## Abstract

Partial and complete anterior cruciate ligament (ACL) injuries occur in both pediatric and adult populations and can result in loss of joint stability and function. The sigmoidal shape of knee joint function (load-translation curve) under applied loads includes a low-load region (described by slack length) followed by a high-load region (described by stiffness). However, the impact of age and injury on these parameters is not fully understood. The current objective was to measure the effects of age and injury on the shape of joint function in a porcine model. In response to an applied anterior–posterior tibial load, in situ slack did not change (p > 0.05), despite sevenfold increases in joint size with increasing age. Joint stiffness increased from an average of 10 N/mm in early youth to 47 N/mm in late adolescence (p < 0.05). In situ ACL stiffness increased similarly, and changes in in situ joint stiffness and ACL stiffness were highly correlated across ages. With complete ACL injury, in situ slack length increased by twofold to fourfold and in situ stiffness decreased threefold to fourfold across ages (p < 0.05). Partial ACL injury resulted in less dramatic, but statistically significant, increases in joint slack and significant decreases in in situ joint stiffness in the adolescent age groups (p < 0.05). This work furthers our understanding of the interaction between joint biomechanics and ACL function throughout growth and the impact of ACL injury in the skeletally immature joint.

## Introduction

Traumatic sports injuries requiring treatment, including knee injuries such as partial and complete anterior cruciate ligament (ACL) tears, impact roughly one-third of all children in the U.S. [1]. In a recent study, 60% of injuries treated in patients between 5 and 17 years of age were in the lower extremity, with ACL tears representing 9% of all injuries in the study. Interestingly, this injury was the sixth most common primary diagnosis in children between 5 and 12 years of age and the second most common injury in 13–17-year-old patients [2]. Treatments for ACL injuries can range from conservative approaches such as functional bracing and physical therapy to surgical reconstruction or repair, depending on both the severity of the injury and the remaining skeletal growth of the patient [3]. Specifically, partial tears affecting <50% of the tissue and injuries in young patients have been suggested for conservative treatment in previous studies [4]. While the intent of these conservative treatments is to improve joint stability by strengthening neuromuscular control, any ongoing instability may contribute to irreparable damage to the articular cartilage, potentially contributing to the near 50% incidence rates of osteoarthritis within 10 years of initial injury [5]. Although joint instability is generally well established as an issue in knee injuries, less work has been done in quantifying changes in joint stability throughout skeletal growth, particularly in cases of partial and complete ACL deficiency.

Joint instability, or laxity, can be assessed as the displacement of one bone relative to another in response to an applied load. Knee laxity is frequently studied under applied anterior–posterior tibial loads, resulting in a measure of anterior–posterior tibial translation (APTT) relative to the femur [6,7]. APTT is commonly assessed in patients via manual clinical exams [8] or in situ in cadaveric joints using force-sensing six degrees-of-freedom (6DOF) robotic systems in the laboratory [912]. In the case of clinical assessments, the presence and severity of ACL injuries can be assessed through the presence of a hard or soft end point to APTT tests [13]. A soft end point suggests injury. However, these findings are only applicable if the uninjured joint stiffness is high (resulting in a hard end point). As such, in this work, we studied age-dependent changes in joint slack and stiffness in response to applied loads in order to identify potential complicating factors for using clinical exams to diagnose ACL injuries in young populations. Studies have established that the instability associated with complete ACL injuries results in an increased APTT under maximum applied anterior–posterior tibial loads [10,14]. In addition to work measuring APTT as an effect of ACL injury, a previous study by our laboratory has shown that skeletal growth [15] can have a considerable effect on APTT, with decreased laxity in older age groups when normalized to the size of the joint (anterior–posterior tibial plateau length) although differences were not significant in non-normalized cases.

While APTT provides an end point measurement of joint laxity, a few studies have reported on the shape of the anterior–posterior tibial load-translation curve between these end points. A recent paper by Imhauser et al. established parameters for describing this behavior for knee joints and knee ligaments at submaximum loads, and related their findings back to the laxity of the joints under applied tibial loads [16]. Imhauser et al. described in situ slack as the relative motion in the joint between the points where the soft tissues began carrying considerable force in opposing directions, and in situ stiffness as the slope of the linear region of the load-translation curve after the slack region [16]. Through this study, the group was able to correlate in situ slack of the cruciate ligaments to anterior–posterior joint laxity, and both in situ slack and in situ stiffness of the medial collateral ligament to valgus laxity [16]. These findings led us to ask whether in situ slack and stiffness could be used to describe age- and injury-related changes in joint function during skeletal growth.

