The interaction of in vivo muscle operating lengths and passive stiffness in rat hindlimbs

The force output of a skeletal muscle is primarily determined by its length, contraction velocity and activation level (Zajac, 1989). The force–length relationship of muscle is a function of the amount of myofilament overlap within a sarcomere, with an optimal plateau region corresponding to lengths that allows for the greatest number of actin-myosin cross-bridges to be formed (Gordon et al., 1966). This optimal length (L_o) is the length at which the muscle may generate the maximum force for a given activation level, and muscles are believed to operate at lengths close to this (Lutz and Rome, 1996; Burkholder and Lieber, 2001; Lieber and Ward, 2011). However, a muscle that is generating or dissipating significant amounts of mechanical work will have to alter its length and thus shift to lengths outside of this optimal range. Where muscles operate on the force–length relationship is an important determinant of force output and as such is critical for understanding in vivo muscle performance.

A muscle's mechanical function influences its operating length (the range of lengths a muscle utilizes in vivo during normal activities). For muscles functioning as a strut and remaining largely isometric during active force production, it is possible for operating length to remain within the plateau of the force–length relationship (Arnold and Delp, 2011). For muscles functioning as motors and undergoing significant shortening during active force production, contractions must span a larger range than the plateau. In some instances, muscles start at lengths that are longer than the optimal length, allowing for shortening onto the plateau where higher peak forces can be developed (Azizi and Roberts, 2010). This kind of behavior may be particularly important for muscles operating in series with elastic elements, where shortening against a compliant tendon may shift a muscle to the ascending limb of the force–length relationship where force can be compromised (Azizi and Roberts, 2010; Sutton et al., 2019). Finally, for muscles functioning as brakes and dissipating energy through active lengthening, the muscle's initial length may be shorter than the optimal length to avoid the potentially damaging effects of being stretched onto the descending limb of the force–length relationship (Lieber and Friden, 1993; Proske and Morgan, 2001; Roberts and Azizi, 2011). While these patterns may hold for muscles that are specialized for a single function (Azizi, 2014), most muscles readily shift and can operate as struts, motors or brakes, even within a single locomotor mode, thereby obscuring such patterns (Roberts et al., 1997; Daley and Biewener, 2003).

A muscle's possible range of operating lengths is influenced by its passive mechanical properties. Muscles that develop passive forces at shorter lengths or have greater stiffness may be restricted from operating at relatively long lengths. Whether loaded by inertial, gravitational or antagonistic muscle forces, resistance to stretch through increased passive forces is likely to limit operating lengths on the descending limb of the force–length curve. Passive forces are enhanced by increases in density and stiffness of intramuscular connective tissues that operate in parallel with myofibers, as well as increasing stiffness of series elastic tissues (Lieber and Ward, 2013; Purslow, 2020). Previous work has shown that the influence of parallel elastic structures on muscle operating length is not limited to resistance to stretch at long lengths but also can limit shortening in muscle fascicles needing to expand radially to maintain a constant volume (i.e. bulging; Azizi et al., 2017). Therefore, the condition of intramuscular connective tissues and the passive mechanical properties of muscle may be critical in determining where muscles operate on the force–length relationship.

The aging process is associated with a suite of structural changes to musculoskeletal tissues, including increases in collagen concentration and an increase in cross-linking due to the accumulation of advanced glycation end products (AGEs) (Kjaer, 2004; Gao et al., 2008; Kragstrup et al., 2011). The increase in intramuscular connective tissues has been implicated in a reduction of overall muscle quality, resulting in a lower capacity to generate force (Brooks and Faulkner, 1988). In very aged rodents, this shift has also been implicated in a reduction in lateral force transmission from fibers and fascicles operating in parallel and using the extracellular matrix (ECM) to transmit forces (Ramaswamy et al., 2011). The remodeling of intramuscular connective tissues such as the perimysium and endomysium tends to increase the stiffness of muscle fibers and fascicles, and recent work has suggested that the properties of these intramuscular connective tissues contribute significantly to passive stiffness (Meyer and Lieber, 2018). An increase in passive stiffness may also restrict muscles from operating at long lengths, such that antagonist muscles are incapable of shortening against the additional passive load on opposite sides of a joint (Azizi and Roberts, 2010; Azizi, 2014). An inability to effectively utilize passive forces at long lengths may therefore reduce overall force capacity (Danos et al., 2016). Increases in intramuscular connective tissue and passive stiffness are therefore likely to alter many aspects of muscle–tendon function, but here we will focus on in vivo muscle operating length.

