delta XTEND, DePuy-Synthes™	38
P6	M	67	R	Delta XTEND, DePuy-Synthes™	38
P7	F	66	L	Aequalis Ascend Flex Wright-Tornier™	36
P8	F	75	L	Delta XTEND, DePuy-Synthes™	38

P = Patients; OS = Operated Shoulder; F = Female; M = Male; L = Left; R = Right

2.2 MRI protocol

The images were taken with a 1.5T MRI scanner (Siemens™ Magnetom Aera, Munich, Germany). The subjects were supine, with an angle of 80° between the humeral diaphysis and the scapula (measured with a goniometer) and palms up. 3D measurement of this angle was not possible due to artefacts on the MRI near the glenosphere. The images were taken in Spin-Echo T1-weighted sequence (472/8 for the coronal plane and 350/7.5 for the axial plane, field of view: 560X640) with a fat hypersignal suppression option: Fat Sat 1. Slice thickness was 3 mm, joined without overlapping.

2.3 3D modeling

The deltoid, the humeral diaphysis, the clavicle and acromion were manually segmented on each slice and automatically reconstructed in 3D with the SliceOmatic™ software (Tomovision™, Montreal, Canada). The implants could not be reconstructed because of the presence of several artifacts (Fig 1).

Fig 1

Manual segmentation of the slices and 3D modeling with SliceOmatic™ software.

In Green: acromion; in Red: deltoid; in Blue: clavicle; in Grey: humeral diaphysis.

2.4 Static analysis

The model used in this study computed the CER on MD planar slices, taken from the 3D models. The MD was defined as a mechanical system and the external forces applied to it were inventoried (Fig 2). Mass and thickness of MD, and other muscles were not taken into consideration. The MD encapsulates the implant like a string on a pulley. The MD’s action on the pulley at its distal insertion site is defined as with . The action of MD on the pulley is defined as with . Considering the external forces inventoried and the principles of statics, the following equation was defined within the plane: .

Fig 2

Biomechanical models used in the present study.

(A) External forces and fundamental principles of the static model. corresponds to the distal insertion Point (PID). is the proximal insertion point (PIP). is equivalent to the reaction force on the MD. (B) The Y’Y axis is parallel to the humeral diaphysis. represents the angle between MD muscle fiber orientation and the humeral diaphysis axis. represents the MD’s change in direction. . Only the normal F1 and vectors are used to compute the CER (forces directly in contact with the humerus). This model makes it possible to compute the CER using angle measurements.

The forces projected on the y’y axis were as follows:

Ry = F1 cos(E)+F1 cos(2T+E)

Hence: Ry = 2F1 cos(T) cos(T+E)

The CER is computed based on standard forces directly in contact with the humerus:

Coaptation force = action of MD on the pulley, as ′

Elevator force = distal effect of the MD on the humerus, as: ′

The formula used was: .

Finally:

′ −2 cos(T)cos(T+E)

′y = cos (E)

Finally, to compute the CER, angle and have to be measured on MD planar slices.

2.5 3D model segmentation

To compute the CER based on and , we used various MD slices of the planar model extracted from the 3D models (Fig 2B). For this part of the study the mechanical model developed and validated by Billuart et al. [20] and then by Hereter Gregori et al. [21] on degenerative shoulders was used and transposed to prosthetic shoulders. In the present study, the following methodology was used: the MD was considered the sum of “n” muscle fibers, starting at the anterior and lateral aspect of the acromion and terminating on the deltoid V (DIP) which lay on a sphere representing the contact area between the prosthetic implant and the internal aspect of the MD. This sphere called ILSS (Implant Least Squared Sphere) was positioned within the 3D model using the least squared method in SliceOmatic™. The following methodology was used to build ILSS: a mesh sphere was created in the software, which allows manual point selection on the internal aspect of the MD. Its size (radius ILSS) and its position were adjusted manually in the 3D model, as close to the desired position as possible (Fig 3). Then the least square methodology was used: the software eliminates all the points for which the normal vectors are not in the same direction as the sphere’s normal vector. If the scalar product between the two directions: "normal" x "dir (node—center)" is over 0, the point is eliminated. Then, the software’s “distance” function eliminates 10% (with each click) of the points most distant from the surface of the sphere, using the following equation: dist2 = ABS((node-cent)2 –r2)). The radius of this sphere was identified as ILSS radius and recorded.

Fig 3

Positioning of the least square spheres (ILSS and acromion).

(A) A mesh sphere is created which allows manual point selection on the internal aspect of the MD: its size (radius ILSS) and position are adjusted manually in the 3D model, as close to the desired position as possible. (B) The grey sphere is the 2nd least squared sphere going through the acromion to find Point 1.

Then, the 3D models were segmented in several plane sections using 3 points:

Point 1: center of a 2nd least squared sphere going through manually chosen points on the acromion, using the same methodology as ILSS (Fig 3B).

