Effect of knee position on hip and knee torques during the barbell squat

Some recommendations suggest keeping the shank as vertical as possible during the barbell squat, thus keeping the knees from moving past the toes. This study examined joint kinetics occurring when forward displacement of the knees is restricted vs. when such movement is not restricted. Seven weight-trained men (mean +/- SD; age = 27.9 +/- 5.2 years) were videotaped while performing 2 variations of parallel barbell squats (barbell load = body weight). Either the knees were permitted to move anteriorly past the toes (unrestricted) or a wooden barrier prevented the knees from moving anteriorly past the toes (restricted). Differences resulted between static knee and hip torques for both types of squat as well as when both squat variations were compared with each other (p < 0.05). For the unrestricted squat, knee torque (N.m; mean +/- SD) = 150.1 +/- 50.8 and hip torque = 28.2 +/- 65.0. For the restricted squat, knee torque = 117.3 +/- 34.2 and hip torque = 302.7 +/- 71.2. Restricted squats also produced more anterior lean of the trunk and shank and a greater internal angle at the knees and ankles. The squat technique used can affect the distribution of forces between the knees and hips and on the kinematic properties of the exercise. PRACTICAL APPLICATIONS: Although restricting forward movement of the knees may minimize stress on the knees, it is likely that forces are inappropriately transferred to the hips and low-back region. Thus, appropriate joint loading during this exercise may require the knees to move slightly past the toes.     

The effect of the partially restricted sit-to-stand task on biomechanical variables in subjects with and without Parkinson’s disease

The aim of this study was to explore the electromyographic, kinetic and kinematic patterns during a partially restricted sit-to-stand task in subjects with and without Parkinson’s disease (PD). If the trunk is partially restricted, different behavior of torques and muscle activities could be found and it can serve as a reference of the deterioration in the motor performance of subjects with PD. Fifteen subjects participated in this study and electromyography (EMG) activity of the tibialis anterior (TA), soleus (SO), vastus medialis oblique (VMO), biceps femoris (BF) and erector spinae (ES) were recorded and biomechanical variables were calculated during four phases of the movement. Subjects with PD showed more flexion at the ankle, knee and hip joints and increased knee and hip joint torques in comparison to healthy subjects in the final position. However, these joint torques can be explained by the differences in kinematic data. Also, the hip, knee and ankle joint torques were not different in the acceleration phase of movement. The use of a partially restricted sit-to-stand task in PD subjects with moderate involvement leads to the generation of joint torques similar to healthy subjects. This may have important implications for rehabilitation training in PD subjects.     

Kinematic, kinetic and EMG patterns during downward squatting.

The aim of this study was to investigate the kinematic, kinetic, and electromyographic pattern before, during and after downward squatting when the trunk movement is restricted in the sagittal plane. Eight healthy subjects performed downward squatting at two different positions, semisquatting (40 degrees knee flexion) and half squatting (70 degrees knee flexion). Electromyographic responses of the vastus medialis oblique, vastus medialis longus, rectus femoris, vastus lateralis, biceps femoris, semitendineous, gastrocnemius lateralis, and tibialis anterior were recorded. The kinematics of the major joints were reconstructed using an optoelectronic system. The center of pressure (COP) was obtained using data collected from one force plate, and the ankle and knee joint torques were calculated using inverse dynamics. In the upright position there were small changes in the COP and in the knee and ankle joint torques. The tibialis anterior provoked the disruption of this upright position initiating the squat. During the acceleration phase of the squat the COP moved posteriorly, the knee joint torque remained in flexion and there was no measurable muscle activation. As the body went into the deceleration phase, the knee joint torque increased towards extension with major muscle activities being observed in the four heads of the quadriceps. Understanding these kinematic, kinetic and EMG strategies before, during and after the squat is expected to be beneficial to practitioners for utilizing squatting as a task for improving motor function.     