To investigate the interactions of muscle passive properties and operating length, we collected in vivo locomotion and in situ contractile mechanics from aged and young rat muscles. We assumed a priori that aged rats would have stiffer muscle–tendon units (MTUs) because of accumulations in the ECM and increased stiffness of the tendons (Alnaqeeb et al., 1984; Holt et al., 2016). However, the exact timing and effect of age on tendon mechanical properties remains unresolved (reviewed in Svensson et al., 2016). We utilized an experimental approach that permitted us to measure muscle lengths in vivo during locomotion and use the same markers to characterize the muscle force–length relationship in situ (Camp et al., 2016) using small, radio-opaque markers (<1.0 mm diameter tantalum spheres) implanted directly into muscle fascicles and visualized using high-speed biplanar x-ray videography (‘fluoromicrometry’). This minimally invasive approach allowed us to compare the in vivo and in situ operating lengths in muscles across a wide range of passive stiffnesses and investigate the correlation of MTU stiffness with muscle operating length. This work advances our understanding of how passive muscle properties affect in vivo function and potentially reveals new mechanisms influencing the decline in force capacity in aged muscles.

Twelve male (young: N=6, 7 months old; aged: N=6, 30 months old) Fischer 344×Brown Norway rats (Rattus norvegicus Berkenhout 1769) were obtained from the National Institutes of Health aged colonies (Bethesda, MD, USA). Each rat was housed singly and maintained on a standard ad libitum diet, 18±2°C temperature, and 12 h:12 h light:dark cycle. Rats were trained for an average of 20 min a day over a period of 4–7 days to run downhill (–30 deg), uphill (30 deg) and flat across (0 deg) a wooden trackway suspended ∼1 m above the ground by placing a hide box at one end of the trackway and using hand movements and tail touches to encourage speed. Prior to in situ experimentation, four individuals were necessarily excluded from the experiment as a result of mortality or behavioral intractability. All experimental protocols were conducted at Brown University with the approval of the Institutional Care and Use Committee (IACUC). We performed in vivo locomotion experiments and in situ muscle contractile experiments with the trained young (N=4) and aged (N=4) rats. Small (<1.0 mm) tantalum beads were surgically implanted into the triceps surae muscles of the right hindlimb (more details below). Rats were then filmed running across the trackway positioned at either −30, 0 and 30 deg via biplanar X-ray machines. Following in vivo locomotion recordings, muscle contractile properties were measured in situ via a muscle ergometer with the muscle positioned in the field of view of the X-ray machines. From the videos, bead position was tracked using custom software and muscle length changes were calculated from inter-bead distances (fluoromicrometry; Camp et al., 2016).