As such, the objective of this study was to assess the effect of age and injury on the shape of the load-translation curve of both the joint and the ACL under applied anterior–posterior tibial loads during skeletal growth in a porcine model. In order to do so, we used a force-sensing robotic system to apply loads to joints ranging from early youth through skeletal maturity and recorded both the 6DOF kinematics and 6DOF kinetics throughout loading. Load-translation plots were created for each joint and the ACL, and the in situ slack and in situ stiffness were compared across ages and injury states.

## Methods

### Specimen Collection.

Hind limbs were collected from 30 female Yorkshire cross-breed pigs from early youth through skeletal maturity (1.5, 3, 4.5, 6, and 18 months of age, n = 6 per age group). These ages were equivalent to early juvenile, juvenile, early adolescent, adolescent, and late adolescent groups in humans, respectively, based on a combination of skeletal and sexual age scales in both species [17]. The animals used in this study were obtained from a university owned herd, and all animals were healthy and of normal size. All swine were cared for according to the management practices outlined in the Guide for the Care and Use of Agricultural Animals in Teaching and Research, and their use in the current experimental protocols was approved by the N.C. State University Institutional Animal Care and Use Committee [18]. Hind limbs were dissected to the stifle (knee) joint and wrapped in saline-soaked gauze and stored at −20 °C. To prepare the joints for testing, the joints were thawed at room temperature overnight. The femur, tibia, and fibula were cut at the mid-diaphysis and the bones on either side of the joint were fixed within an epoxy compound in custom molds. The joints were wrapped in saline-soaked gauze and stored again at −20 °C.

### Biomechanical Testing.

Biomechanical tests were performed using a 6DOF robotic testing system (KR300 R2500, Kuka, Shelby Charter Township, MI) powered by a controller (KRC4, Kuka, Shelby Charter Township, MI) along with a 6DOF force/moment sensor (Omega160 IP65, ATI Industrial Automation, Apex, NC). This system was integrated and controlled using a commercial software package (simVitro, Cleveland Clinic, Cleveland, OH). The robotic system used in this study can operate under both kinematic and kinetic control and has a kinematic repeatability of 0.1 mm and 0.1 deg and a load cell sensitivity of 0.25 N. Joints were attached to the robotic system using custom clamps with the femur attached to a clamp fixed to the floor and the tibia attached to the end effector of the robot. The anatomic coordinate system of the joint was defined relative to the coordinate system of the robotic manipulator as described previously using a 3D point digitizer (G2X, Microscribe, Amherst, VA) [10,15,19].

The following robotic protocol is summarized in Table 1. A passive path was determined for each joint by changing the flexion angle of the joint from full extension (40 deg in the pig stifle joint) to 90 deg of flexion in 1 deg increments while minimizing the forces and moments in the other 5DOF. The kinematics of each passive position were recorded for each flexion angle. Joint kinematics were then recorded for the intact joint under applied anterior–posterior tibial loads (scaled by joint size for each age group) at full extension (40 deg), 60 deg, and 90 deg of flexion. These “intact” kinematic paths were repeated under kinematic control, and the resulting forces were recorded. The anteromedial (AM) bundle of the ACL was then transected, and the anterior–posterior loads were applied again at 40 deg, 60 deg, and 90 deg of flexion. The resulting “AM-deficient” kinematic paths and the intact kinematic paths were repeated in this state. Then the remainder of the ACL (the posterolateral bundle) was transected and the anterior–posterior loads were applied in the ACL-deficient state. The ACL-deficient kinematics were then repeated along with the AM-deficient and intact kinematics.