Lower extremity biomechanics during a regular and counterbalanced squat

If the efficiency of human movement patterns could be improved using exercise, this could lead to more effective musculoskeletal disease-injury prevention and rehabilitation programs. It has been suggested that an efficient squat movement pattern emphasizes the use of the large hip extensors instead of the smaller knee extensors. The purpose of this study was to determine whether a counterbalanced squat (CBS) could produce a more hip-dominant and less knee-dominant squat movement pattern as compared with a regular squat (RS). There were 31 recreationally trained college-aged participants (15 male, 16 female) who performed 10 squats (5 CBS and 5 RS), while segment kinematics, ground reaction forces, and muscle (gluteus maximus [GM], quadriceps, hamstrings) electromyographic (EMG) activations were recorded. Peak sagittal plane net joint moments and joint ranges of motion at the hip, knee, and ankle joints along with peak and integrated EMG activation levels for all 3 muscles were compared using analysis of variance (squat type × sex). The results revealed that the CBS increased the hip joint moment and GM activation, while it decreased the knee joint moment and quadriceps activation as compared with the RS. Therefore, the CBS produces a more hip-dominant and less knee-dominant squat movement pattern and could be used in exercise programs aimed at producing more hip-dominant movement patterns.     

Propulsion Phase of the Single Leg Triple Hop Test in Women with Patellofemoral Pain Syndrome: A Biomechanical Study

Asymmetry in the alignment of the lower limbs during weight-bearing activities is associated with patellofemoral pain syndrome (PFPS), caused by an increase in patellofemoral (PF) joint stress. High neuromuscular demands are placed on the lower limb during the propulsion phase of the single leg triple hop test (SLTHT), which may influence biomechanical behavior. The aim of the present cross-sectional study was to compare kinematic, kinetic and muscle activity in the trunk and lower limb during propulsion in the SLTHT using women with PFPS and pain free controls. The following measurements were made using 20 women with PFPS and 20 controls during propulsion in the SLTHT: kinematics of the trunk, pelvis, hip, and knee; kinetics of the hip, knee and ankle; and muscle activation of the gluteus maximus (GM), gluteus medius (GMed), biceps femoris (BF) and vastus lateralis (VL). Differences between groups were calculated using three separate sets of multivariate analysis of variance for kinematics, kinetics, and electromyographic data. Women with PFPS exhibited ipsilateral trunk lean; greater trunk flexion; greater contralateral pelvic drop; greater hip adduction and internal rotation; greater ankle pronation; greater internal hip abductor and ankle supinator moments; lower internal hip, knee and ankle extensor moments; and greater GM, GMed, BL, and VL muscle activity. The results of the present study are related to abnormal movement patterns in women with PFPS. We speculated that these findings constitute strategies to control a deficient dynamic alignment of the trunk and lower limb and to avoid PF pain. However, the greater BF and VL activity and the extensor pattern found for the hip, knee, and ankle of women with PFPS may contribute to increased PF stress.     

Effect of squat depth and barbell load on relative muscular effort in squatting

ABSTRACT: Bryanton, MA, Kennedy, MD, Carey, JP, and Chiu, LZF. Effect of squat depth and barbell load on relative muscular effort in squatting. J Strength Cond Res 26(10): 2820-2828, 2012-Resistance training is used to develop muscular strength and hypertrophy. Large muscle forces, in relation to the muscle's maximum force-generating ability, are required to elicit these adaptations. Previous biomechanical analyses of multi-joint resistance exercises provide estimates of muscle force but not relative muscular effort (RME). The purpose of this investigation was to determine the RME during the squat exercise. Specifically, the effects of barbell load and squat depth on hip extensor, knee extensor, and ankle plantar flexor RME were examined. Ten strength-trained women performed squats (50-90% 1 repetition maximum) in a motion analysis laboratory to determine hip extensor, knee extensor, and ankle plantar flexor net joint moment (NJM). Maximum isometric strength in relation to joint angle for these muscle groups was also determined. Relative muscular effect was determined as the ratio of NJM to maximum voluntary torque matched for joint angle. Barbell load and squat depth had significant interaction effects on hip extensor, knee extensor, and ankle plantar flexor RME (p < 0.05). Knee extensor RME increased with greater squat depth but not barbell load, whereas the opposite was found for the ankle plantar flexors. Both greater squat depth and barbell load increased hip extensor RME. These data suggest that training for the knee extensors can be performed with low relative intensities but require a deep squat depth. Heavier barbell loads are required to train the hip extensors and ankle plantar flexors. In designing resistance training programs with multi-joint exercises, how external factors influence RME of different muscle groups should be considered to meet training objectives.     

