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BASIC SCIENCES: Symposium—Ground/Foot Impacts: Measurement, Attenuation, and Consequences

The Effects of Knee Contact Angle on Impact Forces and Accelerations

DERRICK, TIMOTHY R.

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Medicine & Science in Sports & Exercise: May 2004 - Volume 36 - Issue 5 - p 832-837
doi: 10.1249/01.MSS.0000126779.65353.CB
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Abstract

Compared with most exercise and sport activities, running is highly unconstrained. It can take place in a wide variety of environments: indoors or outdoors; on a track or over rough terrain; up hills, on level ground or down hills; in the heat of summer or the cold of winter; during daylight hours or nighttime conditions. The level of exertion is also highly diverse. Some participants prefer a leisurely jog while others elevate heart rates to near maximum levels by running at higher velocities and utilizing rest intervals.

During a typical heel-toe running cycle the foot impacts the ground and causes a very rapid increase in the vertical ground reaction force that reaches a maximum at about 25 ms after heel contact (Fig. 1). This impact force accelerates a portion of the lower extremity so that there is also a peak impact acceleration (Fig. 1). Peak impact accelerations occur for individual body segments as the impact is transmitted through the skeletal system from the leg to the head (Fig. 1). The local segment peak accelerations occur at successively later times as the shock moves up the body. Researchers and clinicians often associate impacts with overuse injuries in runners, yet there is little epidemiological evidence to suggest high impacts are a substantial cause of running injuries in the typical runner. In fact, it has been suggested that typical impacts caused by running can provide a positive stimulus for cartilage and bone growth (11). It is likely that impacts are a contributor to injury only when they are coupled with such items as abnormal anatomy or kinematics, excessive duration or inadequate rest between bouts. It appears that most runners successfully adapt to a changing environment by maintaining impact severity below a threshold level and thus optimize performance and injury potential (Fig. 2). These adaptations may take the form of altered kinematics, such as the knee angle during ground contact. For those individuals that do not adapt to the environment, it may signify decreased performance or increased injury potential for an individual runner. Adaptation failures (Fig. 2) are also an important area of research but they are more difficult to study and are not considered in this article.

FIGURE 1
FIGURE 1:
The stance phase of a running cycle showing the relative times of occurrence and magnitudes of the impact peak for the vertical ground reaction force (+), leg acceleration (†), and head acceleration (✖).
FIGURE 2
FIGURE 2:
An altered running environment forces the runner to make adaptations in order to maintain optimal performance or injury potential. This article examines these adaptations. Adaptation failures (grayed branch) are not covered in this article.

The purpose of this article was to synthesize results from several studies to examine: 1) the effect that knee contact angle has on the severity of the resulting impact, 2) the relationship between impact forces and impact accelerations, and 3) the adaptations that occur in response to running during changing environmental conditions. Evidence will be presented to suggest runners generally respond to unusual environmental conditions by increasing the amount of knee flexion during ground contact. This increases the peak impact acceleration of the leg and impact attenuation but does not necessarily lead to increased peak vertical ground reaction impact forces. The resulting improved attenuation of the impact between the leg and the head may incur a performance decrement in the form of greater metabolic cost.

EFFECTIVE MASS

An impact between a multi-segmented body and a rigid surface produces a complex pattern of segment accelerations. The acceleration of each segment will depend on the forces being applied to that segment. As the ground initiated force is transmitted through the musculoskeletal system it is partially attenuated such that the segments further from the point of application of the force will undergo lesser accelerations. The accelerations of these segments will depend on the geometry of the segments, apparent stiffness of the joints (caused primarily by muscle tension), segment deformations (caused primarily by deformation of biological tissue), segment masses, and segment moments of inertia. The effective mass (me) is the portion of the total system mass that would be needed to accurately model the impact if a single mass particle were used instead of the system of rotating and deforming segments. Effective mass values have been estimated for falls on the hip (9), walking, running and landing from a jump (2), and in many activities in which a person impacts a ball with a segment or an implement (12). The latter is often termed striking mass instead of effective mass.

Effective mass can be calculated from the linear impulse-momentum relationship (18):

EQUATION

where, me is the effective mass, ∫ Fdt is the linear impulse due to the impact, and Δv is the change in velocity.