Table 1

Biomechanical testing protocol

Joint stateRobotic commandKinematic outputsKinetic outputs
Intact jointPassive flexion–extensionPassive path positions
Intact jointRepeat intact kinematic pathIntact path forces
AM-deficient jointRepeat AM-deficient pathAM-deficient path forces
ACL-deficient jointRepeat intact pathACL in situ forces
ACL-deficient jointRepeat ACL-deficient pathACL-deficient path forces
Joint stateRobotic commandKinematic outputsKinetic outputs
Intact jointPassive flexion–extensionPassive path positions
Intact jointRepeat intact kinematic pathIntact path forces
AM-deficient jointRepeat AM-deficient pathAM-deficient path forces
ACL-deficient jointRepeat intact pathACL in situ forces
ACL-deficient jointRepeat ACL-deficient pathACL-deficient path forces

### Biomechanics Data Processing.

Force and translation data were plotted against one another to create load-translation plots for the joint and ACL represented schematically in Fig. 1. Anterior–posterior tibial translation, in situ forces in the joint, and in situ forces in the ACL were measured. APTT was calculated as the distance in the anterior–posterior plane between the point of maximum translation under applied anterior and posterior tibial loads (Fig. 1). In situ forces in the ACL and the joint were calculated using the principle of superposition to calculate the force components in three degrees-of-freedom under applied anterior tibial loads [10,19].

Fig. 1
Fig. 1
Close modal
Biomechanical data at submaximum loads were assessed under applied anterior–posterior loads in a manner similar to that published by Imhauser et al. [16]. Force (either specific to individual tissues or the total joint) and displacement (measured at the joint level) data were collected at intermediate points defined at increments of 20% of the peak applied load for each specimen (Fig. 1). A custom matlab code was developed to fit data to biphasic curves in the anterior and posterior regions with an exponential fit (Eq. (1)) ranging from the passive path position to a transition point and a linear fit from that transition point to the maximum load position. The form of the exponential function is
$Force=a*eb*displacement$
(1)

where a and b are parameters to be fit. This process was iterated with each of the intermediate points defined as the transition point. The transition point resulting in the greatest combined r2 value from the exponential and linear regions was selected, and a single curve combining the curve fits of the exponential and linear regions was generated. The process of selecting and generating a biphasic curve was repeated between the passive path position and the maximum applied posterior drawer. Parameters shown in Fig. 1 were defined as follows based on previous literature [16,20]. A point of maximum curvature was determined for the new plot, and this was defined as the engagement point of the tissue. In situ slack was defined as the distance between the engagement point in the anterior and posterior directions. The stiffness of the tissue of interest, e.g., joint or ACL, was defined as the slope of the linear region of the plot under anterior load [16,20].

### Statistical Analysis.

Statistical analysis was performed with commercial software (JMP Pro 13.0, SAS Institute, Cary, NC). Data normality was confirmed using a Shapiro-Wilk test. Analyses for APTT, in situ slack, and in situ stiffness consisted of multiway ANOVA tests with Tukey's post hoc analysis using age as a between subjects effect, and flexion angle and injury state as repeated measures with significance set at p < 0.05. In situ stiffness of the joint and the ACL were compared via linear regression. Slope of the line, the r2 value, and p value are reported.

## Results

### Joint Biomechanics Change During Skeletal Growth.

Average anterior–posterior load-translation curves for the joints at all age groups are shown in Fig. 2. Data are shown for 60 deg of flexion, but similar behavior was found at 40 deg and 90 deg of flexion (see Fig. 1 available in the Supplemental Materials on the ASME digital collection). These plots reveal a shift from shallow, linear curves in juvenile groups to steep, nonlinear curves in late adolescence in both the anterior and posterior directions. These changes are partly driven by an increase in the age-specific target loads in both anterior and posterior directions (20 N in early youth to 140 N in late adolescence). However, concurrent with these sevenfold increases in load, there are no meaningful changes in APTT.

Fig. 2
Fig. 2
Close modal

In order to better understand these changes in the shape of the load-translation curve, the in situ slack and in situ stiffness were calculated for each joint. First, analysis of the in situ joint slack versus age shows that the overall slack length of the joints (the length between anterior and posterior engagement points) did not vary substantially with age (Fig. 3). Specifically, in situ slack length slack ranged from 3.2 ± 1.1 mm to 5.5 ± 0.8 mm across ages and flexion angles (Fig. 3, See Table 1 available in the Supplemental Materials on the ASME digital collection). Statistical analysis of the in situ joint slack revealed that there were no significant differences due to age at any flexion angle tested (p > 0.05) (Fig. 3, See Fig. 2 available in the Supplemental Materials on the ASME digital collection).