We measured muscle length changes from the medial gastrocnemius muscle of the right hindlimb. This muscle was chosen for its superficial location within the limb, and its relatively large size among ankle extensor muscles. Rats were anesthetized and maintained at 1.0–2.0% isoflurane using a closed-system ventilator with a small cone mask (Parkland Scientific, Coral Springs, FL, USA). The animals were placed prone on a small heating pad covered by a towel, and temperature was monitored via an internal probe. A small incision was made over the right medial gastrocnemius and two pairs of spherical tantalum markers (0.8 mm) were inserted along a pair of fascicles (one proximal fascicle pair closer to the knee joint, one distal fascicle pair closer to ankle) of the medial gastrocnemius using an18-gauge hypodermic needle and 0.25 mm steel rod plunger. Proximal beads were inserted as close to the proximal insertion as possible to capture the maximal proportion of a muscle fascicle; distal insertion beads were inserted at the raphe between the medial and lateral gastrocnemii. In aged rats with smaller muscles, proximal placement was noticeably more difficult and so additional care was needed. An additional bead was sutured at the muscle–tendon junction of the gastrocnemii and calcaneal tendon, and a final bead was drilled into the calcaneus bone (Fig. 1). The small bead wounds were lightly sealed with cyanoacrylate glue, and the incision was sutured with absorbable thread. Surgical wounds healed quickly, with no visible ‘puckering’ around the wound within 72 h, but all rats were given a minimum of 7 days to recover completely. Rats were observed by individual inspection every 6–12 h in the first 2 days after surgery, and daily for the remaining recovery time. Lastly, rats were run on trackways to assess gait and behavior just prior to experimentation.

Biplanar X-ray videos were recorded at 200 Hz from orthogonal X-ray generators (EMD Technologies 425 model EPS 45-80) fitted with high-speed Phantom cameras (Vision Research, Wayne, NJ, USA). The image intensifiers (Dunlee model TH9447/QXH590) were placed obliquely relative to a wooden trackway to record two lateral views, which best captured the full bead array in the hindlimb. Animals were encouraged with hand movements and sound to move across the trackway at −30 deg, 0 deg and 30 deg until at least five trials had been obtained for each slope for each individual (total trials per individual ≥15). Trials were excluded if animals paused or were otherwise not utilizing steady speed locomotion.

Following a standard protocol for fixed-end contractions (e.g. Roberts and Azizi, 2011), within 24 h of in vivo data collection, in situ muscle contractile and whole muscle–tendon unit (MTU) passive properties were recorded. Rats were anesthetized and maintained at 1.5–2.5% isoflurane concentration using a closed system anesthesia machine with a small cone mask and placed prone on a heating pad wrapped in a towel. The sciatic nerve was exposed, and a small custom-made nerve cuff was attached. The nerve was then severed proximally to prevent sensory feedback and interaction with the spinal cord. Warmed mineral oil was injected into the small cavity surrounding the nerve to aid in maintaining temperature and conductance, and the incision was closed with suture. Tantalum beads were positioned along the raphe of the lateral and medial gastrocnemius, making it impossible to separate the gastrocnemii in some of the individuals for in situ surgery without disrupting the beads (which were particularly prone to disturbance in the aged rats). Therefore, individuals were tested with the gastrocnemii complex intact. The calcaneus at the insertion of the triceps surae was severed and attached via Kevlar thread to the lever arm of a servomotor (310 B-LR, Aurora Scientific Inc., Ontario, CAN). To minimize off-axis movements and compliance the femur of the same limb was exposed and clamped to a rigid steel frame that also housed the servomotor. The muscle was kept moist with 37°C saline solution.

Real-time measurements of force and whole MTU length and velocity were recorded at 1000 Hz via a computer with a 16-bit analog-to-digital converter (PCI-MIO-16, National Instruments, Austin, TX, USA) controlled by Igor Pro software (Wavemetrics, Oswego, OR, USA). The animal and apparatus were positioned in the field of view of the X-ray videos and recordings from X-ray and servomotor were synchronized via an external trigger. Owing to the length of time required to digitize bead position from X-ray video, the servomotor length was used as a real-time estimate for MTU length. Before recordings began, the stimulus voltage and twitch force-length curves were obtained to determine supramaximal stimulation and optimal length (L_o). Contractions were elicited by applying supra-maximal square-wave 0.2 ms impulses via a Grass S48 stimulator (Warwick, RI, USA). After resting length was obtained from a twitch force–length curve (where resting length is the length at which maximum isometric force is produced), tetanic contractions were conducted at 100–150 Hz to determine maximum isometric force (P₀) and to generate force–length curves. Between measurements muscles were rested for 3 min with no tension applied, then passively stretched to resting lengths before initiation of a new tetanic contraction. After obtaining data for force–length curves the rats were euthanized via an overdose of sodium pentobarbital. The muscles were dissected and positioned at resting length to obtain muscle mass and muscle fascicle length, and the position of the beads relative to the length of the whole muscle fascicle was measured for segment length correction.