Sitting movement in elderly subjects with and without Parkinson’s disease: A biomechanical study

The aim of the present study was to compare kinetic, kinematic, and electromyographic variables during the sitting movement between healthy elderly and in those with Parkinson’s disease (PD) with moderate involvement. We hypothesized that subjects with PD would show difficulty in selecting the muscles for the task and that this could be related to the co-activation pattern and would be reflected in the behavior of some biomechanical variables. Fifteen subjects participated in this study, seven healthy subjects (NN group) and eight with Parkinson’s disease. Electromyography (EMG) activity of the tibialis anterior (TA), soleus (SO), vastus medialis oblique (VMO), biceps femoris (BF), and erector spinae (ES) were recorded, and biomechanical variables were calculated, during four phases of the sitting movement. Compared to healthy subjects, the subjects with PD showed more flexion at the ankle, knee, and hip joints in the initial position and lower joint velocity. However, the EMG activity and hip, knee, and ankle joint torques were not different during all phases of movement. The sitting movement in PD subjects with moderate involvement generates EMG activity and joint torques similar to healthy elderly subjects. Only a reduced movement velocity was found in PD patients during the sitting task.     

Bilateral differences in the net joint torques during the squat exercise

Bilateral movements are common in human movement, both as exercises and as daily activities. Because the movement patterns are similar, it is often assumed that there are no bilateral differences (BDs; differences between the left and right sides) in the joint torques that are producing these movements. The aim of this investigation was to test the assumption that the joint torques are equal between the left and right lower extremities by quantifying BDs during the barbell squat. Eighteen recreationally trained men (n = 9) and women (n = 9) completed 3 sets of 3 repetitions of the squat exercise, under 4 loading conditions: 25, 50, 75, and 100% of their 3 repetition maximum, while instrumented for biomechanical analysis. The average net joint moment (ANJM) and maximum flexion angle (MFA) for the hip, knee, and ankle as well as the average vertical ground reaction force (AVGRF) and the average distance from the ankle joint center to the center of pressure (ADCOP) were calculated. Group mean and individual data were analyzed (alpha = 0.05). At each joint, there was a significant main effect for side and load, no main effect for gender, with few significant interactions. The hip ANJM was 12.4% larger on the left side, the knee ANJM was 13.2% larger on the right side, and the ankle ANJM was 16.8% larger on the left side. Differences in MFAs between sides were less than 2 degrees for all 3 joints (all p > 0.20 except for the knee at 75% [p = 0.024] and 100% [p = 0.025]), but the AVGRF and the ADCOP were 6% and 11% larger on the left side. Few subjects exhibited the pattern identified with the group mean data, and no subject exhibited nonsignificant BDs for all 3 joints. These findings suggest that joint torques should not be assumed to be equal during the squat and that few individual subjects follow the pattern exhibited by group mean data.     

Quantified in vitro tibiofemoral contact during bodyweight back squats

Squats are a common lower extremity task used in strength and conditioning, balance training, and rehabilitation. It is important to understand how slight alterations in lower extremity kinematics during a squat affect the internal joint loading of the knee. This study directly quantified tibiofemoral contact throughout the in vitro simulation of a bodyweight back squat performed two ways: a heel squat (knees in line with toes) and a toe squat (knees anterior to the toes) at peak knee flexion. Three cadaveric right lower extremities were instrumented and positioned into the University of Texas Joint Load Simulator. Kinematics, kinetics, and predicted muscle forces from a 20-year-old athletic male performing the two back squats were used as inputs for the in vitro simulations. The quantified tibiofemoral contact area, peak pressure, net force, and center of pressure location were significantly different between squat types (p > 0.05). Net contact area on the tibial plateau at peak knee flexion was significantly larger in the heel versus toe squat (599 ± 80 mm² vs. 469 ± 125 mm²; p < 0.05). Peak lateral pressure was significantly higher in the heel versus toe squat (2.73 ± 0.54 MPa vs. 0.87 ± 0.56 MPa; p < 0.05). Results suggest the heel squat generates an even load distribution, which is less likely to affect joint degeneration. Future in vitro simulations should quantify the effects lower extremity kinematics, kinetics, and individual muscle forces have on tibiofemoral contact parameters during common athletic tasks.     