Point 2: manual selection on A2 insertion of MD [22], changing in 10° increments with each slice and running through all the acromion (Fig 4).

Fig 4

Plane Slices selection and angle measurements.

(A) Point 2 changes on each slice: S4 = A2, S3 = A3, S2 = M1 and S4 = P1. (B) Each plane slice includes a MD string (red), a pulley (part of the ILSS, purple), a part of the acromion (green) and of the clavicle (blue). The CER is computed using the and measurements with the straight yellow lines. (C) Caption credit: Sakoma et al. [22].

Point 3: center of the humeral diaphysis.

From these three points, a 4x4 homogeneous transformation matrix of the new plane was defined. For each pixel of this new plane, the cubic interpolation data was computed from the eight neighboring pixels from the original model using the following formula: 2t3 - 3t2 + 1, where t is the distance between the new point and one of the points from the original model. Then, four plane slices were chosen manually for each shoulder, according to the study by Sakoma et al. [22]. Indeed, the slices passing through the insertion points on the acromion and corresponding to the four MD intramuscular tendons insertions described by Sakoma et al. [22] were selected (Fig 4C). Thus, the Slice 4 in the present study (S4) goes through the A2 insertion described by Sakoma et al. [22]. In the same way: S3 = A3, S2 = M1, S1 = P1 (Fig 4). The different steps from the manual selection of the slices to the incorporation of the biomechanical model by Billuart et al. [20] and then the measurement of the angles is summarized in Fig 5.

Fig 5

Summary of the steps from the selection of slices to angle measurements.

(A) The 3D model is segmented in several plane sections according to the methodology presented above. (B) After selecting the slices according to the anatomical description by Sakoma et al. [22] and in which a portion of the ILSS is “stamped”, the biomechanical model developed by Billuart et al. [20] (C) is used to carry out the angle measurements (D).

2.6 CER computation

The angles were measured manually on each of the four slices (Fig 4B). A straight line in contact with the pulley and following the internal aspect of the MD was called the MD line. The intersection between the MD line and the humeral diaphysis axis defines . The PIP of the MD and a point of contact with the pulley define another straight line called the proximal line. The intersection between the proximal line and the MD line formed , knowing that . The ratio was then computed with the equation presented previously.

2.7 Lateralization of the glenosphere

The lateralization was simulated in SliceOmatic™ by translating the ILSS (on the X-axis) in 6, 9 and 12 mm increments compared to its initial postoperative position without lateralization (Fig 6). For this part of the study, the following simplifying hypothesis was used: the ILSS radius was non-significantly modified by the lateralization of the prosthetic implant.

Fig 6

Simulation of lateralizations on SliceOmatic™ in axial view.

2D representation on an MRI image of the displacement of a 2D slice of ILSS (stamped in the MRI image) along the X axis at 0, 6, 9 and 12mm (from left to right). Yellow circle = slice of ILSS in 2D; In red = deltoid muscle.

2.8 DMA measurement

The DMA was measured on each slice as the distance between the center of the ILSS and the line perpendicular to (with the tool “Measurement” of the software).

2.9 Inter- and intra-rater assessment

To assess the reliability of the 3D models and the segmentation method, an inter- and intra-rater agreement study was undertaken. Two raters created the 3D models and positioned the ILSS. Rater 1 did the models and positioned the ILSS twice on each study subject’s images, one week apart. Rater 2 completed the same protocol on all subjects. To assess intra-rater agreement, the models created one week apart were compared for each rater. For the inter-rater agreement, the models of the three common subjects were compared.

2.10 Statistical analysis

The data were analyzed with R version 2.14 (Bell Laboratories, Murray Hill, USA). Non-parametric tests were used because normal data distribution could not be guaranteed. The significance level was set at 0.05. The inter- and intra-rater agreement was evaluated with an intraclass correlation coefficient (ICC) for the 3D models and the ILSS radius. The mean/standard deviation of the angles, the CER and DMA were used for the analysis. The comparison of CER, angles and DMA between initial and lateralized conditions were done with the Mann-Whitney test.

3 Results

P2 was excluded because of motion during MRI acquisition and thus, the different MRI slices were not usable for the 3D reconstruction.

3.1 Reliability assessment

The results from the reliability assessment are presented in Table 2. For intra-rater agreement of 3D model, the mean ICC was 0.999 for Rater 1 and Rater 2. For intra-rater agreement of ILSS radius, the mean ICC was 0.996 for Rater 1 and 0.973 for Rater 2. For inter-rater agreement of 3D models, the mean ICC was 0.994 at Week 1 and 0.989 for the second comparison at Week 2. For inter-rater agreement of ILSS radius, the mean ICC was 0.957 at Week 1 and 0.925 at Week 2.

Table 2

Intra- and inter-rater agreement.