Fig. 3
Fig. 3
Close modal

In situ joint stiffness increased between 1.5 and 18 months of age as shown in Fig. 4. Increases of fourfold to fivefold were observed with age, as group averages ranged from 9 N/mm to 17 N/mm in juvenile age groups while group averages ranged from 31 N/mm to 72 N/mm in adolescent age groups across all flexion angles. The greatest increase between consecutive time points occurred at the onset of adolescence, between 3 and 4.5 months of age. Statistically significant changes occurred due to age (p < 0.05) but not flexion angle (p > 0.05) (see Fig. 3 and Table 2 available in the Supplemental Materials on the ASME digital collection). Relative to juvenile age groups (1.5 and 3 months), these increases were statistically significant in adolescent (4.5–18 month) age groups (p < 0.05). There were no statistically significant differences detected between the adolescent age groups (p > 0.05).

Fig. 4
Fig. 4
Close modal

### Anterior Cruciate Ligament Biomechanics Change During Skeletal Growth.

The anterior load-translation curves derived from the anterior load carried by the ACL were also evaluated (Fig. 5). Visually, the engagement of the ACL under anterior tibial translation was evident across age groups, as the slope increased with increasing anterior tibial translation. With increasing age, the shape of the ACL curve varied from a shallow curve in the juvenile groups to a steep curve in late adolescence. Similar changes were seen across flexion angles (see Fig. 4 available in the Supplemental Materials on the ASME digital collection).

Fig. 5
Fig. 5
Close modal

These qualitative assessments matched quantitative measures of in situ ACL stiffness (Fig. 6). Between 1.5 and 18 months of age, in situ ACL stiffness increased by fourfold to fivefold. Specifically, in situ ACL stiffness ranged from an average of 9 N/mm in early youth to 45 N/mm in late adolescence across flexion angles. Similar to changes in in situ joint stiffness, significant increases occurred primarily between juvenile and adolescent groups, with no significant change following the onset of adolescence (p > 0.05). Higher values were found at 90 deg of flexion compared to 40 deg and 60 deg of flexion (p < 0.05) (see Table 3 and Fig. 5 available in the Supplemental Materials on the ASME digital collection).

Fig. 6
Fig. 6
Close modal

### Relationship of Anterior Cruciate Ligament Stiffness and Joint Stiffness Throughout Skeletal Growth.

In order to assess the relationship between the in situ stiffness of the joint and the in situ stiffness of the ACL throughout skeletal growth, the two parameters were plotted and the linear correlation was assessed (data at 60 deg of flexion shown in Fig. 7). The in situ ACL stiffness was closely correlated with the in situ stiffness of the joint for all flexion angles. At 60 deg of flexion, the resulting slope was 1.01 (r2 = 0.91, p < 0.001), suggesting equal change in the two parameters (Fig. 7). At full extension (40 deg of flexion), the slope was 0.71 (r2 = 0.81, p < 0.001), while at 90 deg of flexion, the slope was 1.08 (r2 = 0.93, p < 0.001) (see Fig. 6 available in the Supplemental Materials on the ASME digital collection).

Fig. 7
Fig. 7
Close modal

### Impact of Partial and Complete ACL Injury on Joint Biomechanics.

Building from the analysis of age-related changes in the load-translation curve for in situ parameters of the intact joint during growth, the next analysis assessed the impact of partial (AM bundle) and complete (total ACL) transections on these biomechanical parameters. The impact of injury on in situ slack is shown in Fig. 8. Although age alone did not impact in situ joint slack in the intact joint, the introduction of partial and complete ACL transections did result in changes to this parameter. Specifically, in situ slack increased twofold to fourfold between the intact and ACL-transected states across ages and flexion angles (p < 0.05) (see data in Table 4 available in the Supplemental Materials on the ASME digital collection, additional flexion angles shown in Fig. 7 available in the Supplemental Materials on the ASME digital collection). AM bundle transection resulted in significant increases in in situ joint slack only in the late adolescent group (p < 0.05). Comparing between injury states, in situ joint slack was significantly greater with complete injury relative to partial injury regardless of age (p < 0.05).

