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. Author manuscript; available in PMC: 2025 Aug 1.
Published in final edited form as: J Electromyogr Kinesiol. 2024 May 15;77:102889. doi: 10.1016/j.jelekin.2024.102889

Older age is associated with decreased overall shoulder strength but not direction-specific differences in the three-dimensional feasible torque space

Emma M Baillargeon 1, Amee L Seitz 2, Daniel Ludvig 3,4, Constantine P Nicolozakes 3,4,5, Swati D Deshmukh 6, Eric J Perreault 3,4,7
PMCID: PMC11302932  NIHMSID: NIHMS2001130  PMID: 38820987

Abstract

Shoulder strength is reduced in older adults but has only been assessed in planar motions that do not reflect the diverse requirements of daily tasks. We quantified the impact of age on strength spanning the three degrees of freedom relevant to shoulder function, referred to as the feasible torque space. We hypothesized that the feasible torque space would differ with age and expected this age-effect to reflect direction-specific deficits. We measured strength in 32 directions to characterize the feasible torque space of the shoulder in participants without shoulder pain or tendinous pathology (n=39, 19–86 years). We modeled the feasible torque space for each participant as an ellipsoid, computed the ellipsoid size and direction-specific metrics (ellipsoid position, orientation, and shape), and then tested the effect of age on each metric. Age was negatively associated with ellipsoid size (a measure of overall strength magnitude; −0.0033 ± 0.0007 (Nm/kg)/year, p<0.0001). Contrary to our expectation, the effect of age on the direction-specific metrics did not reach statistical significance. The effect of age did not differ significantly between male and female participants. Three-dimensional strength measurements allowed us to constrain the direction of participants’ maximum torque production and characterize the entire feasible torque space. Our findings support a generalized shoulder strengthening program to address age-related shoulder weakness in those without pain or pathology. Clinical exam findings of imbalanced weakness may suggest underlying pathology beyond an effect of age. Longitudinal studies are needed to determine the positive or negative impact of our results.

Keywords: Older adults, feasible torque space, aging, age-related shoulder weakness, isometric torque

Introduction

Dressing, bathing, and other essential daily tasks rely on shoulder strength in many different directions [Gates et al., 2016, Santago et al., 2017]. Therefore, age-related shoulder weakness [Andrews et al., 1996, Bradley and Pierpoint, 2023, Hughes et al., 1999a, b, Kim et al., 2009, Kuhlman et al., 1992, Vidt et al., 2012, Yassierli et al., 2007] threatens whole arm function and older adults’ independence [Kenny et al., 2008, Santago et al., 2017]. However, age-related shoulder weakness has only been studied in anatomical planes of motion. No study has quantified the impact of age on shoulder strength across the entire span of directions used in everyday tasks. Therefore, our goal was to quantify the impact of age on three-dimensional shoulder strength using a previously developed method to model strength in all directions [Baillargeon et al., 2022]. By quantifying the impact of age on overall shoulder strength, these findings expand upon prior planar measures and can be used to guide strengthening recommendations for middle-aged and older adults.

The impact of age on shoulder strength varies with shoulder posture [Hughes et al., 1999a] and across anatomical planes [Andrews et al., 1996, Hughes et al., 1999a, Kim et al., 2009]. Age-related weakness appears to be greater in shoulder extension/flexion and abduction/adduction than in external/internal rotation, but these findings may be confounded by differences in arm posture between torque directions during testing [Andrews et al., 1996, Bradley and Pierpoint, 2023, Hughes et al., 1999a, Kim et al., 2009]. In addition, these prior data were collected using single-axis dynamometers, meaning that forces or torques generated out-of-plane with the measurement axis were not quantified [Coats-Thomas, 2022, Ericson et al., 2002, Pan et al., 2005]. Therefore, the direction that participants generated torque could not be constrained and likely varied across participants and trials. This limitation of single-axis dynamometers is particularly important for measuring strength the shoulder, where muscles often generate force in multiple axes [Baillargeon et al., 2022, Lipps et al., 2020]. Finally, the impact of age on shoulder strength has only been studied for planar motions (abduction/adduction, external/internal rotation, and extension/flexion), which describe only a small subset of the shoulder torque directions used daily. Given these limitations, three-dimensional (3D) assessments of shoulder strength at a consistent posture are needed to understand the impact of age-related weakness on shoulder torque production in all axes, including task-relevant, combined directions.

The feasible torque space, a measure of strength in all directions, provides a more complete understanding of how age impacts the shoulder strength available for daily tasks [Baillargeon et al., 2022]. A feasible torque space is the set of all torques a person can produce, defining a functional boundary. The shoulder torques required to accomplish different tasks lie in different portions of the feasible space. Tasks or torques that are not feasible for a person to achieve lie outside the boundary of their feasible space. Age-related changes to the overall size, position, orientation, or shape of an individual’s feasible torque space could result in certain tasks becoming more difficult (closer to their feasible bounds) or impossible (outside of their feasible bounds) to complete. A uniform decrease in strength across all directions would be captured by an age-related difference in ellipsoid size, whereas differences in position, orientation, or shape of the feasible torque space would indicate direction-specific age effects. Feasible spaces have been used to describe the strength of various limbs and joints [Gruben et al., 2003, Hernandez et al., 2015, Kutch and Valero-Cuevas, 2011, Makhsous et al., 1999], including the shoulder [Baillargeon et al., 2022, Coats-Thomas et al., 2022], but have not yet been used to compare how shoulder strength differs with age. By combining measurements of strength in multiple directions, this approach not only quantifies the overall magnitude of strength, but also the relative balance and distribution of strength across torque directions. Quantifying the effect of age on these 3D measures of shoulder strength will provide further insight into how shoulder strength differs with age and may help to identify specific tasks that are most sensitive to age-related weakness.