	P1	P3	P4	P5	P6	P7	P8	Mean
ICC 3D model for Rater 1 (Week 1 vs Week 2)	0.999	0.999	0.999	0.999	0.993	0.999	0.999	0.999
ICC 3D model for Rater 2 (Week 1 vs Week 2)	0.998	0,990	0,990	0,993	0,999	0.999	0.999	0.999
ICC ILSS radius for Rater 1 (Week 1 vs Week 2)	0.997	0.999	0.998	0.992	0.997	0.999	0.990	0.996
ICC ILSS radius for Rater 2 (Week 1 vs Week 2)	0.995	0.949	0.992	0.995	0.907	0.998	0.999	0.973
ICC Rater 1 vs 2: Week 1 (for 3D models)	0.990	0.998	0.990	0.999	0.993	0.999	0.990	0.994
ICC Rater 1 vs 2: Week 2 (for 3D models)	0.989	0.997	0.987	0.999	0.988	0.991	0.992	0.989
ICC Rater 1 vs 2: Week 1 (for ILSS radius)	0.957	0.933	0.762	0.911	0.895	0.713	0.862	0.957
ICC Rater 1 vs 2: Week 2 (for ILSS radius)	0.957	0.963	0.877	0.996	0.929	0.83	0.925	0.925

P = Patient

3.2 ILSS radius

The ILSS radius of every patient is presented in Table 3. The mean ILSS radius was 32.89±4.29 mm.

Table 3

Radius of the ILSS.

Patients	Radius (mm)
P1	31.25
P3	36.30
P4	33.64
P5	25.72
P6	39.42
P7	32.16
P8	31.75
Mean ±SD	32.89 ± 4.29

3.3 Biomechanical parameters

Table 4 presents the values of the biomechanical parameters for different lateralization options and for each slice selected. , Mean and Standard Deviation (Mean±SD, for all slices) are 54.93±0.77° for Angle T; 7.94±1.24° for Angle E; 0.54±0.03 for the CER, and 38.44±8.80 mm for the DMA. , Mean and Standard Deviation (Mean±SD, for all slices) are 45.60±0.99° for Angle T; 11.47±0.81° for Angle E; 0.81±0.03 for the CER, and 39.67±8.25 mm for the DMA. , Mean and Standard Deviation (Mean±SD, for all slices) are 42.54±1.03° for Angle T; 14.07±0.93° for Angle E; 0.83±0.04° for the CER, and 40.67±9.05 mm for the DMA. , Mean and Standard Deviation (Mean±SD, for all slices) are 40.07±0.90° for Angle T; 15.25±1.02° for Angle E; 0.88±0.03 for the CER, and 41.28±5.25 mm for the DMA.

Table 4

Means, standard deviation, minimum and maximum values of the biomechanical parameters for different lateralization options.

		0 mm	6 mm	9 mm	12 mm
ANGLE T (degrees)	S1	55.40±1.68	42.71±2.04	41.40±1.34	38.75±1.71
		(53–57)	(42–43.5)	(40–44.5)	(37–41)
	S2	55.43±2.23	42.86±1.86	41.75±1.77	40.20±0.45
		(52–59)	(40.5–45)	(39.5–43)	(40–36.5)
	S3	54.36±1.65	44.79±3.49	43.71±3.68	40.60±2.07
		(53–58)	(40–51)	(42–50)	(37–47.5)
	S4	54.14±1.31	44.00±2.90	42.50±2.78	40.71±1.89
		(53–56)	(40–47.5)	(39–46)	(38–43)
ANGLE E (degrees)	S1	9.14±3.44	13.43±2.57	15.14±2.61	16.86±2.41
		(3–13)	(10–16)	(12–19)	(14–21)
	S2	6.71±2.21	11.57±3.10	13.14±2.48	14.86±2.61
		(3–10)	(7–15)	(10–16)	(11–18)
	S3	7.29±1.60	12.29±2.43	13.71±2.43	14.57±2.15
		(4–9)	(8–16)	(9–17)	(11–17)
	S4	7.43±2.30	13.00±3.92	14.71±3.73	16.00±3.21
		(3–9)	(6–18)	(8–20)	(10–20)
CER	S1	0.49±0.08	0.82±0.08	0.84±0.08	0.90±0.05
		(0.39–0.60)	(0.71–0.97)	(0.73–0.98)	(0.86–0.98)
	S2	0.53±0.09	0.87±0.07	0.88±0.06	0.91±0.04
		(0.44–0.70)	(0.73–0.98)	(0.79–0.99)	(0.85–0.96)
	S3	0.55±0.06	0.79±0.11	0.79±0.11	0.84±0.09
		(0.44–0.62)	(0.63–0.93)	(0.67–0.98)	(0.8–1.01)
	S4	0.56±0.05	0.79±0.06	0.8±0.05	0.86±0.05
		(0.47–0.61)	(0.69–0.88)	(0.73–0.88)	(0.78–0.94)
DMA (mm)	S1	41.52±3.31	43.32±3.54	47.16±2.93	49.49±2.94
		(36.55–47.08)	(39.03–49.95)	(43.65–52.94)	(45.77–55.29)
	S2	48.65±4.45	50.66±4.50	54.31±5.07	56.04±5.77
		(39.71–53.17)	(48.90–56.12)	(45.29–60.34)	(45.29–63.14)
	S3	33.88±5.86	36.01±5.81	38.31±6.36	40.17±5.58
		(27.91–42.62)	(28.67–43.25)	(31.34–47.1)	(34.53–48.85)
	S4	28.54±6.36	31.09±6.33	33.01±6.65	34.43±6.59
		(21.07–38.19)	(24.05–40.01)	(25.81–42.09)	(25.99–44.03)