Fig. 8
Fig. 8
Close modal

The impact of injury on in situ stiffness is shown in Fig. 9. In situ joint stiffness decreased significantly following the introduction of ACL injury to the joints in many cases. Specifically, complete ACL transection resulted in threefold to fourfold decreases in total joint stiffness relative to the intact state across all ages and flexion angles (p < 0.05 in 3–18 month age groups). Meanwhile, relative to the intact state, AM bundle transection resulted in a 67–86% decrease in in situ joint stiffness in the 6- and 18-month age groups (p < 0.05), while there were no statistically significant changes between these states in the younger groups (p > 0.05). Comparing between injury states, joint stiffness decreased significantly with complete ACL injury relative to partial ACL injury in age groups between 3 and 18 months (p < 0.05). Data for all flexion angles are provided in Table 5 and Fig. 7 available in the Supplemental Materials on the ASME digital collection.

Fig. 9
Fig. 9
Close modal

## Discussion

In this work using a porcine model, we found that the shape of the load-translation curve of the knee joint changes under applied anterior tibial loads throughout skeletal growth. While there was a lack of substantial changes in the low-load region of these curves, represented by the in situ slack, increasing age resulted in fourfold to fivefold increases to the slope of the high-load portion of the load-translation curve, represented by the in situ joint stiffness. Additionally, the in situ ACL stiffness increased by a similar amount throughout skeletal growth. Combined with the lack of significant changes in the toe region of these curves, these differences result in a change in the shape of the load-translation curve of the ACL during growth. Additionally, we report that the in situ slack increases and the in situ stiffness decreases with complete ACL injury across all ages and with partial (AM bundle) injury in adolescent and late adolescent groups.

The findings presented here fit with the current understanding of changes in joint laxity with skeletal growth. Specifically, previous studies in humans show greater joint laxity in the knee in children and adolescents compared to mature populations [2123]. Furthermore, a study by Ford et al. analyzed active knee stiffness from computational models measured in the sagittal plane during the stance phase of a jump landing task [24]. This group reported ∼5–7% increases in knee stiffness within the same adolescent subjects over a period of one year. Moreover, postpubertal subjects (14.5 ± 1.4 years) had stiffness values ∼15% higher than pubertal subjects (12.4 ± 0.9 years). In this study, we found similar increases in joint stiffness of ∼10% between early adolescent (4.5 months) and adolescent (6 months) age groups. We also found a doubling of joint stiffness between the prepubertal (3 months) and postpubertal (4.5 months) ages in this study, suggesting this may be a critical age range for joint function and one worth stratifying in future human studies. Our work has expanded on and reinforced this body of knowledge by reporting changes in an in situ measure of joint slack and stiffness at ages ranging from early youth to late adolescence in a common preclinical model for the knee.

There is less information available regarding the function of the skeletally immature ACL. Through this analysis of ACL function throughout the load-translation curve, we have developed an improved understanding of how its function changes with age. The ACL acts to stabilize the porcine stifle joint against anterior tibial loads across ages, with similar low-load (or “toe region”) behavior across age groups, but major increases in the in situ stiffness describing the high-load portion of the load-translation curve. The mechanisms behind these changes in apparent tissue stiffness are likely multifaceted, with potential ties to changes in composition, microscale structure, material properties, and macroscale tissue geometry. Previously, our group has reported an interesting relationship between age and ACL geometry in the porcine model [15]. Specifically, the ACL increases in length consistently throughout skeletal growth, while the cross-sectional area increases rapidly during childhood followed by a plateau in adolescence, resulting in a change from relatively short but wide shape to a long and skinny shape over the age range reported in this study [15]. Ongoing work analyzing age-specific biochemical composition and microscale structure and mechanics may further elucidate the mechanisms behind these tissue-level changes.

The stiffness values reported for the late adolescent group in this work were similar to mature human values reported by Imhauser et al., as our adolescent and late adolescent in situ ACL stiffness values ranged from 24 to 52 N/mm across ages and flexion angles, while the in situ ACL stiffness for skeletally mature humans reported by Imhauser et al. was 33 N/mm at 30 deg of flexion [16], suggesting that both the tissue properties and methods are repeatable across research groups.