Details and validation of fluoromicrometry and X-ray videography are available in Camp et al. (2016) and Brainerd et al. (2010). Briefly, still images of a metal grid taken before and after recordings were used to measure and remove distortion introduced by the X-ray machines and servomotor. A calibration cube was placed in the same volume occupied by the animal and trackway in order to convert inter-bead distances to mm (±0.09 mm; Camp et al., 2016). All videos were undistorted, calibrated and beads tracked using a custom script (xromm.org) running in MATLAB (R2014b; MathWorks, Natick, MA, USA). For both in vivo and in situ recordings, xyz coordinates were generated for each individual bead and lengths were calculated between bead pairs (Fig. 2). The range of in vivo muscle operating lengths was quantified during the stance phase using the difference in length between maximum length and minimum length, which typically corresponded to the beginning of stance and just prior to swing.

Inter-bead distance data were imported into Igor and matched to force recordings to obtain force–length curves for each individual. Passive force and length were measured from the recordings ∼15 ms prior to initiation of tetanic contractions, while active force was calculated from subtracting passive from total force generated during tetanic contractions. This method may overestimate passive force because muscles shorten series-compliant elements during fixed end contractions (e.g. Fig. 2B; MacIntosh and MacNaughton, 2005) but owing to the timing of experiments versus digitizing, we were unable to obtain passive force at ‘active lengths.’ To compare data among all animals, all lengths and forces were normalized to proportions of maximum isometric force, and length at maximum isometric force production (P₀ and L_o). Active and passive curves were fit using equations following Otten (1987) and Fung (1967). The relative length at which the passive curves reached 20% of P₀ (L₂₀) was determined for each individual and used as a fixed factor in subsequent statistical analyses (Azizi and Roberts, 2010). In vivo muscle operating lengths were converted to strain [(L–L_o)/L_o] and plotted on force–length curves. For in vivo stride characteristics, footfalls were manually digitized and animal speed, stride length and contact time were calculated using a custom macro. All statistical tests were performed in JMP (SAS, Cary, NC, USA). In order to reduce error introduced by a limited number of individuals with repeated measurements, we employed a general linear mixed model with individual nested within age group as a random factor and trackway type and L₂₀ as fixed factors. This approach mirrors a repeated measures ANOVA by accounting for the fact that observations within individuals are correlated but is more robust in that it is able to accommodate unbalanced data as well as factor nesting. We used an alpha level of 0.05 to determine significance intests.

A total of 99 trials were used for final analyses after elimination of any trials with erratic behavior (e.g. pausing mid-run, scratching), significant acceleration or deceleration (i.e. average speed across reference frames must be within one standard deviation of variance), or obstructions to the field of view of the implanted marker beads (e.g. some bead placements resulted in overlap in one camera view and precise location could not be satisfactorily resolved). We did not elicit maximal speeds by design, but instead recorded a range of voluntary speeds on downhill (–30 deg), flat (0 deg) and uphill (30 deg) trackways. All stride characteristics measured (speed, stride frequency, length, contact time) were significantly longer/slower among aged rats compared with young rats, regardless of trackway condition (incline, decline and flat; Table 1). There were no significant interactions between age and condition, indicating that the trackway position did not differentially impact one age group more than the other. Across all trackway conditions, young rats moved faster at an average speed of 0.42 m s⁻¹ (Table 1), while aged rats moved at an average speed of 0.25 m s⁻¹. Although all rats tended to take slower and shorter steps during downhill locomotion, across all conditions young rats averaged a higher stride frequency (2.83 Hz) and longer stride length (14.92 cm) than aged rats, which had lower stride frequencies (1.98 Hz) and shorter strides (11.35 cm; Table 1). Contact time differed in a similar manner, with young rats averaging hindfoot contact times of 0.20 s during a stride, compared with 0.31 s for aged rats (Table 1).