Our goal was to quantify the impact of age on 3D shoulder strength. We accomplished this goal by quantifying 3D shoulder strength in younger, middle-aged, and older adults without shoulder pain or injury. We measured strength in all directions from a single posture and used three degree-of-freedom torque measurements to ensure that we quantified the magnitude and direction of all voluntarily produced torques. Our hypothesis was that age-related weakness would alter the feasible torque space describing 3D strength of the shoulder. Given that the effect of age on shoulder strength has been reported to differ across anatomical planes [Andrews et al., 1996, Hughes et al., 1999a, Kim et al., 2009], we expected the feasible torque space would not simply shrink uniformly in size but rather change in ways that reflected these direction-specific deficits (position, orientation, or shape). Our results expand upon previous unidimensional measures of shoulder strength to quantify the impact of age on the entire 3D range of shoulder strength and inform clinical monitoring and guidance for older adults.

Methods

This cross-sectional study was approved by the Northwestern University Institutional Review board (protocol STU00206400). All participants gave informed consent prior to data collection.

Participants

Adults with no history of shoulder pain or injury were recruited to participate. We excluded individuals with current shoulder pain or past substantial shoulder pain. Consistent with prior literature [Mall et al., 2010], we defined substantial pain as pain that was: 1) self-rated as greater than 3 out of 10 (on an 11-point numeric pain rating scale [Michener et al., 2011]) and 2) lasted longer than six weeks, required medication, prompted a physician visit, or was considered greater than normally experienced in daily life. To ensure an unbiased assessment of current pain, participants were asked to not take over-the-counter pain medication on the day of testing, and those taking prescribed pain medication were excluded. All participants were right-hand dominant, and their right arm was tested to eliminate possible confounding due to laterality. We chose to only test one arm because prior studies have not found a difference in the effect of age between dominant and nondominant shoulder strength, therefore not justifying for the increased participant burden of bilateral testing [Andrews et al., 1996, Hughes et al., 1999a, b, Kim et al., 2009]. We selected the dominant arm because rotator cuff tears are more common and more often painful in the dominant arm [Keener et al., 2010, Minagawa et al., 2013, Sayampanathan and Andrew, 2017]. Additional exclusion criteria were previous fracture of the right arm, surgery to the right shoulder, rotator cuff tear on imaging, sustained use of arms for mobility, neurological or inflammatory disease, or current pregnancy.

We screened all participants for asymptomatic tendon pathology, as asymptomatic rotator cuff tears are common in older adults and may influence shoulder strength [Milgrom et al., 1995, Minagawa et al., 2013, Morise et al., 2017, Teunis et al., 2014, Yamamoto et al., 2010]. We collected ultrasound images of the biceps and rotator cuff tendons prior to strength testing in all participants. Images were rated as no tear, partial-thickness tear, or full-thickness by a board-certified musculoskeletal radiologist (S.D.D.) who was blinded to the participants’ strength and demographic data.

All participants completed the PENN Shoulder Score to self-report their shoulder pain, satisfaction, and function [Leggin et al., 2006], and self-reported their height, weight, age, and sex.

Experimental Set-up

Participants were seated during strength testing with their arm in 90 degrees of shoulder abduction and elbow flexion and 0 degrees of shoulder rotation (Figure 1A). We chose this posture because the impact of age on shoulder strength has been shown to be greater when the arm is elevated [Hughes et al., 1999b]. One participant was tested at 85 degrees of shoulder abduction due to mild paresthesia at 90 degrees. Padded straps at the participant’s hips and across their chest provided trunk support and aided in isolating torque generation to the shoulder. Scapular motion was not restricted.

Figure 1. Experimental set-up and data processing.

Figure 1.

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A) Participants were seated with their right arm in 90 degrees of shoulder abduction and elbow flexion. A pre-made fiberglass cast attached the participant’s arm to the load cell. Forces and torques measured at the load cell were transformed to a humeral reference frame centered at the glenohumeral joint. B) Participants maximized their shoulder torque in 32 different directions. In each trial, the maximum torque generated within the target bounds was identified. C) Together, the set of maximum torques defined the feasible torque space of the shoulder (shaded region), a representation of strength in all directions. The feasible torque spaces for two representative participants are illustrated in both a 3D and superior view overlaid on an illustration of the participant. ABD: abduction, ADD: adduction, ER: external rotation, IR: internal rotation, EXT: extension, FLEX: flexion

To measure strength, participants generated maximum shoulder torques with their arm secured to a six degree-of-freedom load cell (45E15A4, 630N80 load rating, JR3 Inc.). A pre-made fiberglass cast extending from mid-hand to mid-humerus secured the participant’s arm to the load cell and supported their arm against gravity. Forces and torques were measured at the attachment point of the cast to the load cell. Resting forces and torques from the weight of the arm were subtracted, and the remaining data were transformed to a local humeral-defined coordinate system (Figure 1A) [Wu et al., 2005].