If minimal segment deformations are assumed and the line of action of the ground reaction force vector passes through the joint centers, then the effective mass is essentially the mass of the body. Centric forces do not promote joint rotations and thus the whole body would be accelerated as a single rigid unit (Fig. 3a). However, if the joints are flexed the force vector will become eccentric, causing the individual segments to decouple so that the greatest accelerations occur at the segments closest to the impact surface (Fig. 3b).

FIGURE 3
FIGURE 3:
Impacts with an extended (a) or flexed (b) body. The line of action (dashed lines) of an impulsive vertical ground reaction force (arrows) goes through the joints centers in an extended body but not a flexed body. This causes the entire extended body to be accelerated but only the lower extremity of the flexed body to be accelerated (background shadows represent segment movement). Effective mass is therefore reduced in the flexed body.

Figure 3 illustrates the point that effective mass of an extended body is greater than the effective mass of a flexed body given realistic values for the apparent stiffness of the joints. Infinite joint stiffnesses will produce an effective mass equal to body mass whether the joints are flexed or extended. Experimental data support the view that effective mass is determined in part by impact geometry. Denoth (2) demonstrated the dependency of effective mass on knee angle using a combination of modeling results and experimental data for activities such as walking, running, and jumping. For a single barefoot subject with a body mass of 65 kg, the results showed that increasing knee flexion from 5° to 20° would decrease effective mass of the body from 11 to 5 kg. The relationship between knee flexion and effective mass appears to be relatively linear within this range.

IMPACT FORCES AND ACCELERATIONS

The relationship between the net force, body mass and center of mass (COM) acceleration is dictated by Newton’s second law. Any increase in the force will produce an associated increase in the acceleration. A simulation study by Gerritsen et al. (6) estimated that a more flexed knee position at contact would decrease the peak impact force by approximately 68 N per degree of flexion. Taken alone, this result might suggest that peak impact acceleration (acceleration of the effective mass) would also decrease with increased flexion. However, Denoth’s results showed that as the knee attained a more flexed position during contact the effective mass decreased (2). Because both the impact force and the effective mass are altered the question becomes which factor has the dominant effect on the resulting leg acceleration when the body impacts the ground with greater knee flexion. If the decreased force effect dominates, then decreased accelerations would be predicted. If the decreased effective mass effect dominates, then increased accelerations would be predicted. The remainder of this section will provide evidence to support the latter as the dominant effect, and thus a more flexed knee position during contact will reduce the effective mass, reduce the peak impact force, and increase the peak impact acceleration of the leg.

The knee contact angle is easier to manipulate during an activity in which it is not continually flexing and extending. The gliding phase of inline skating provides a convenient protocol for studying the effects of impacts in a more controlled manner than running. In an unpublished pilot study, nine inline skaters were recruited to glide on a treadmill with a belt speed of 2.24 m·s−1. A 3-mm bump was attached to the belt, and the subjects were asked to maintain a knee angle of approximately 0° or 60° (0° = full extension). Acceleration signals were digitized at 1000 Hz from 1.7-g accelerometers attached to the skate and the head. The decreased force effect predicts decreased peak accelerations of the skate, whereas the decreased effective mass effect predicts increased peak accelerations of the skate. Thus, the results of the skate accelerations will provide evidence for the dominant effect. Average peak skate accelerations increased from 6.7 ± 2.1 g during the 0° condition to 7.8 ± 2.3 g during the 60° condition. Although this was a nonsignificant increase (effect size: 0.5), it was presumed that flexing the knee decreased the effective mass and allowed the bump reaction force to accelerate the lower-extremity mass more easily. This provides evidence that the dominant concept was that of decreased effective mass. Although the peak skate acceleration increased when the knee was flexed, ± 0.20 g to 0.20 ± 0.09 g. Thus, the attenuation of the impact from the skate to the head increased from 93.9% with extended knee to 97.4% when the knee was flexed.