Muscle length changes were recorded from multiple locations initially, including from fascicle pairs placed distally and proximally, and from the proximal-most bead to the insertion of fascicles along the distal raphe between medial and lateral gastrocnemius (‘muscle belly’). Two aged rats displayed inconsistent values indicative of a dislodged bead; one set of bead pairs had inconsistent in vivo length changes during stance, and presented lengthening during isotonic (i.e. shortening) contractions. These beads were confirmed as ‘loose’ in post-mortem dissections. This phenomenon was similarly observed in validation of fluoromicrometry methods (Camp et al., 2016). Future studies may achieve more consistent results with sutured beads in certain types of muscles; aged rats were typical in that they tended to have less muscle mass and more adipose tissue overall, and placement of proximal beads was difficult to achieve consistently. For analyses comparing data among all rats, we therefore used data from the muscle belly bead pair for both in vivo and in situ measurements.

Aged rats tended to have lower peak isometric force values, but there was no significant difference between groups when values were normalized to cross-sectional area. Active force–length curves were typical parabolas, with no significant differences in shape between aged and young rats (Fig. 3). Passive curves were much more variable, with some individuals not developing significant force until well beyond L_o. Although aged rats tended to have stiffer MTUs, as evidenced by steeper and narrower passive curves, one individual demonstrated surprising compliance (Fig. 3A). The L₂₀ value provided the relative length of fibers at biologically relevant passive tensions (20% of P₀). L₂₀ did not differ significantly between age groups (Table 1), though individual variation was considerable. Therefore, for variables of interest we focused on relationships of muscle operating lengths with L₂₀ rather than age-based comparisons.

In addition to mean operating length, we measured total muscle operating length range, minima and maxima. Trackway elevation significantly impacted muscle operating length among rats (Table 2; Fig. 4) such that mean operating length and minimum operating length were significantly correlated with L₂₀; individuals with smaller L₂₀ values had correspondingly shorter mean operating lengths (Fig. 4). Stride length did not correlate significantly with L₂₀ despite a significant relationship with the speed and L₂₀ interaction term, and a significant correlation within aged rats (Fig. 5B; Table 2).

In this study we recorded kinematics and in vivo muscle operating lengths during voluntary locomotion in young (7 month old) and aged (30 month old) rats. Using a novel, minimally invasive procedure (fluoromicrometry), we were able to directly compare in vivo muscle operating length to in situ maximal contractile properties. Our data demonstrate standard age-related kinematic differences between young and aged rats, with young rats traveling at higher voluntary locomotory speeds, higher stride frequencies, longer stride lengths and with shorter limb contact times (Table 1). The mean, minimum and total range of in vivo muscle operating lengths in the medial gastrocnemii of rat hindlimbs did not differ significantly with speed but were significantly affected by trackway elevation and passive tension (Table 2). Although passive stiffness was not well correlated with age in our individuals, our data show a strong correlation of passive stiffness with muscle operating length regardless of age (Table 2; Fig. 5).