Experimental Protocol

We measured isometric shoulder strength in 32 directions using a protocol described previously [Baillargeon et al., 2022]. Participants used real-time visual feedback of shoulder torque to maximize their torque in 6 unconstrained and 26 constrained target directions. Participants first generated their maximum torque about each of our measurement axes (Figure 1A) using only feedback of their torque magnitude in the target direction (1D visual feedback). We describe these trials as unconstrained because out-of-plane torques were not shown, and therefore participants were not tasked with precisely controlling their torque direction in these trials. These trials mimic traditional 1D strength measurements. In the remaining 26 directions, participants maximized their shoulder torque in a constrained target direction while controlling 3D visual feedback. Constrained target directions allowed us to match torque directions across participants and to measure strength along directions that may otherwise not be explored in unconstrained trials due to natural anatomical coupling. The 26 constrained target directions were uniformly distributed and spaced at 45-degree intervals, including pure torques about each of the measurement axes and equal combinations of torques about two and three axes [Vasavada et al., 2002]. Participants maintained their maximum torque for at least one second in each direction and were allowed multiple attempts to accomplish this task. Participants rested for at least 30 seconds between trials and target order was randomized to minimize the influence of fatigue. Participants completed a standardized set of practice targets prior to data collection.

Data processing

We used the strength data to estimate the feasible torque space of the shoulder for each participant. Torque data were smoothed using a 1-second moving average filter and the maximum torque within the target bounds was identified for each trial (Figure 1B). If multiple attempts were made, then the maximum across all attempts for a given torque direction was used. This resulted in a set of 32 strength measurements for all but 3 participants who each had one direction accidentally omitted during data collection.

Since shoulder strength increases with both body-mass-index (BMI) and weight, age-related differences in either could confound the effect of age on strength [Hughes et al., 1999a, Hurd et al., 2011, Kim et al., 2009, Lannersten et al., 1993]. Both BMI and weight tended to increase with age in our participants (BMI: slope = 0.078 ± 0.031 (kg/m2)/year, p = 0.015; weight: slope = 0.16 ± 0.092 kg/year, p = 0.085). We chose to divide each participant’s 32 maximum strength measures by their weight prior to computing the feasible torque space metrics. Not normalizing the strength data or normalizing strength to BMI rather than weight did not change our conclusions (see supplemental material).

We fit an ellipsoid model to each participant’s set of strength measurements to parameterize the feasible torque space enclosing these measurements. We did this using principal components analysis (PCA) on the strength measurements to identify the direction (eigenvectors) and magnitude (eigenvalues) of the strongest axis, weakest axis, and an intermediate axis perpendicular to the strongest-weakest plane. If shoulder strength was equal in all directions, the feasible torque space would be a sphere centered at the origin (Figure 2A: green, orange, and magenta axes of equal length). However, because the shoulder is stronger in some directions than in others, the feasible torque space instead resembles a flattened disc with its center shifted toward the shoulder’s stronger directions (Figures 1C and 2B) [Baillargeon et al., 2022]. To assess how well an ellipsoid represented the shoulder strength data of each participant, we quantified the normalized mean square error between the measured strength data and the torque in the same direction predicted by the participant-specific ellipsoid model.

Figure 2. Illustration of 3D shoulder strength modeled as an ellipsoid and simulated changes in each of the four metrics quantifying this model.

Figure 2.

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In all panels, the feasible torque space, modeled by a three-dimensional ellipsoid, is depicted by the shaded region. The ellipsoid center is the red point and the strongest (green), weakest (orange), and intermediate (magenta) principal radii are illustrated. A) Hypothetically, if shoulder was equally strong in all directions, the feasible torque space would be a sphere centered at the origin with green, orange, and magenta radii of equal length. B) However, shoulder strength is not the same in all directions. In this example participant, the magnitude of each axis varies, yet the center remains very close to the origin (this participant is also shown in Figure 1C). The bottom panels illustrate simulated changes to this participant’s strength ellipsoid for a 50% reduction in overall strength magnitude (C), a translation by 40% of their overall strength magnitude in FLEX and IR (D, note that in this exaggerated example the person would not be able to generate torque in extension or external rotation), a change in the ratio of strength between strongest and intermediate radii (E), and a 45-degree rotation about the ABD/ADD axis. ABD: abduction, ADD: adduction, ER: external rotation, IR: internal rotation, EXT: extension, FLEX: flexion