S = MD slice number.

Fig 7 represents a set of images containing all slices at all lateralizations with the angles overlay for Patient 1.

Fig 7

Example of images extracted from SliceOmatic™ representing the different slices at each lateralization with angle measurements for Patient 1.

S1 = Slice 1; S2 = Slice 2; S3 = Slice 3; S4 = Slice 4; Blue Circle = 2D ILSS for Slice 1; Orange Circle = 2D ILSS for Slice 2; Purple Circle = 2D ILSS for Slice 3; Green Circle = 2D ILSS for Slice 4. In red: deltoid muscle; in green = acromion; in blue = clavicle; in white = humeral diaphysis. B = Angle B in degree; E = Angle E in degree; T = B/2.

3.4 Comparisons of lateralization simulations

The comparison of the different lateralization simulations is presented in Table 5. For Angle T and E, there are significant differences for all the slices when comparing 0mm of lateralization versus 6mm, 9mm and 12mm (significance level was p = 0.002* for Angle T and between p = 0.04* and p = 0.002* for Angle E). When lateralization increases, for all the slices, Angle T decreases and inversely, Angle E increases. CER increase significantly (significance level was between p = 0.002* and p = 0.0006*) when comparing the initial position without lateralization (0mm) versus 6mm, 9mm and 12mm, for all the slices. There was no significant difference when comparing lateralization results 2x2 (significance level was p> 0.05 for 6vs9, 6vs12, 9vs12). For DMA, there are no significant difference (significance level was p>0.05) when comparing initial position (0mm) versus 6mm, 9mm and 12mm; except for S1 and S2 when comparing 0mm versus 9mm and 12mm. (significance level was between p = 0.04* and p = 0.001*).

Table 5

Comparison of the different lateralization simulations.

	MD slice	P values	P values	P values	P values	P values	P values
		0vs6	0vs9	0vs12	6vs9	6vs12	9vs12
Angle T	S1	0.002 *	0.002 *	0.002 *	0.27	0.007 *	0.05 *
	S2	0.002 *	0.002 *	0.002 *	0.19	0.006 *	0.05 *
	S3	0.002 *	0.002 *	0.002 *	0.61	0.1	0.24
	S4	0.002 *	0.002 *	0.002 *	0.48	0.05 *	0.08
Angle E	S1	0.04 *	0.005 *	0.002 *	0.27	0.05 *	0.22
	S2	0.01 *	0.002 *	0.002 *	0.22	0.1	0.27
	S3	0.005 *	0.002 *	0.002 *	0.14	0.1	0.5
	S4	0.02 *	0.01 *	0.002 *	0.41	0.16	0.4
CER	S1	0.0006 *	0.002 *	0.002 *	0.56	0.06	0.22
	S2	0.0006 *	0.002 *	0.002 *	0.27	0.11	0.22
	S3	0.002 *	0.002 *	0.002 *	1.00	0.61	0.34
	S4	0.002 *	0.002 *	0.002 *	0.75	0.05 *	0.07
DMA	S1	0.46	0.004 *	0.001 *	0.03 *	0.01 *	0.1
	S2	0.32	0.04 *	0.03 *	0.13	0.05 *	0.48
	S3	0.38	0.21	0.1	0.46	0.16	0.54
	S4	0.46	0.26	0.1	0.54	0.38	0.54

* = significantly different.

4 Discussion

The aim of this study was to assess the effect of lateralizing the glenosphere on the DMA and coaptation role of MD. To this end, the reliability of the methodology needed to be evaluated. The rater’s proficiency in identifying and selecting anatomical structures on MRI is key. The results of the inter- and intra-rater agreement assessment of the 3D models and ILSS positioning (Table 2) gave strength to our methods. They were also consistent with other studies describing the SliceOmatic™ software as a reliable 3D reconstruction tool [23, 24]. Therefore, using the model developed by Billuart et al. [20] and then by Hereter Gregori et al. [21], we compared four RSA lateralization options: 0, 6, 9, 12 mm. Our hypothesis that lateralization increases the coaptation role of the MD was confirmed. Lateralizing the glenoid implant led to a significant increase in the coaptation role of the Middle Deltoid. With a simulated lateralization of 6, 9 and 12 mm, the CER increased significantly compared to initial conditions (Table 4), with values closer to 1. This was especially true in the posterior (S1 = 0.90) and middle (S2 = 0.91) portions of MD. The glenoid implants are anatomically angled towards the S1 and S2 portions which may explain this trend. The CER seems to increase with lateralization but there was no significant difference when comparing lateralization results 2x2 (Table 5). Our findings are like those reported in the literature. Indeed, the studies published by Boileau et al. [10-12] or Hettrich et al. [4] and Hoenecke et al. [13], promote lateralization to improve mobility, stability and strength.