Passive stiffness may positively influence muscle mechanics by developing forces at the extremes of joint motion and contributing to cyclic energy fluctuations (Whittington et al., 2008); however, an increase in passive stiffness of tissues is typically associated with pathology and results in a net reduction of locomotory performance via reduced range of motion (Kang and Dingwell, 2008), altered force transmission between muscle and tendon (Ramaswamy et al., 2011), and reduction in energy storage and return (Liu et al., 2006). Passive stiffness in muscles arises from multiple structures; in addition to the tendon and aponeuroses, the anatomical hierarchy of muscles includes connective tissue wrappings of ECM, which contribute to the integrity and stiffness of the muscle–tendon unit (Purslow, 2020). Collectively, these structures passively resist stretch, but the connective tissues within and surrounding muscle fascicles also contribute to active muscle mechanics; the ECM aids in the transmission of force between adjacent fascicles (Huijing et al., 2007), influences muscle gearing during contraction (Holt et al., 2016) and can potentially constrain mechanical work output (Azizi et al., 2017). Previous studies using whole muscle, fiber bundles and models (Kragstrup et al., 2011; Wood et al., 2014; Holt et al., 2016; Danos et al., 2016) have demonstrated that MTU stiffness generally increases with age, whereas stiffness measured from isolated muscle fibers tends to be similar across age groups (Wood et al., 2014). With increasing age the amount of ECM and its relative stiffness increases (e.g. via accumulation of AGEs; Wood et al., 2014), which is likely to have a significant impact on mechanical performance (Kragstrup et al., 2011; Danos et al., 2016).

Given that aging muscles become more fibrotic, we predicted that aged muscles would be stiffer; however, because of substantial inter-individual variation, the trend of stiffer aged muscles was subsumed by an aged individual with particularly compliant passive tissues (Fig. 3; triangle symbols). Inter-individual variation is a frequent issue in aging studies of the musculoskeletal systems and may be responsible for a seeming lack of consensus on topics such as aged single fiber performance (Miller et al., 2008) and mechanics of aging tendon (Svensson et al., 2016). Furthermore, other factors such as home cage activity can contribute to inter-individual variability. For example, the strain of rats we used here are well-studied in aging research, but typically are housed in standardized rodent cages and experience a mostly sedentary life. The training protocol we employed with the rats to capture a range of locomotory behaviors (∼2 weeks of acclimation to trackway running) was probably more activity than any of the aged animals had experienced prior to arrival and may have contributed to the observed variation. Although individual variance can be minimized by using rodents from laboratory bred strains with known genotypes, many of these strains are not as robust at a later age.

Regardless of age, our data demonstrate that smaller L₂₀ values (i.e. relatively stiffer passive tissues) correlated with decreased mean muscle operating length (Fig. 4; Table 2). It is likely that as passive tissues stiffen the MTU, muscle operating length is restricted via two pathways: first, owing to stiffening of intramuscular connective tissue, as evidenced by the shifts in the passive force–length relationship, muscles operating at longer lengths would incur greater resistance to stretch and such forceful stretches at long lengths have the capacity of damaging myofibrils (Proske and Morgan, 2001). In aged and/or pathologically stiffer MTUs, this scenario would not be optimal because of a decrease in the ability to repair damaged muscle (Grounds, 1998). Proprioceptive feedback about joints may tune muscles to operate at a range of ‘safer’ lengths in order to prevent eccentric damage (Nagai et al., 2018), and this function may be prioritized over generating force at optimal lengths. Second, intramuscular stiffness (e.g. pathologically fibrotic ECM) may limit the degree to which muscles can shorten by preventing radial expansion (Azizi et al., 2017; Sleboda et al., 2019). As muscle fibers shorten, radial expansion occurs as muscle must maintain a constant volume (Baskin and Paolini, 1967) and the ECM surrounding muscle fibers and fascicles must possess enough compliance to accommodate this phenomenon. However, as ECM stiffens, this radial expansion may be limited, affecting the ability to shorten (Azizi et al., 2017). On the opposite end of the continuum, passive tissue compliance could allow increased muscle operating length. Previous data collected in toads illustrates this phenomenon, with the anconeus and plantaris muscles demonstrating operating lengths well predicted by passive stiffness (Azizi, 2014). These muscles are quite different functionally, with the forelimb anconeus primarily acting as a brake during landings and the hindlimb plantaris being a powerful propulsive muscle during jumps. Operating lengths for these two distinct tasks are seemingly tuned to either limit the rate and degree of stretch during landing (ascending limb of force–length curve; anconeus), or to allow muscles to shorten to optimal length for maximum force output during jumping (descending limb of force–length curve; plantaris).