We computed four metrics (size, position, shape, and orientation) to characterize the ellipsoid describing the 3D shoulder strength of each participant [Baillargeon et al., 2022]. These four metrics quantify the ways in which the feasible torque space could vary across participants. We therefore tested the impact of age on each of these metrics to determine if and how 3D strength differed with age. First, the size of the ellipsoid represents overall strength magnitude, with a larger ellipsoid corresponding to a stronger shoulder (Figure 2B, C). We quantified strength magnitude by computing the Euclidian norm of the three ellipsoid radii (eigenvalues identified from PCA). Second, the location of the ellipsoid’s center is a measure of relative strength balance between opposing directions (i.e., difference in flexion vs. extension strength; Figure 2B, D). The 3D position of the ellipsoid center was computed as the average of all strength data points. In the 3 participants with one direction omitted, the direction opposite the missing point was removed when calculating the center to avoid bias due to unbalanced data. Next, the shape of the feasible torque space quantifies the relative strength ratio between orthogonal axes (i.e., extension/flexion vs. abduction/adduction strength; Figure 2 B, E). Given the space is 3D, we computed the shape in two perpendicular planes as the ratio of weakest to strongest ellipsoid radii and intermediate to strongest ellipsoid radii (therefore, shape is a 2D metric). A shape closer to 1 indicates greater similarity in strength between axes and more circular shape in the corresponding plane (Figure 2A). Lastly, even if the ellipsoid size, center position, and shape were consistent across participants, overall 3D strength could differ if the feasible torque space was rotated between participants (Figure 2 B, F). As a hypothetical example, consider two people who have the same overall strength magnitude and relative ratio of strength across axes, but one person is weakest in shoulder extension (pulling the arm backwards) and the other is weakest in shoulder abduction (raising the arm overhead). The difference in weakest direction between these two people, and hence the orientation of their feasible torque spaces, would impact which tasks they find most difficult and would be most sensitive to a loss of strength in. We used the direction of the weakest principal axis to quantify orientation of the feasible torque space because it has been shown to be a robust measure of orientation given the shape of the feasible torque space of the shoulder [Baillargeon et al., 2022]. The direction of the weakest axis is a unit vector. To reduce dependent degrees of freedom, we chose to represent this direction in spherical coordinates as two angles. First, the angle within the abduction/adduction-external/internal rotation plane (traditionally described as the azimuth; a vector with an azimuth angle of 0 or 180 degrees is colinear with the abduction/adduction axis, whereas 90 or 270 degrees is colinear with the external/internal rotation axis). The second angle is the elevation of the unit vector out of this first plane toward the extension/flexion axis (a vector with an elevation angle of 0 degrees is coplanar with the abduction/adduction-external/internal rotation plane, whereas a vector with an elevation angle of 90 degrees is perpendicular to this plane and colinear with the extension/flexion axis). Note that an ellipsoid is symmetric about its principal axes, and therefore, the orientation of the weakest axis and center position must be used together to interpret which direction along this axis (positive or negative) an individual is weakest in. Together, these four metrics – overall strength magnitude, strength balance, shape, and weakest axis – capture all possible ways in which the feasible torque space could vary across participants. Importantly, a change in any one of these metrics could indicate a change in functional capacity, as the torques required for a particular task could lie close to the edge of a particular feasible strength boundary.

Statistical Analysis

Our hypothesis was that age-related weakness would alter the feasible torque space describing 3D shoulder strength. We expected that the effect of age would not be symmetric across torque directions. More specifically, the ellipsoid characterizing the feasible torque space would not only shrink in size with age, but that we would also observe that ellipsoid strength balance, shape, or weakest axis would differ with participant age. To test our hypothesis, we modeled the effect of age on overall strength magnitude (ellipsoid size), strength balance (center position), strength ratios between orthogonal axes (ellipsoid shape), and the orientation of the weakest direction cross-sectionally across participants of different ages. We used either univariate or multivariate linear regression to model each metric as the dependent variables (4 models in total describing 1D strength magnitude, 3D strength balance, 2D shape, and 2D weakest direction). Age, sex and the interaction between age and sex were included as independent factors in each model. Our null hypothesis was that the strength metrics did not differ with age (slope equal to zero). Our secondary hypothesis was that the effect of age did not differ between male and female participants. For the multivariate models, these hypotheses were tested using Pillai’s trace as the MANOVA test statistic on our fitted parameters.

In addition to our primary analyses, we used a one-sample Hotelling’s T2-test to determine if the 3D strength bias (ellipsoid center) was significantly different than zero across all participants regardless of age. We also modeled the effect of age on participants’ weight and self-reported pain, satisfaction, and function sub-scores of the PENN shoulder score using linear regression models with age and sex as fixed factors to characterize our participant group. All statistical tests were performed in RStudio using R version 4.1.1 (The R Foundation for Statistical Computing). We selected a threshold of alpha=0.05 to evaluate statistical significance without correcting for multiple comparisons in this exploratory analysis.

Results

Participant characteristics

Thirty-nine adults 19 to 86 years old were included in these analyses (Table 1). Two participants were excluded from analyses because they did not complete the full protocol due to fatigue or comprehension. All participants were free from full-thickness biceps, subscapularis, supraspinatus, and infraspinatus/teres minor tendon tears as confirmed by ultrasound imaging. Participants reported high satisfaction and function of their shoulder and low self-reported shoulder pain as quantified by the PENN shoulder score (Table 1) [Leggin et al., 2006]. Self-reported shoulder pain (slope = −0.005 ± 0.004, p = 0.200), satisfaction (slope = 0.008 ± 0.006, p = 0.175), and function (slope = −0.019 ± 0.015, p = 0.202) did not significantly differ with age.