The two types of implants used in this study (Onlay for Wright-Tornier™ and Inlay for DePuy-Synthes™) do not have the same effect on lateralization. The Onlay is more lateralizing because of its design and its implantation concept. However, considering that each implant was compared to itself in the different lateralization simulations, the methodology remains sound.

Lateralization leads to tensioning of muscle fibers but its impact on DMA remains unclear. Werthel et al. [15, 16] showed that a few millimeters of lateralization did not affect the DMA. Our findings appear to agree with these results. Indeed, whatever the amount of lateralization, the DMA of the S3 and S4 portions were not significantly different, and 6 mm of lateralization had no effect on the DMA. However, a few millimeters’ increase was seen in DMA with 9 mm and 12 mm of lateralization, but only for S1 and S2 (Tables 4 and 5). Moreover, lateralization did not appear to have a significant impact on DMA for all portions of the MD whereas there was a significant increase in the coaptation effect on the entire MD.

Clinically, the CER is a biomechanical factor that helps explain the Middle Deltoid’s more prominent role in joint stability after RSA, as described in the literature [10-12]. This improvement in stability is therefore achieved by the Middle Deltoid actively, not only through passive fiber tensioning that results from humerus lengthening during surgery.

This study has limitations. The imaging is realized with a patient in supine position which could presses and deforms the posterior deltoid on the MRI. In addition, the supine position in the MRI scanner could change the position of the scapula on the rib cage. However, we positioned the arm so that it was not in extension. This positioning of the arm limits the modification of the anatomical relationships between the MD and the elements constituting the ILSS, inherent in the supine position. The methodology to identify the joint’s center of rotation and the DMA was based on approximations. In this study, a choice was made to explore only the deltoid as a mechanical system, excluding other muscles (rotators’cuff, playing a key role on stability of the shoulder is not functional for these patients). Indeed, the MD has a key functional role after surgery since Li et al. [17] and Smith al. [18] showed a significant increase in the EMG activity of the MD after surgery during abduction. Furthermore, Yoon et al. [25] indicate that clinicians should pay attention to the deltoid volume for good functional outcomes: a larger deltoid indicates a stronger muscle. Anatomically, MD has been specifically studied because of the 4 fibrous bands described by Sakoma et al. [22]. In our opinion, these fibrous bands reflect the adaptation of the MD to transmit forces to the underlying anatomical or prosthetic elements. The path of the anterior deltoid also reflecting on the ILSS may have a certain efficiency, but we did not assess this point quantitatively. The simplifying hypothesis developed to explain the lateralization of ILSS is considered acceptable. Indeed, the lateralization of the implant tends to increase the contacts between the ILSS and the MD and therefore to increase the coaptator effect of the MD. However, we have not quantitatively assessed this point. Finally, considering the lateral translation of the humerus with the lateralization of the glenosphere: translating the metaglene increases the coaptator effect of the MD. On the other hand, lateralization of the metaglene is accompanied by a lateralization of the humerus which therefore results in conservation of the DMA.

5 Conclusion

This study is the first to analyze the effects that lateralizing the glenosphere has on the coaptation role of the Middle Deltoid with a previously developed model. Simulating 6, 9 and 12 mm of lateralization on a personalized model derived from MRI showed improved coaptation of the Middle Deltoid, compared to no lateralization. The DMA was only affected starting at 9 mm of lateralization and only on some portions of the MD. The improvement in stability would then be the result of an increase in the coaptation role of the Middle Deltoid rather than an increase in its DMA. The coaptation effect of the MD could be doubly beneficial from a clinical standpoint. On the one hand, improved joint stability during anterior elevation would make it possible to lift heavier weights, and on the other, it would also help lower the dislocation rate.

10 Jun 2021

PONE-D-21-12682

Analysis of the coaptation role of the deltoid in reverse shoulder arthroplasty. A preliminary biomechanical study.

PLOS ONE

Dear Dr. Martinez,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Jul 25 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

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Katherine Saul

Academic Editor

PLOS ONE

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

**********

2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: Yes

**********

3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

**********

4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

**********

5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: Summary: This is a computer model simulation of deltoid coaptation with simulated increases in lateralization to the glenosphere based on MRI scans of patients that are postop from a non-lateralized rTSA. This study shows that lateralization does little to affect the moment arm of the deltoid, but does increase its coaptation. This gives credence that lateralization leads to increased stability in rTSA not through affecting the deltoid moment arm, but due to the coapt effect of the middle deltoid. Weaknesses to this study remain the relatively small number of patients included (n=7) and the variability of the implants used.