Muscles that operate close to the plateau of the force–length relationship maximize force output at a given activation level, and thus it is often assumed that muscles operate on or near the plateau (e.g. Rome and Sosnicki, 1991; Azizi and Roberts, 2010). A comprehensive survey of studies of force–length operating lengths found a broad range, including muscles operating over a substantial portion of the ascending limb and plateau, while muscle operation on the descending limb appears to be minimal (Burkholder and Lieber, 2001). Muscle function on the ascending limb assures that muscle fascicles will operate within a safe range of lengths, although with the trade-off of less force production (Lieber et al., 2017). Thus, passive tissue stiffness notwithstanding, one prediction for aged muscle is to limit operating lengths to the relatively ‘safe’ ascending limb of the force–length curve, potentially contributing to age-related muscle weakness (Narici et al., 2003). Our data were not consistent with this finding; with the exception of one individual, aged rats predominantly maintained operating lengths on the ascending limb of the force–length curve (Figs 3A, 4A), whereas young rats operated at longer relative lengths. Rather than age, the best correlate of operating length was passive stiffness. Thus, a young rat with stiffer tissues was more likely to maintain shorter operating lengths (Fig. 4B) than an aged rat with compliant tissues (Fig. 4A). This intriguing finding could be further explored in systems with pathologies known to increase ECM fibrosis (e.g. muscular dystrophy) and in modeling individual fascicle behaviors experiencing varying external forces.

The wide variations in muscle lengths observed in aged rats are in some cases surprising, particularly at short lengths. The operating lengths of three of the aged rats and one of the young rats (Fig. 3A) spanned very short lengths, including lengths that the in situ force–length curve suggests are below the range where active force can be produced. There are a few possible explanations for this observation. First, it is important to note that measurements of muscle length encompassed all observed muscle lengths, not just those where muscles were actively producing force. It is possible that the very short lengths observed were in passive muscles, possibly even including periods of passive muscle buckling that allowed beads to move very close together. Second, while we endeavored to assess bead motion for signs of ‘loose’ or dislodged beads, it is possible that there was some motion of beads within their encapsuled zone, and this ‘wiggle’ might increase at short muscle lengths. Generally, we found that the beads in the aged rat muscle were less likely to remain fixed within the muscle, despite ample time for healing to occur. Future studies should endeavor to secure bead placement with surgical glue or suture. Third, strain heterogeneity has been observed in some muscles (Ahn et al., 2003) and such heterogeneity might affect the mapping of in vivo muscle lengths to in situ force–length relationships.

Passive stiffness is an emergent property of intracellular components (e.g. titin), ECM and tendon. In addition to force transmission, the latter connective tissues also play a role in muscle shape change, force development, gearing and work done by the muscle. Aging is well documented to have cascading detrimental effects on passive tissues, including increased collagen cross-linking (and thus stiffness), reduced and altered collagen content, and reduced elasticity (Roberts et al., 2019; Sinha et al., 2020). Here, we show that increased passive stiffness in rats is correlated with a shorter muscle operating length with activity shifted to the ascending limb of the force–length curve. Although our study focused only on the medial gastrocnemius muscle, this is the largest of the plantarflexor muscles in the rat hindlimb and contributes a proportional amount of force during stance (De Ruiter et al., 1996). Any reductions in force and operating length are likely to negatively impact the hindlimb's contribution to locomotor performance, but the direct mechanisms involved remain undefined. Future studies should explore potential mechanisms underlying limitations of muscle operating length in stiffer tissues, such as whether proprioceptive feedback may be limiting length excursions and/or how much ECM stiffness may be limiting muscle work in vivo.

The authors are grateful for discussions with Natalie Holt, Roberts lab members and Azizi lab members. We also thank three anonymous reviewers whose careful commentary improved this manuscript. Special thanks to Greg Mouradian and Sean Grogan for their assistance with all things rat, as well as Erika Tavares for assistance and expertise in the Brown University Keck Lab XROMM facilities.