Table 1. Participant characteristics and 3D strength metrics.

Data are presented as mean ± standard deviation where applicable. The PENN shoulder scale is a self-reported measure of shoulder pain (subscale range 0–30, lower is less pain), satisfaction (subscale range 0–10, higher is more satisfied) and function (subscale range 0–60, higher is better function) [Leggin et al., 2006]. Participants were well distributed across younger, middle, and older adult age ranges. Age groups are presented here for presentation. All analyses were performed with age as a continuous variable. ABD: abduction, ADD: adduction, ER: external rotation, IR: internal rotation, EXT: extension, FLEX: flexion

Younger adults (18–39 years) Middle-aged adults (40–59 years) Older adults (> 59 years) All participants
Number of participants 15 12 12 39
Sex, female (%) 9 (60%) 8 (67%) 5 (42%) 22 (56%)
Age (years) 28 ± 5.6 range: 19–37 51 ± 5.7 range: 40–59 70 ± 7.9 range: 60–86 48 ± 19.0 range: 19–86
PENN shoulder score
 Pain subscale 0.33 ± 0.62 0.08 ± 0.29 0.08 ± 0.29 0.18 ± 0.45
 Satisfaction subscale 9.5 ± 0.92 9.9 ± 0.29 9.6 ± 0.90 9.6 ± 0.78
 Function subscale 58.9 ± 1.7 59.0 ± 1.3 58.1 ± 2.0 58.7 ± 1.7
3D Strength Metrics
Strength magnitude (Nm/kg) 0.44 ± 0.11 0.40 ± 0.13 0.34 ± 0.11 0.40 ± 0.12
Strength bias (% strength magnitude)
 ABD(−)/ADD(+) 6.8 ± 4.0 6.6 ± 6.3 10.9 ± 9.9 8.0 ± 7.0
 ER(−)/IR(+) −4.3 ± 4.5 −4.6 ± 4.1 −2.9 ± 4.3 −4.0 ± 4.3
 EXT(−)/FLEX(+) 7.8 ± 3.2 9.0 ± 3.8 6.1 ± 5.5 7.6 ± 4.3
Weakest axis (degrees)
 Azimuth (in ABD/ADD-ER/IR plane) 108 ± 15 114 ± 5 115 ± 8 112 ± 11
 Elevation (toward EXT/FLEX axis) −6 ± 6 −6 ± 9 −8 ± 6 −7 ± 7
Strength ratio (unitless ratio 0 to 1)
 weakest/strongest ratio 0.56 ± 0.10 0.55 ± 0.09 0.50 ± 0.07 0.54 ± 0.09
 intermediate/strongest ratio 0.82 ± 0.08 0.85 ± 0.08 0.83 ± 0.09 0.83 ± 0.08
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An ellipsoid feasible torque space as a model of 3D shoulder strength

An ellipsoid feasible torque space model characterized the participants’ shoulder strength data well, as indicated by a normalized mean square error of 0.93 ± 0.05 (mean ± 1 standard deviation across participants). On average, the feasible torque space of the shoulder was similar in shape to a disc. Strength in the intermediate and strongest directions were more similar (intermediate-to-strongest axis strength ratio = 0.83 ± 0.08), with more substantial flattening along the weakest direction (weakest-to-strongest axis strength ratio = 0.54 ± 0.09; Figure 1C and Table 1). We observed a small strength bias across all participants (Hotelling’s one-sample T2=86.7, p<0.0001), with the shoulder being stronger in adduction (bias = 8.0 ± 7.0 % strength magnitude), external rotation (bias = 4.0 ± 4.3 % strength magnitude), and flexion (bias = 7.6 ± 4.3 % strength magnitude) than the antagonist directions (Table 1). The shoulder’s weakest axis was internal rotation combined with abduction and external rotation combined with adduction (rotated 112 ± 11 degrees from the abduction/adduction axis). This axis was closely aligned with the external/internal rotation-abduction/adduction plane (only 7 ± 7 degrees out-of-plane toward the extension/flexion axis; Figures 1C and 3C, Table 1).

Figure 3. The effect of age on each 3D strength metric derived from the feasible torque space ellipsoid.

Figure 3.

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Male (blue) and female (red) participants are represented by each point. Blue and red lines depict the predicted mean and 95% confidence interval (shading) for male and female participants respectively from linear regression. Multivariate regression was used to fit the multidimensional variables (B-D), with the univariate fit for each dimension illustrated here (see Table 2 for regression results).

Impact of age on the feasible torque space of the shoulder

The shoulder was weaker in older participants. However, counter to our expectation, we found a significant effect of age only on overall strength magnitude of the feasible torque space. As anticipated, the ellipsoid model of 3D shoulder strength was smaller in older participants (beta±SE for the slope of the effect of age from the model; −0.0033 ± 0.0007 (Nm/kg)/year, p<0.0001; Table 2 and Figure 3A). This age-related difference in strength magnitude was large, with a 39% strength decrease predicted from 20 to 80 years old. Although we observed an age-related trend in some of the other metrics (Figure 3), none reached statistical significance (strength bias, p=0.388; weakest axis orientation, p=0.221; strength ratio, p=0.060; see Table 2 and Figure 3B–D). The effect of age on each of the 3D strength metrics also did not differ significantly between male and female participants (Table 2).