It is possible for peak impact accelerations to increase when peak impact forces decrease if the decreased effective mass effect dominates over the decreased force effect. Derrick et al. (4) used a mass-spring-damper model (1) of human running (Fig. 4) to demonstrate that increased peak impact accelerations do not necessarily reflect increased peak impact forces. The initial conditions of this model were derived from actual running (3), and the spring stiffnesses were optimized so that the model ground reaction forces closely resembled the actual vertical ground reaction forces of the runners (3). The upper spring is relatively compliant and is responsible for the low-frequency portion of the vertical ground reaction force curve (Fig. 1). The spring-damper system is responsible for the higher-frequency portion of the vertical ground reaction force curve and therefore represents the impact. An arbitrary 5% of body mass was shifted from the lower mass to the upper mass, whereas all other parameters were held constant. Because the change in system momentum is constant between the two conditions, the total impulse will be the same except for changes that may occur as a result of energy absorbed by the damper. This simulated decreasing the effective mass because a lesser mass was accelerated during the impact. The resulting ground reaction forces and lower mass (M2) accelerations were compared. The shift of mass from M2 to M1 resulted in a slower deformation of the spring and decreased damper velocities. Thus, there was a decrease in the peak impact force from 950 to 850 N. Even with this decreased force, the lesser mass resulted in an increase in the peak impact acceleration of M2 from 5.5 to 6.6 g (4). This model is a simplification of human running and may not contain all of the relevant features (3). For instance, humans may simultaneously change effective mass and impact stiffness. If the ratio of spring stiffness values to mass values (K1/M1 and K2/M2) were kept constant in the model, then peak impact forces would decreases even more (788 N) because of the reduced absolute stiffness of K2. The peak accelerations of M2 would not change (5.5 g) relative to the greater effective mass condition because the decreased mass of M2 is countered by the decreased absolute stiffness of K2. This illustrates that decreases in effective mass can simultaneously decrease peak impact force while increasing or maintaining peak impact acceleration. It is currently unknown which model (constant stiffness or constant K/M ratios) most accurately portrays actual running.

FIGURE 4
FIGURE 4:
The influence of effective mass (M2) on impact force peaks and impact acceleration peaks. M2 mass was changed from 20% of body mass to 15% of body mass. Impact force peak decreased and impact acceleration increased. Forces and accelerations were derived from the mass-spring-damper model shown in the schematic. Total mass = 56 kg; K1 stiffness = 16.6 kN·m−1; K2 stiffness = 112 kN·m−1; C damping ratio = 0.35; From Derrick et al. (4). the head acceleration was significantly decreased from 0.41

Preliminary data from a study in progress supports these modeling results. Ten subjects (age: 25.3 ± 6.5 yr; body mass: 68.6 ± 8.0 kg) ran off of a 22.5-cm raised runway onto a force platform. The force platform was placed such that contact would be made with the right foot on the first step off the raised runway. Subjects were asked to run with a heel-toe running style at a self-selected running velocity while kinematics (120 Hz), ground reaction forces (3600 Hz), and head and leg accelerations (3600 Hz) were digitized. Ten trials of self-regulated exaggerated knee extension (10.3 ± 4.4° of flexion at contact) and exaggerated knee flexion (20.4 ± 5.2° of flexion at contact) were averaged for each subject. Peak impact forces decreased by 439 N during the exaggerated knee flexion, whereas peak impact leg accelerations increased by 2.8 g. This supports the model results that show decreasing the effective mass can simultaneously decrease peak impact force and increase peak impact acceleration.

According to the decreased force effect, increased knee flexion will produce decreased forces and therefore decreased peak leg accelerations. Thus, this effect predicts a negative correlation between knee flexion and peak leg acceleration. On the other hand, the decreased effective mass effect predicts that increased knee flexion will produce decreased effective mass and therefore increased peak leg accelerations. This would result in a positive correlation between knee flexion and peak leg acceleration. Table 1 shows the average knee contact angle and the average peak leg acceleration results of several running experiments that were collected using similar instrumentation and collection and analysis procedures (4,5,15). Each of these 14 conditions is within the range of what could be considered a typical running environment. There are 7–12 subjects in each protocol, and the conditions within each protocol contain the same subject pool. Each protocol has a control condition that is bolded in Table 1. Running speed was not constant between studies, so running speed was statistically removed as a source of variance from both knee contact angle and peak leg acceleration. There are a total of 1755 impacts that were analyzed in these studies. The data can be used to help establish the relationship between the knee contact angle and peak leg acceleration. Figure 5 shows that the correlation is positive (r = 0.79), indicating that as the knee flexion at contact increases, the peak leg acceleration also increases (0.27 g per degree of flexion). This supports the decreased effective mass effect and suggests that the effects of decreased effective mass dominate over the effects of decreased forces when examining the influence of knee flexion on peak leg accelerations during running.