Reduced knee joint moment in ACL deficient patients at a cost of dynamic stability during landing

The current study aimed to examine the effect of anterior cruciate ligament deficiency (ACLd) on joint kinetics and dynamic stability control after a single leg hop test (SLHT). Twelve unilateral ACLd patients and a control subject group (n=13) performed a SLHT over a given distance with both legs. The calculation of joint kinetics was done by means of a soft-tissue artifact optimized rigid full-body model. Margin of stability (MoS) was quantified by the difference between the base of support and the extrapolated center of mass. During landing, the ACLd leg showed lower external knee flexion moments but demonstrated higher moments at the ankle and hip compared to controls (p<0.05). The main reason for the joint moment redistribution in the ACLd leg was a more anterior position of the ground reaction force (GRF) vector, which affected the moment arms of the GRF acting about the joints (p<0.05). For the ACLd leg, trunk angle was more flexed over the entire landing phase compared to controls (p<0.05) and we found a significant correlation between moment arms at the knee joint and trunk angle (r2 = 0.48;p<0.01). The consequence of this altered landing strategy in ACLd legs was a more anterior position of the center of mass reducing the MoS (p<0.05). The results illustrate the interaction between trunk angle, joint kinetics and dynamic stability during landing maneuvers and provide evidence of a feedforward adaptive adjustment in ACLd patients (i.e. more flexed trunk angle) aimed at reducing knee joint moments at the cost of dynamic stability control.     

Obesity is not associated with increased knee joint torque and power during level walking

While it is widely speculated that obesity causes increased loads on the knee leading to joint degeneration, this concept is untested. The purpose of the study was to identify the effects of obesity on lower extremity joint kinetics and energetics during walking. Twenty-one obese adults were tested at self-selected (1.29m/s) and standard speeds (1.50m/s) and 18 lean adults were tested at the standard speed. Motion analysis and force platform data were combined to calculate joint torques and powers during the stance phase of walking. Obese participants were more erect with 12% less knee flexion and 11% more ankle plantarflexion in self-selected compared to standard speeds (both p<0.02). Obese participants were still more erect than lean adults with approximately 6 degrees more extension at all joints (p<0.05, for each joint) at the standard speed. Knee and ankle torques were 17% and 11% higher (p<0.034 and p<0.041) and negative knee work and positive ankle work were 68% and 11% higher (p<0.000 and p<0.048) in obese participants at the standard speed compared to the slower speed. Joint torques and powers were statistically identical at the hip and knee but were 88% and 61% higher (both p<0.000) at the ankle in obese compared to lean participants at the standard speed. Obese participants used altered gait biomechanics and despite their greater weight, they had less knee torque and power at their self-selected walking speed and equal knee torque and power while walking at the same speed as lean individuals. We propose that the ability to reorganize neuromuscular function during gait may enable some obese individuals to maintain skeletal health of the knee joint and this ability may also be a more accurate risk indicator for knee osteoarthritis than body weight.     

Persons with multiple sclerosis show altered joint kinetics during walking after participating in elliptical exercise

Patients with multiple sclerosis (MS) experience abnormal gait patterns and reduced physical activity. The purpose of this study was to determine if an elliptical exercise intervention for patients with MS would change joint kinetics during gait toward healthy control values. Gait analysis was performed on patients with MS (n = 24) before and after completion of 15 sessions of supervised exercise. Joint torques and powers were calculated, while also using walking velocity as a covariate, to determine the effects of elliptical exercise on lower extremity joint kinetics during gait. Results show that elliptical exercise significantly altered joint torques at the ankle and hip and joint powers at the ankle during stance. The change in joint power at the ankle indicates that, after training, patients with MS employed a walking strategy that is more similar to that of healthy young adults. These results support the use of elliptical exercise as a gait training tool for patients with MS.     

Comparison of joint kinetics during free weight and flywheel resistance exercise

The most common modality for resistance exercise is free weight resistance. Alternative methods of providing external resistance have been investigated, in particular for use in microgravity environments such as space flight. One alternative modality is flywheel inertial resistance, which generates resistance as a function of the mass, distribution of mass, and angular acceleration of the flywheel. The purpose of this investigation was to characterize net joint kinetics of multijoint exercises performed with a flywheel inertial resistance device in comparison to free weights. Eleven trained men and women performed the front squat, lunge, and push press on separate days with free weight or flywheel resistance, while instrumented for biomechanical analysis. Front squats performed with flywheel resistance required greater contribution of the hip and ankle, and less contribution of the knee, compared to free weight. Push presses performed with flywheel resistance had similar impulse requirements at the knee compared to free weight, but greater impulse requirement at the hip and ankle. As used in this investigation, flywheel inertial resistance increases the demand on the hip extensors and ankle plantarflexors and decreases the mechanical demand on the knee extensors for lower extremity exercises such as the front squat and lunge. Exercises involving dynamic lower and upper extremity actions, such as the push press, may benefit from flywheel inertial resistance, due to the increased mechanical demand on the knee extensors.     