Table 2. Summary of the effect of age and difference in the effect of age between male and female participants from linear regression models (n=39 participants for all models).

SE: standard error ABD: adduction, ADD: adduction, ER: external rotation, IR: internal rotation, EXT: extension, FLEX: flexion

Effect of age Difference in the effect of age by sex
Beta ± SE F p-value Beta ± SE F p-value
Strength magnitude (Nm/kg)/year −0.0033 ± 0.0007 19.97 p<0.0001 0.0018 ± 0.0011 1.417 p=0.242
Strength bias (%/year)
 ABD(−)/ADD(+) 0.09 ± 0.06 1.041 p=0.388 −0.04 ± 0.11 0.196 p=0.899
 ER(−)/IR(+) 0.02 ± 0.04 −0.06 ± 0.08
 EXT(−)/FLEX(+) −0.04 ± 0.04 0.01 ± 0.08
Weakest axis (deg/year)
 Azimuth (ABD/ADD-ER/IR plane) 0.14 ± 0.09 1.579 p=0.221 0.34 ± 0.17 2.43 p=0.103
 Elevation (toward EXT/FLEX axis) −0.03 ± 0.06 0.19 ± 0.13
Strength ratio (unitless/year)
 weakest/strongest ratio −0.0014 ± 0.0007 3.057 p=0.060 0.0010 ± 0.0015 0.311 p=0.734
 intermediate/strongest ratio 0.0005 ± 0.0007 −0.0001 ± 0.0015
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Discussion

Our goal was to quantify the impact of age on 3D shoulder strength. We accomplished this by quantifying 3D shoulder strength in younger, middle-aged, and older adults without shoulder pain or injury using an ellipsoid model of the feasible torque space. We hypothesized that age-related weakness would alter the feasible torque space of the shoulder, and we expected the effect of age would not be captured by differences in strength magnitude alone. Unlike previous studies, we measured strength in all directions from a single posture and used three degree-of-freedom torque measurements to ensure that we quantified the magnitude and direction of all voluntarily produced torques. Age had a substantial impact on overall strength magnitude, quantified by the size of the feasible torque space, with our experimental results predicting a 39% decrease in shoulder strength from 20 to 80 years of age. However, the effect of age on our additional measures of the strength bias within each axis (ellipsoid position), weakest axis orientation (ellipsoid orientation), and strength ratio between orthogonal axes (ellipsoid shape) did not reach statistical significance. This study is the first to demonstrate the impact of age-related weakness on shoulder strength across the wide variety of torque directions used during daily tasks. Our methods build upon prior work in two important ways. First, using a six degree-of-freedom load cell to measure 3D torque production enabled us to quantify the direction of torque production in contrast to 1D dynamometers which cannot detect torques outside of the measurement axis. Providing real-time, visual feedback of the 3D torque to our participants [Coats-Thomas, 2022, Ericson et al., 2002, Lipps et al., 2020, Pan et al., 2005] then allowed us to match torque directions precisely across participants. Second, by measuring strength in many uniformly distributed directions, we were able to model the entire feasible torque space of the shoulder. Using this approach, we quantified the impact of age across the entire range of shoulder torque production, including combined directions used during daily tasks, in a way that single measures previously could not.

Overall shoulder strength decreased with older age

Our finding that overall strength magnitude decreased with age is consistent with most studies, which have reported decreased shoulder strength with age in 1D measurements [Andrews et al., 1996, Backman et al., 1995, Hughes et al., 1999a, b, Kim et al., 2009, Kuhlman et al., 1992, Murray et al., 1985, Vidt et al., 2012, Yassierli et al., 2007]. Our results are not consistent with the few studies that have found no effect of age [Cavuoto and Nussbaum, 2013, Lannersten et al., 1993], which only included participants up to 65 years, did not normalize by weight or BMI, and did not assess age as a continuous variable but instead grouped participants using either a 45 or 50 year age threshold between younger and older groups. We found that overall 3D shoulder strength magnitude, computed from the feasible torque space, decreased 39% from 20 to 80 years-old on average, a 0.67% global strength decrease per year. This is similar in magnitude to the age-related differences reported previously, which range from 0.47 to 1.1% decrease in shoulder strength per year between younger adults in their 20s or 40s to older adults in their 60s or 70s [Hughes et al., 1999a, Kim et al., 2009, Yassierli et al., 2007].

All older adults in our study continued to report high levels of shoulder function and satisfaction despite the age-related weakness we measured (Table 1). We did not ask participants if they changed their activities due to shoulder weakness, so perhaps participants modified their behaviors in a way to allow them to maintain function [Manty et al., 2007, Weiss et al., 2007]. Without this information, though, our data suggest that the shoulder weakness we measured likely does not limit performance of activities of daily living, which require submaximal strength [Murgia et al., 2018, Santago et al., 2017]. Instead, age-related weakness likely impacts how older adults perform daily tasks [Baillargeon, 2020] even when not limiting what they are able to perform – effecting their functional reserve rather than daily function. Future studies will be needed to examine the consequences of this weakness, which will likely result in lower endurance, reduced resilience to injury, greater fatigue, or ability to perform high intensity or frequency than performance of activities of daily living.