TABLE 1
TABLE 1:
The relationship between knee contact angle and peak leg acceleration for a variety of experimental protocols.
FIGURE 5
FIGURE 5:
The relationship between knee contact angle and peak leg impact during running under a variety of conditions. Variability due to running speed has been removed from both variables. Each data point represents the average from a condition in one of the studies described in Table 1. Open diamonds indicate control conditions and the light intensity conditions. Peak leg acceleration is seen to increase as the knee becomes more flexed at ground contact.

IMPACT ATTENUATION

It may seem intuitive that increases in peak leg acceleration would be associated with greater injury potential. It has been shown that it is possible for peak leg accelerations to increase as peak impact forces decrease. This occurs because placing the knee in a more flexed position at contact reduces the effective mass. It is often more convenient to use accelerometry techniques to assess the potential for injury in runners. Multiple strides are easily collected, there is no targeting of a force platform, different surfaces can be examined, and treadmill analysis is possible without a special instrumented treadmill bed. It would be useful to find an accelerometry variable that could more accurately reflect injury potential (or at least impact severity) when effective mass is not constant. Impact transmission may be useful in this regard. Transmission or attenuation of the acceleration can be accomplished by measuring the magnitude of the peak impact acceleration at two points on the body. Transmission is the amount of the peak impact acceleration that reaches the second accelerometer relative to the first. Attenuation is the reduction in the peak impact acceleration from the first accelerometer to the second. These calculations can be accomplished in the time domain (15,17) or the frequency domain (5,14).

The inline skate results presented earlier showed that peak skate acceleration increased as the knee position was changed from fully extended to 60° of flexion. Without further data it may be tempting to conclude that it is bad to flex the knees while going over a bump. However, the results show an increase in attenuation from 93.9% with the extended knees to 97.4% with the flexed knees. The attenuation is not as great during the extended knee position because the line of action of the ground reaction force vector tends to go through, or close to, the knee joint center. Thus, joint rotations and stretching of the elastic components in the muscle-tendon complex are minimized and muscular energy absorption is decreased relative to the flexed knee position. There is also less transfer of impact energy into rotational energy of the segments.

ADAPTATION TO AN ALTERED ENVIRONMENT

The influence that the knee contact angle can have on the effective mass, impact force, and impact acceleration has been established, but the effects that environmental changes have on the knee contact angle need to be examined. It is obviously not possible to assess all environmental changes because of the infinite possibilities. There can be changes to the internal environment such as fatigue, injury, stride characteristics, uncertainty, frailty, pain, and stress levels. There can also be changes to the external environment such as light, temperature, shoe and surface stiffness, terrain, and grade.

It is doubtful that all changes to the environment will produce the same kind of adaptation, yet there is a tendency for the protocols in Table 1 to produce increased knee flexion at contact relative to the control conditions. The single exception was that the light-intensity level did not seem to have an effect on knee angle. Figure 5 shows that the runners in the control and light-intensity conditions (marked with open diamonds) tended to have a more extended knee contact angle and lower accelerations than the remaining experimental conditions. On average, the experimental conditions that affected the knee contact angle (stride length, fatigue, surface, and grass length) had an average increase of 2.5°. Although this does not seem like a large amount, simulation models indicate this change in knee angle would decrease the ground reaction forces by approximately 170 N (6) if other variables were kept constant. Despite this decrease in the ground reaction force, the presumed decrease in effective mass caused by the increased knee flexion resulted in an average increase in the peak leg acceleration of 0.7 g.