Electromyographic and kinematic analysis of females with excessive medial knee displacement in the overhead squat

Dynamic knee valgus is a multi-planar motion that has been associated with anterior cruciate ligament injuries and patellofemoral pain syndrome. Clinical assessment of dynamic knee valgus is usually performed through visual appearance of medial knee displacement (MKD) during the overhead squat. The aim of this study is to identify the kinematic and neuromuscular parameters associated with MKD. Twenty-two females performed an overhead squat and were assigned to the control group (n = 14) or the MKD group (n = 8). Electromyography and kinematic data of the lower extremity were collected. We observed MKD to exhibit greater muscle activity in the following muscles: adductor magnus, biceps femoris, vastus lateralis and vastus medialis muscles during the eccentric phase of the overhead squat. No group differences were observed during the concentric phase. Regarding the kinematics, the MKD group showed higher knee internal rotation and, knee abduction and ankle abduction, compared to controls. The combined information from the muscle activity results and kinematics of squat helps to explain the occurrence of excessive medial knee displacement and, hence, providing relevant information for health professionals to address this injury risk factor.     

Lower extremity joint kinetic responses to external resistance variations

The purpose of this investigation was to determine if increases in external resistance during a squat movement would be controlled by proportionally scaling the net joint moment work or average net joint moment (NJM) at the hip, knee, and ankle. Eighteen experienced subjects performed 3 sets of 3 repetitions each of a squat movement using resistances of 25, 50, 75, and 100% of their 3-repetition maximum, while instrumented for biomechanical analyses. Standard inverse dynamics techniques and numerical integration were used to calculate the NJM work and average NJM of each joint. A combination of single-subject and group mean statistical analyses indicated that the neither the NJM work nor average NJM increased proportionately in response to increases in external loading. Results suggest a complex control strategy in which the hip was the dominant contributor, increased linearly with the external load, and had low variability. The knee and ankle contributions were neither as great nor as linear, and were highly variable, suggesting that they were influenced by more than just the external load. The disproportionate response of each joint to varying external resistances suggests that controlling the force output of multijoint chains requires further study and modifications to existing motor control theories.     

Alignment of the human body in standing

Alignment of the body in typical symmetrical standing was studied by photographing fifteen subjects in profile on a reaction board. Two aspects of alignment were studied: (1) the anteroposterior position of the body landmarks of knee joint, hip joint, shoulder joint, and ear, compared to the ankle joint; and (2) the positions of the partial centers of gravity above the knee and hip, as a measure of how the body is balanced above these joints. The knee, hip, shoulder, and ear were forward of the ankle in all subjects. On average, the knee was 3.8 (+/- 2.0), the hip 6.2 (+/- 1.3) the shoulder 3.8 (+/- 1.9), and the ear 5.9 (+/- 1.6) cm (+/-S.D.) anterior to the ankle. The positions of landmarks were positively correlated with one another but not highly. The position of the center of gravity could be predicted well from the positions of the landmarks within individual subjects' data, but not across subjects. The centers of gravity above the knee and hip were calculated by subtracting the mass and position of the segments below the joint from the whole-body center of gravity. The center of gravity above the knee was located on average 1.4 (+/- 1.1) cm in front of the joint, and that of the hip 1.0 (+/- 1.6) cm behind the trochanter. Thus, at both knee and hip in typical standing, there exist slight gravitational torques tending to extend the joints.     