Line 43: Change main to common, it is less commonly seen with modern implant designs and improved techniques.

Line 218-222: Why was the second rater not used for patient’s 3-6? This should be addressed in the text

Reviewer #2: The authors attempt to model how lateralization of shoulder implant impacts the deltoid. It is an important and interesting topic, but it is a little difficult to for the reader to visualize and conceptualize. Including a set of images that contains all slices at all lateralizations with the angles overlay may help. There definitely should be a visualization for how the lateralization is modeled and how this affects the position and visualization of the deltoid.

Below are more specific comments:

Abstract:

Line 34: Should ‘portions’ be slices?

Introduction:

The introduction would benefit from a description of scapular notching, its causes, and its effects.

Line 61: I realize the CER has been described in previous literature, but since this is a major component of this study, I believe it needs to be described in the introduction. At least a basic definition.

Materials and Methods

Line 81: The results indicate that one participant was excluded due to movement during the MRI making the images unusable for the model creation. Here you imply that one subject was excluded based on exclusion criteria. Insufficient imaging is not an exclusion criteria.

Line 104/Fig 1: Identify what colors represent which anatomic segments.

Line 128: Is RCE the same as CER? If not, what is RCE?

Line 203: From the results, it looks like rater 2 only completed the model creation and not the ILSS positioning.

Results

Table 2: You may want to consider changing “model” to “week” in the last two rows of the table.

Lines 239-246: In the text I think you should list the overall (for all slices) mean and SD rather than the range. Additionally you should list the overall mean and SD for the DMA

Line 254: Typically significance levels are presented as p=0.002, etc.

Discussion

Line 283: Can you explain the different effects on lateralization. Did you see differences in the two patients with the Onlay for Wright-Tornier implants?

**********

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Reviewer #1: No

Reviewer #2: No

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30 Jun 2021

To the Editorial Board and the Reviewers,

First, we would like to thank you deeply for all the precious comments the 2 reviewers have done for our manuscript. These comments have helped us to improve the quality and the robustness of our manuscript. We have meticulously considered all the comments made by the 2 reviewers. We are very honored to submit our new manuscript and we hope that this new version will meet all your expectations. Please find below our answers to each point mentioned by the 2 reviewers. As requested, you will find in our new submission, a version highlighting the changes (Revised Manuscript with tracked changes) made with comments visible in Word with elements highlighted in yellow and an unmarked version without tracked changes. Please note that we have chosen to add a new author to the manuscript (Margaux Machefert, PT). Indeed, her contribution was very important during the review of our manuscript. During the first submission, she did not have time to complete her work for the study. She was able to do so for the reviewing.

For Reviewer #1:

We thank you very much for this very insightful review of our manuscript. In response to your remark about the weakness of the study relating to the small sample: yes, the sample of this preliminary study is small, but we think that our results are reliable given that the values all evolve in the same direction for all the subjects. More about implants, the 2 implants do not have the same effect on lateralization. The Onlays are more lateralizing. However, we do not compare the Onlay / Inlay implants in this study but rather different simulations of lateralizations for each patient.

Line 43 : Change main to common, it is less commonly seen with modern implant designs and improved techniques.

We replaced the word "main" by the word “common", according to your advice.

Line 218-222 : Why was the second rater not used for patient’s 3-6? This should be addressed in the text.

Rater 2 was a PT student, she participated in the reliability study for this project, constituting her thesis for PT Diploma. At the time we decided to submit our work, she had not finished carrying out all the 3D modeling, ILSS positioning and the statistical part. We made the choice to publish our work quickly. Since then, she has been able to complete the reliability study and we have been able to add her data in this new version.

For Reviewer #2:

We thank you for your careful review of our work and your comments which have greatly improved our manuscript. We took the time to take each of your comments into consideration. Your main remark concerned the addition of figures to improve the understanding of our methodology. We have thus added 3 new Figures that will improve these points. We hope that these figures will meet your expectations

The introduction would benefit from a description of scapular notching, its causes, and its effects.

We added a description of notching in the introduction (its causes and effects) in accordance with your remark.

Line 34: Should ‘portions’ be slices?

You are right, it is indeed "slice" and not "portion". Even if in French it is the same word.

Line 61: I realize the CER has been described in previous literature, but since this is a major component of this study, I believe it needs to be described in the introduction. At least a basic definition.

We added a basic description of CER to make the study easier to understand.

Line 81: The results indicate that one participant was excluded due to movement during the MRI making the images unusable for the model creation. Here you imply that one subject was excluded based on exclusion criteria. Insufficient imaging is not an exclusion criteria.