Some studies have examined the effects of partial and complete ACL injury, particularly in the context of diagnosing injury [25,26]. In the context of skeletally immature joints, another study in human patients reported a sensitivity of 76.5% for detecting partial ACL tears via clinical examination [26]. This study went on to report that the diagnostic performance of clinical examinations for ACL tears was not significantly different between children younger or older than 12 years of age, although this comparison includes data for both complete and partial injuries. Furthermore, the specific type of partial injury was not reported, making comparison to the current study difficult. We found that younger, pre-adolescent age was related to less drastic changes to both partial and complete ACL injuries. This could be due to the high level of natural laxity in the young intact joints. It could also be due to subtle differences in anatomy or in the role of secondary soft tissue stabilizers. These age-specific properties have the potential to complicate clinical assessments where hard end points to anterior tibial translations tests suggest a healthy or partially injured ACL while soft end points suggest a total injury. Additionally, ACL reconstruction grafts should mimic the function of the natural ACL throughout the range of motion, not just an end point. The data in this study suggest ways that the load–displacement curve of the ACL changes with age which surgeons may want to consider in reconstruction procedures. Poor outcomes in both children and adolescents are likely the result of many variables, and the shifts in ACL stiffness may be one contributing factor. Further investigations should be pursued to examine joint behavior following ACL reconstruction procedures in joints of different ages throughout growth.

There were several limitations to this work. While the porcine model has been presented as a surrogate for the human knee in many studies [2731], there are some differences between human joints and porcine joints. Notably, porcine joints are limited in extension to approximately 40 deg of flexion while human knees can extend much further (0 deg of flexion). Additionally, the translation between porcine and human stages of growth requires consideration of multiple factors such as skeletal and sexual maturity, and as such, there is no confirmed direct correction factor between chronological ages in the two species. The calculation of load-translation curves were limited to data points at discrete load levels between maximum posterior and maximum anterior translation, which may impact curve fitting and resulting values for in situ slack and stiffness. These parameter estimates could be improved by using more continuous data points in the future. Nevertheless, interspecimen variability observed in in situ slack values was very similar to that observed in total translation values (∼10–35% standard deviation relative to the mean for both in situ slack and anterior–posterior tibial translation across ages and flexion angles), leading us to believe that the variability observed here represented biological variability and was likely not a result of inaccurate curve fitting. Another limitation is that each age group had a relatively low sample size (n = 6/group), but one in line with prior ex vivo animal studies. However, the data revealed effect sizes due to age ranging from 2 to 12 for our parameters of interest, suggesting that additional samples would not change the overall age-related effects observed.

These findings motivate several avenues of future research. In order to assess sex-dependent changes in joint biomechanics at submaximum loads, we intend to repeat this study in the same age groups and injury conditions in a male porcine population. This work also motivates future in vivo studies analyzing changes in submaximum joint kinematics due to growth or due to tissue remodeling following ACL injury and reconstruction in skeletally immature animals. For example, in this study, we found no change in absolute slack (in mm) despite a nearly sevenfold increase in overall joint size across the ages studied. Future work will aim to study the mechanism behind this mismatch. It is unclear if the absolute value for slack is set by anatomy early in life or if there is a process to actively maintain slack through a homeostatic mechanism during growth.

In conclusion, the biomechanical response of the porcine stifle joint to applied anterior tibial loads varies with age during skeletal growth due to increases in the in situ stiffness, but not slack, of the joint. Furthermore, in situ ACL stiffness increased during skeletal growth in a similar manner to in situ joint stiffness. Regardless of age, complete ACL injuries resulted in significant increases in the in situ slack length of the joint, and significant decreases in the in situ stiffness of the joint, with partial injury also causing similar, but less drastic, results in adolescent age groups. Clinically, these findings suggest that the kinematic response of knees to standard clinical exams may be age dependent. As such, both patient age and specific ACL injury type are important factors to consider during clinical examinations to assess ACL function.

## Acknowledgment

The authors would like to thank Ms. Emily Lambeth, Mr. Sean Simpson, and the Swine Educational Unit at North Carolina State University for their contributions to this work.

## Funding Data

• National Science Foundation Graduate Research Fellowship Program under Grant No. DGE 1252376 (Funder ID: 10.13039/100000001).

• National Institute of Arthritis and Musculoskeletal and Skin Diseases of the National Institutes of Health under Award Nos. R03AR068112 and R01AR071985 (Funder ID: 10.13039/100000069).

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