Relationship between eccentric hip torque and lower-limb kinematics: gender differences

The purposes of this study were to compare lower-limb kinematics between genders, and determine the relationships among eccentric hip abductor and lateral rotator torques and lower-limb kinematics. The movements of the pelvis, femur, and knee were calculated for 16 women and 16 men during the single-leg squat. Eccentric hip abductor and lateral rotator torques were measured using an isokinetic dynamometer. The results showed that women had greater contralateral pelvic depression, femur adduction, and knee abduction than men. The eccentric hip abductor and lateral rotator torques were correlated with coronal plane femur and knee movements in the overall sample. When the genders were analyzed separately, it was observed that women with greater eccentric hip abductor torque exhibited less femur adduction and femur medial rotation, and greater knee adduction excursion. No significant relationship was observed between the isokinetic and kinematic variables in the male group. The differences between the genders help to explain the greater rate of knee disorders observed in women. Moreover, the eccentric hip abduction action seemed to be more important in women to control the lower-limb movements.     

Lower extremity biomechanics during weightlifting exercise vary across joint and load

The purpose of this study was to determine the effect of load on lower extremity biomechanics during the pull phase of the clean. Kinematic and kinetic data of the 3 joints of the lower extremity were collected while participants performed multiple sets of cleans at 3 percentages: 65, 75, and 85% of 1 repetition maximum (1RM). General linear models with repeated measures were used to assess the influence of load on angular velocities, net torques, powers, and rates of torque development at the ankle, knee, and hip joint. The results suggest that the biomechanical demands required from the lower extremities change with the lifted load and to an extent depend on the respective joint. Most notably, the hip and knee extended significantly faster than the ankle independent of load, whereas the hip and ankle generally produced significantly higher torques than the knee did. Torque, rate of torque development (RTD), and power were maximimal at 85% of 1RM for the ankle joint and at 75% of 1RM for the knee joint. Torque and RTD at the hip were maximal at loads >75% of 1RM. This study provides important novel information about the mechanical demands of a weightlifting exercise and should be heeded in the design of resistance training programs.     

Gait and neuromuscular pattern changes are associated with differences in knee osteoarthritis severity levels

Knee osteoarthritis (OA) is a multifactoral, progressive disease process of the musculoskeletal system. Mechanical factors have been implicated in the progression of knee OA, but the role of altered joint mechanics and neuromuscular control strategies in progressive mechanisms of the disease have not been fully explored. Previous biomechanical studies of knee OA have characterized changes in joint kinematics and kinetics with the disease, but it has been difficult to determine if these biomechanical changes are involved in the development of disease, are in response to degenerative changes in the joint, or are compensatory mechanisms in response to these degenerative changes or other related factors as joint pain. The goal of this study was to explore the association between biomechanical changes and knee OA severity in an effort to understand the changing role of biomechanical factors in the progression of knee OA. A three-group cross-sectional model was used that included asymptomatic subjects, subjects clinically diagnosed with moderate knee OA and severe knee OA subjects just prior to total joint replacement surgery. Principal component analysis and discriminant analysis were used to determine the combinations of electromyography, kinematic and kinetic waveform pattern changes at the knee, hip and ankle joints during gait that optimally separated the three levels of severity. Different biomechanical mechanisms were important in discriminating between severity levels. Changes in knee and hip kinetic patterns and rectus femoris activation were important in separating the asymptomatic and moderate OA gait patterns. In contrast, changes in knee kinematics, hip and ankle kinetics and medial gastrocnemius activity were important in discriminating between the moderate and severe OA gait patterns.     

Trunk position influences joint activation pattern and physical performance during vertical jumping

Eight well-trained males carried out squat jump and countermovement jump with large (SJL and CMJL) and with small (SJS and CMJS) range of motion to study the influence of trunk position on joint recruitment pattern and jumping height. The main criteria in SJS and CMJS were to maintain trunk in near vertical position during execution. Joint angles, activation time, time at maximum joint velocity for ankle joint, knee joint and hip joint, vertical propulsion time and jumping height were determined using film analysis. The joint activation followed proximal to distal pattern in CMJL, SJL and CMJS, but the pattern was reversed in SJS. The ratio of active state and vertical propulsion time was similar for all joints (63.1 and 72.8%) in CMJL, SJL and CMJS except in SJS where the ratio was significantly less for hip (46.9%) and knee (51.9%). The difference between CMJL and SJL in jumping height was 6.9 ± 2.8 cm which is significantly less than that between CMJS and SJS (14.5 ± 5.3 cm). We concluded that knee joint and hip joint muscles could not contribute to the positive work during the push-off phase when the range of motion is small, the trunk is vertical and the activation level of the muscles is low.