We forgot to mention that movements during the acquisition of the MRI images (making the images uninterpretable), was a criterion for excluding the patient. We apologize for this oversight. One of the patients was therefore effectively excluded after the MRI examination, because images could not be interpreted.

Line 104/Fig 1: Identify what colors represent which anatomic segments.

We update the caption with the colors representing the anatomic segments.

Line 128: Is RCE the same as CER? If not, what is RCE?

It is indeed the CER! It is an oversight of translation. in French CER is written RCE for “Ratio Coaptateur/Elévateur”. We apologize for this mistake.

Line 203: From the results, it looks like rater 2 only completed the model creation and not the ILSS positioning.

We echo the remark also made by reviewer 1: Rater 2 was a PT student, she participated in the reliability study for this project, constituting her thesis for PT Diploma. At the time we decided to submit our work, she had not finished carrying out all the 3D modeling, ILSS positioning and the statistical part. We made the choice to publish our work quickly. Since then, she has been able to complete the reliability study and we have been able to add her data in this new version.

Table 2: You may want to consider changing “model” to “week” in the last two rows of the table.

We replaced the term "model" with "week" as requested.

Lines 239-246: In the text I think you should list the overall (for all slices) mean and SD rather than the range. Additionally you should list the overall mean and SD for the DMA

As requested, we have included the mean and standard deviation of each parameter for each lateralization and each slice, directly in the text of Results, part “Biomechanical parameters”.

Line 254: Typically significance levels are presented as p=0.002, etc.

As requested, we added "p =" before the significance levels for this paragraph and wherever needed in the manuscript.

Line 283: Can you explain the different effects on lateralization. Did you see differences in the two patients with the Onlay for Wright-Tornier implants?

In response to this remark, indeed the 2 implants do not have the same effect on lateralization. The onlays are more lateralizing. However, we do not compare the onlay / inlay in this study but rather different simulations of lateralizations for each patient.

We thank you in advance for the new reviewing and we hope that you will find it suitable for your journal. Do not hesitate to contact us with any questions (l.martinez@ifmk.fr; + 33 684174961).

Yours truly,

Submitted filename: Rebuttal Letter.docx

Click here for additional data file.

21 Jul 2021

PONE-D-21-12682R1

Analysis of the coaptation role of the deltoid in reverse shoulder arthroplasty. A preliminary biomechanical study.

PLOS ONE

Dear Dr. Martinez,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Sep 04 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Katherine Saul

Academic Editor

PLOS ONE

Journal Requirements:

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

[Note: HTML markup is below. Please do not edit.]

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

**********

2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: The authors did a commendable job addressing all comments and concerns.

I apologize for any confusion. My previous comment "Lines 239-246: In the text I think you should list the overall (for all slices) mean and SD rather than the range. Additionally you should list the overall mean and SD for the DMA" I was suggesting the average for all slices, not the average of each slice. Your edits essentially repeat the data from the table in the text. I believe the previous version had one range for slices 1 through 4, I was simply suggesting replace the range with one mean of slices 1 through 4.

**********

7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

23 Jul 2021

To the Editorial Board and the Reviewers,

We would like to thank again the Editorial Board and the Reviewers for the new precious comments they have done for our manuscript. These last comments will certainly make the manuscript more robust and understandable. We have considered the comment of Reviewer 2 concerning the Results and we have modified accordingly. We apologize for our misunderstanding of his first remark. We hope that our modifications will correspond to his expectations. Likewise, in accordance with your request, we have added information on patients' consent to participate in the study and how consent was obtained. Again, we are very honored to submit our new manuscript and we hope that this new version will meet all your expectations. We left in this letter the comments of the first review from the 2 reviewers. We have also highlighted the comment of this new reviewing with our response. As requested, you will find in our new submission, a version highlighting the change made with comments visible in Word with elements highlighted in yellow (Revised Manuscript with tracked changes). Please note that only the last comment from Reviewer 2 appears in this version. You will also find an unmarked version without tracked changes.

First reviewing

For Reviewer #1:

We thank you very much for this very insightful review of our manuscript. In response to your remark about the weakness of the study relating to the small sample: yes, the sample of this preliminary study is small, but we think that our results are reliable given that the values all evolve in the same direction for all the subjects. More about implants, the 2 implants do not have the same effect on lateralization. The Onlays are more lateralizing. However, we do not compare the Onlay / Inlay implants in this study but rather different simulations of lateralizations for each patient.

Line 43 : Change main to common, it is less commonly seen with modern implant designs and improved techniques.

We replaced the word "main" by the word “common", according to your advice.

Line 218-222 : Why was the second rater not used for patient’s 3-6? This should be addressed in the text.

Rater 2 was a PT student, she participated in the reliability study for this project, constituting her thesis for PT Diploma. At the time we decided to submit our work, she had not finished carrying out all the 3D modeling, ILSS positioning and the statistical part. We made the choice to publish our work quickly. Since then, she has been able to complete the reliability study and we have been able to add her data in this new version.