The effect of age on direction-specific strength metrics did not reach significance

We did not find a significant effect of age on strength bias within each axis, quantified as the 3D position of the ellipsoid feasible torque space. In our data, shoulder strength was biased toward greater adduction (8.0±7.0), external rotation (−4.0±4.3), and flexion strength (7.6±4.3) compared to their opposing directions (Table 1). Although not significant, we observed a trend toward greater adduction bias with older age (slope: 0.09±0.06), with no such trend observed for external/internal rotation (slope: 0.02±0.04) or extension/flexion (−0.04±0.04) bias (Table 2). In comparison, Hughes et al. reported strength ratios biased toward stronger shoulder adduction, internal rotation, and extension. They observed a significant decrease in abduction/adduction strength bias with older age, consistent with the trend observed in our data, which may be in part due to their much larger sample size (n=120) than ours. In addition, Hughes et al. reported an age-related decrease in shoulder extension/flexion bias and increase in the external/internal rotation strength bias in elevated arm postures [Hughes et al., 1999b]. Notably, both studies tested abduction/adduction strength in the same posture. However, postural differences between studies likely contributed to our differences for external/internal rotation and extension/flexion. All our data were collected at 90 degrees of shoulder abduction with 0 degrees of shoulder rotation, whereas Hughes et al. used 90 degrees of shoulder flexion for extension/flexion bias and 90 degrees of abduction with 30 degrees of external rotation for external/internal rotation bias. These differences across studies provide further support for expanding our approach to different postures (see limitations of the study and recommendations for future research). In addition, Hughes et al. collected data using a 1D dynamometer, which would not have detected out-of-plane torques generated by participants [Coats-Thomas, 2022, Ericson et al., 2002, Pan et al., 2005]. Therefore, we are not able to directly compare our results because the ratios reported previously are calculated without considering torques not aligned to the measurement plane (see measurement consideration and strengths of our approach).

The effect of age on shoulder strength did not differ between male and female participants

We observed that the effect of age on shoulder strength did not differ between male and female participants. Prior studies have found conflicting evidence. Some have found no difference in the effect of age on strength between men and women [Andrews et al., 1996, Hughes et al., 1999a, b], whereas others have reported greater age-related weakness in men than in women for certain directions [Kim et al., 2009, Yassierli et al., 2007]. Differences in whether strength was normalized to weight, BMI, or not at all, and differences in task and measurement protocols likely contribute to this variability seen in the literature. Given that shoulder pain is more prevalent in women [Luime et al., 2004, Vogt et al., 2003] and conflicting evidence on whether men have a higher rate of asymptomatic rotator cuff pathology [Milgrom et al., 1995, Minagawa et al., 2013], there is a strong case for considering sex when clinically assessing shoulder strength and symptoms despite our limited understanding of the mechanisms for these differences. From our current results, it appears that the sex-related differences in pain and pathology prevalence may be independent to the age-related effect we examined. However, we limited our study to those without shoulder pain and tendon pathology, and we do not know if the effects of sex and age on the feasible torque space differ in those with these conditions.

Potential contributions to age-related weakness

Several factors likely contributed to the age-related differences observed in our study. Age-related weakness is not unique to the shoulder, but rather reflects a generalized effect of age on the neuromuscular system. Age-related weakness exceeds the weakness predicted from reduced muscle mass alone, highlighting the interaction of decreased muscle mass with additional factors including increased fat within the muscle, decreased voluntary activation, and impaired excitation-contraction coupling in older adults [Clark and Manini, 2008, 2012, Raz et al., 2015]. In addition to age-associated changes at the individual muscle level, altered coordination across muscles also likely contributes to decreased strength in older adults [Hortobagyi and Devita, 2006, Hortobagyi et al., 2011, Overbeek et al., 2019, Quirk and Hubley-Kozey, 2014, Seidler et al., 2002, Vidt et al., 2012]. Our own work supports this hypothesis, as we found that the directional preference of shoulder muscle activity decreased with age, suggesting greater co-contraction across muscles [Baillargeon, 2020]. Addressing age-related factors that are both intrinsic and extrinsic to muscle will be important to develop treatments able to prevent or reverse the age-related loss of strength.