According to the diagram in Figure 2, there are two reasons why a person might want to adapt to a changing environment: to improve performance or to avoid injury. It is doubtful the knee contact angle adjustments made during the conditions identified in Table 1 were to improve performance. This is because knee contact angle is associated with increased midstance knee angle (Fig. 6). Figure 6 shows a correlation of 0.67 between the knee flexion at contact and at maximum for the conditions listed in Table 1. This indicates there was a tendency for increased initial flexion to be accompanied by greater subsequent maximum flexion. Bending the knee more decreases the mechanical advantage of the limb and thus increases energy cost (8,10,13). The control and light-intensity conditions had an average maximum knee flexion angle of 41.7°, whereas the other experimental conditions had an average maximum knee flexion angle of 46.6°. Valiant (16) estimated an increase of about 25% in the oxygen cost of running for each 5° increase in midstance knee angle during Groucho running (10). If these results hold for the variety of running conditions in Table 1, the 4.9° increase in maximum knee flexion would indicate an increase in oxygen cost of about 24.5% after subjects adapted to the altered environments. This may be an overestimate of the effect, but it is unlikely that the increased knee contact angle adaptation seen in Table 1 conditions were made to improve performance.

FIGURE 6
FIGURE 6:
The relationship between knee contact angle and maximum knee flexion angle during running under a variety of conditions (see Table 1). Variability due to running speed has been removed from both variables. Open diamonds indicate control conditions and the light intensity conditions.

The reason for increased knee flexion at contact may have been an attempt to reduce the potential for injury. In situations that produce uncertainty in the stride of the runners (fatigue, surface irregularities, long grass), individuals may increase knee flexion at contact in order that increased variability will not cause excessive forces during some of the impacts. Peak impact forces increase rapidly as the knee contact angle becomes more extended (6). If there is uncertainty in when the foot will contact the ground (surface irregularities, long grass) or if it becomes difficult to control when the foot will contact the ground (fatigue), then it may be prudent to err on the side of safety by increasing knee flexion at contact. In the case of overstriding, the vertical impact velocity of the foot was greater when the longer strides were taken (overstride: −0.61 m·s−1, normal: −0.47 m·s−1, understride: −0.39 m·s−1). Even though the knee was more flexed at contact during the longer strides, the increased foot contact velocities caused greater peak impact forces (overstride: 20.6 N·kg−1, normal: 18.1 N·kg−1, understride: 15.7 N·kg−1) as well as greater peak leg accelerations (Table 1). A separate study has shown that this amount of overstriding can cause a statistically significant increase in the rate of oxygen consumption (7). It seems likely that at least a portion of this increased rate of oxygen consumption was due to the greater knee flexion, and thus this kinematic alteration was probably an attempt to reduce impact forces rather than improve performance during overstriding.

If the effective mass of a person changes because of an altered knee contact angle, then peak impact forces may not change in accord with peak impact accelerations. In fact, simulation results (Fig. 4) and preliminary data have provided evidence that it is possible for peak forces to increase, whereas peak impact accelerations decrease if effective mass increases. This can lead to confusing results depending on which variable is measured. Ideally, impact forces as well as impact accelerations of leg and head would be measured. If it is not possible to measure impact forces then knowledge of contact kinematics should be sought, especially knee angle.

Runners seem to run with a near maximal amount of knee extension at contact. If conditions are not ideal (see Table 1), then they appear to increase the amount of knee flexion. This adaptation decreases injury potential by reducing the impact severity and the chances that a miscue would result in a hazardous landing situation. Attaining this margin of error may have a metabolic cost that decreases maximal performance.

Further studies need to be performed that record both impact forces and impact accelerations. Knee angle could then be manipulated so that these relationships could be tested in a more controlled manner. Techniques should be developed that allow the verification that these external variables have some meaning to internal factors that cause injury or performance. Although it is difficult to measure, a complete study of environmental influences must look at the other branch of the diagram in Figure 2. What happens to runners who do not successfully adapt to environmental changes? Finally, additional environmental manipulations and kinematic variables must be examined to get a holistic view of the influences on running.

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Keywords:

INJURY; SHOCK ATTENUATION; PERFORMANCE; EFFECTIVE MASS

©2004The American College of Sports Medicine