For Reviewer #2:

We thank you for your careful review of our work and your comments which have greatly improved our manuscript. We took the time to take each of your comments into consideration. Your main remark concerned the addition of figures to improve the understanding of our methodology. We have thus added 3 new Figures that will improve these points. We hope that these figures will meet your expectations

The introduction would benefit from a description of scapular notching, its causes, and its effects.

We added a description of notching in the introduction (its causes and effects) in accordance with your remark.

Line 34: Should ‘portions’ be slices?

You are right, it is indeed "slice" and not "portion". Even if in French it is the same word.

Line 61: I realize the CER has been described in previous literature, but since this is a major component of this study, I believe it needs to be described in the introduction. At least a basic definition.

We added a basic description of CER to make the study easier to understand.

Line 81: The results indicate that one participant was excluded due to movement during the MRI making the images unusable for the model creation. Here you imply that one subject was excluded based on exclusion criteria. Insufficient imaging is not an exclusion criteria.

We forgot to mention that movements during the acquisition of the MRI images (making the images uninterpretable), was a criterion for excluding the patient. We apologize for this oversight. One of the patients was therefore effectively excluded after the MRI examination, because images could not be interpreted.

Line 104/Fig 1: Identify what colors represent which anatomic segments.

We update the caption with the colors representing the anatomic segments.

Line 128: Is RCE the same as CER? If not, what is RCE?

It is indeed the CER! It is an oversight of translation. in French CER is written RCE for “Ratio Coaptateur/Elévateur”. We apologize for this mistake.

Line 203: From the results, it looks like rater 2 only completed the model creation and not the ILSS positioning.

We echo the remark also made by reviewer 1: Rater 2 was a PT student, she participated in the reliability study for this project, constituting her thesis for PT Diploma. At the time we decided to submit our work, she had not finished carrying out all the 3D modeling, ILSS positioning and the statistical part. We made the choice to publish our work quickly. Since then, she has been able to complete the reliability study and we have been able to add her data in this new version.

Table 2: You may want to consider changing “model” to “week” in the last two rows of the table.

We replaced the term "model" with "week" as requested.

Lines 239-246: In the text I think you should list the overall (for all slices) mean and SD rather than the range. Additionally you should list the overall mean and SD for the DMA

As requested, we have included the mean and standard deviation of each parameter for each lateralization and each slice, directly in the text of Results, part “Biomechanical parameters”.

Line 254: Typically significance levels are presented as p=0.002, etc.

As requested, we added "p =" before the significance levels for this paragraph and wherever needed in the manuscript.

Line 283: Can you explain the different effects on lateralization. Did you see differences in the two patients with the Onlay for Wright-Tornier implants?

In response to this remark, indeed the 2 implants do not have the same effect on lateralization. The onlays are more lateralizing. However, we do not compare the onlay / inlay in this study but rather different simulations of lateralizations for each patient.

Second reviewing

“I apologize for any confusion. My previous comment "Lines 239-246: In the text I think you should list the overall (for all slices) mean and SD rather than the range. Additionally you should list the overall mean and SD for the DMA" I was suggesting the average for all slices, not the average of each slice. Your edits essentially repeat the data from the table in the text. I believe the previous version had one range for slices 1 through 4, I was simply suggesting replace the range with one mean of slices 1 through 4.”

We apologize for misunderstanding the request. As requested by Reviewer 2, we have re-modified the results of “Biomechanical Parameters” as follows: we have computed one Mean±SD of slices 1 through 4 for each parameters and each lateralization (0, 6, 9, 12mm) : Angle T, E, CER and DMA. In this way, we avoid repeating the Table 4. We hope this will meet your expectations.

Likewise, in accordance with your request, we have added information on patients' consent to participate in the study and how consent was obtained:

Line 86-88: Each patient was informed of the study via a newsletter. Then, each patient gave their consent to participate in the study by signing a consent letter informing them that their data will be used for the current study. Patient data has been anonymized.

We thank you in advance for the new reviewing and we hope that you will find it suitable for your journal. Do not hesitate to contact us with any questions (l.martinez@ifmk.fr; + 33 684174961).

Yours truly,

Submitted filename: Rebuttal Letter.docx

Click here for additional data file.

26 Jul 2021

Analysis of the coaptation role of the deltoid in reverse shoulder arthroplasty. A preliminary biomechanical study.

PONE-D-21-12682R2

Dear Dr. Martinez,

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PLOS ONE

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Reviewers' comments:

5 Aug 2021

PONE-D-21-12682R2

Analysis of the coaptation role of the deltoid in reverse shoulder arthroplasty. A preliminary biomechanical study.

Dear Dr. Martinez:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org.

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on behalf of

Dr. Katherine Saul

Academic Editor

PLOS ONE