Measurement considerations and strengths of our approach

To our knowledge, this study is the first to quantify the effect of age on shoulder strength across the full span of torque directions used during daily tasks. We chose to characterize the feasible torque space of the shoulder, the set of all achievable torques, and to compute four metrics that describe this space. Our methods build upon prior work in two important ways. First, we measured participants’ maximum shoulder torque production using a six degree-of-freedom load cell rather than a 1D dynamometer used previously [Andrews et al., 1996, Backman et al., 1995, Bradley and Pierpoint, 2023, Cavuoto and Nussbaum, 2013, Hughes et al., 1999a, b, Kim et al., 2009, Kuhlman et al., 1992, Lannersten et al., 1993, Murray et al., 1985, Vidt et al., 2012, Yassierli et al., 2007]. This allowed us to provide 3D torque as real-time visual feedback to our participants and for them to control this torque direction during maximum strength trials. This type of 3D feedback is not possible with 1D measurements. Without 3D feedback, participants produce substantial off-axis torques during maximum trials, meaning 1) the generated torque direction does not match the targeted direction and 2) the measured torque directions likely vary across participants [Coats-Thomas, 2022, Ericson et al., 2002, Lipps et al., 2020, Pan et al., 2005]. These points should be considered when interpreting shoulder strength measures reported from 1D dynamometer measurements [Andrews et al., 1996, Backman et al., 1995, Bradley and Pierpoint, 2023, Cavuoto and Nussbaum, 2013, Hughes et al., 1999a, b, Kim et al., 2009, Kuhlman et al., 1992, Lannersten et al., 1993, Murray et al., 1985, Vidt et al., 2012, Yassierli et al., 2007]. Second, we measured strength in 32 unique and equally distributed directions. With this approach, we quantified the impact of age across the entire range of possible shoulder torque production, including combined directions used during daily tasks, in a way that analyses of independent 1D strength measures cannot.

Limitations of thecurrent study and recommendations for future research

A few limitations must be considered when interpreting our results. First, our data are cross-sectional; therefore, the age-related differences seen here cannot be interpreted as changes over time. Longitudinal studies are needed to quantify age-related changes within a person and relationships between age-related shoulder weakness and future incidence of shoulder pain, pathology, and function. In addition to longitudinal studies of strength, examining the underlying mechanisms of observed age-related weakness (e.g., altered muscle coordination, atrophy, or impaired muscle quality) will provide further insight into whether the age-related differences in strength we observed are adaptations to maintain a healthy shoulder joint or are preclinical signs of impairment. Our sample size was also smaller in comparison to other prior studies. Limited statistical power may have contributed to our results not reaching statistical significance in some cases, which may be more specifically powered for in a larger sample or as longitudinal within-person changes.

Further, given the time required to test strength in 32 directions and impact of fatigue, we were unable to repeat our measurements in multiple postures, limiting the generalizability of our findings to tasks in other arm postures. We selected an elevated shoulder posture (90-degrees of shoulder abduction) for this study because the impact of age on shoulder strength has been shown to be greater when the arm is elevated [Hughes et al., 1999b]. However, many daily tasks occur with the arm in less elevation and closer to the body. Using the same protocol in a more functional posture (45-degrees shoulder elevation in the scapular plane), our group previously measured a very similar overall strength magnitude (0.33 ± 0.10 Nm/kg) with more symmetric strength balance that was less variable across participants (abduction bias: 0.50 ± 2.4% strength magnitude, internal rotation bias: 2.9 ± 4.0% strength magnitude, flexion bias: 3.0 ± 3.2% strength magnitude) [Coats-Thomas et al., 2022]. However, this prior study pooled data form both dominant and non-dominant arms and was not designed to test the effect of age on these metrics. Therefore, additional studies are needed to further our understanding of how the feasible torque space differs with posture and to identify if there are certain postures where this space is most sensitive to age or pathology. Although limited in capturing the complexity of in vivo function (e.g., influence of pain or altered coordination), we propose that musculoskeletal simulation may provide a good environment to first explore the interaction between age and posture effects [Baillargeon et al., 2019]. Simulation results could then inform which postures to collect in future experiments, perhaps selecting a posture most sensitive to age, certain pathology, or other factors of interest.

Conclusions and clinical implications

Age profoundly impacted shoulder strength in adults without shoulder pain or pathology. However, contrary to our expectation, we only observed significant age-related differences in overall strength rather than direction-specific deficits. Using 3D torque measurements to characterize the feasible torque space of the shoulder allowed us to control for torque direction in our study and to assess the impact of age on strength across the full span of possible torque directions. In addition to quantifying the effect of age on shoulder strength, these data also provide age-specific normative data from which to explore how shoulder strength varies in those with pain, pathology, or functional limitations. Given that we observed a uniform effect of age on shoulder strength, clinical exam findings with imbalanced deficits may suggest underlying dysfunction. Our findings also support a generalized shoulder strengthening program to address age-related shoulder weakness. Finally, because we did not find the effect of age to be direction-specific, tasks which appear more sensitive to age may in fact be those where individuals are performing closer to their feasible strength boundary.

Supplementary Material

1

Acknowledgements

The authors would like to acknowledge Timothy Haswell, MS for his technical assistance during protocol development and data collection and Margaret Coates-Thomas, PhD for her helpful discussion of the results.

Funding

This work was supported by the National Institutes of Health (grant numbers T32EB009406, F31-AG057137) and the American Society of Biomechanics Grant-In-Aid.

All sources of funding for this work have been acknowledged at the end of the manuscript.

Footnotes

Declaration of Interest Statement

All authors confirm that there are no known financial or personal conflicts of interest associated with this manuscript that could have inappropriately influenced its content or conclusions. All sources of funding for this work have been acknowledged at the end of the manuscript.

Conflict of interest statement: All authors confirm that there are no known financial or personal conflicts of interest associated with this manuscript that could have inappropriately influenced its content or conclusions.

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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