## 18 Gait

The underlying causes of pathological gait vary widely. It may be that the muscles do not generate sufficient force, or they do not tolerate the strains required, or perhaps activation does not occur at the right time intervals. The left and right leg lengths may be different, or the geometry of the joints and the orientation of their axes of rotation may differ from normal. The main aims of gait analysis are (1) to classify a person’s gait as normal or pathological, (2) to explore the causes of a pathological gait, (3) to check the effect of internal or external prostheses on gait, and (4) to assess the success of physiotherapy. To do these things, gait analysis documents the course of the motion in space and time. The muscle activation pattern is determined by the recording of electromyography (EMG) signals. Forces and moments acting on the segments of the lower extremity (foot, lower leg, and upper leg) can be calculated using the method of inverse dynamics. The pressure distribution under the sole of the foot and the energy consumption can also be measured. Walking is a complex movement, and one cannot expect that measurement of a single parameter will be enough to classify a person’s gait as normal or pathological.

### 18.1 Gait Pattern

Inspection of the footprints (** Fig. 18.1 **) conveys a first impression of an individual’s gait pattern. The stride length is the sum of the left and right step lengths. Adults have a stride length in the order of 1.4 m. 1, 2 During walking at a comfortable, self-selected speed, stride length is observed to be dependent on the leg length: on average, stride length increases with body height. For the purpose of comparisons, stride length is normalized for stature and the quotient of stride length/body height is used. After normalization, the stride lengths of men and women are almost identical. 3 In healthy persons the left and right step lengths are equal, each making up one half of the total stride length. In pathological gait, the left and right step lengths can be markedly different.

The line of progression runs through the center between the left and right footprints. In normal gait the prints of the right foot lie to the right of this line and the prints of the left foot to the left. If both feet are placed exactly on the line of progression, the gait pattern is conspicuously unusual. In pathological gait, it can even happen that both the right and the left foot cross the line of progression. The step width is defined as the distance between the centers of the heel prints of the right and the left foot, measured perpendicularly to the line of progression. In healthy persons the step width is around 10 cm.

The foot angle is the angle between the line of progression and the line connecting the center of the heel print and the second ray. In large cohorts, Dougan 4 and Patek 5 documented an average foot angle of 6°. In healthy persons, however, there was a wide variation in the range between +20° and −8°. Normally the angles of the left and right feet differed by 2° or more. Ducroquet et al 6 report normal foot angles of approximately 15°, but this value seems unrealistically high: Charlie Chaplin’s unmistakable gait is characterized by foot angles of this magnitude. In a 9-month longitudinal study of 10 healthy adults, Brinckmann 7 observed that foot angles varied considerably, not just from step to step, but throughout the observation period. It follows that determining foot angle from one step alone at a single point in time will give an unreliable result.

Only limited information can be obtained from inspecting a footprint pattern. A marked difference between left and right step length or footprints that cross the line of progression point to a gait disorder, but the cause of the disorder cannot be discerned. Conspicuously short step lengths may be from a small person, or from a person of normal height walking slowly, or from a patient with Parkinson disease. The clinical significance of a deviation of the foot angle from the norm (and its potential influence on the orientation of the knee axis) is unknown. Recent technological advances have made it much easier to measure footprints optically and electronically, and we may expect this issue to be further explored in future cross-sectional and longitudinal studies.

### 18.2 Sequence of Steps in Time

Normal gait consists of a series of virtually identical steps succeeding each other in turn. In this cyclic motion, the basic unit is the so-called gait cycle, the time interval between successive heel strikes of the right or the left foot. **Fig. 18.2 **shows a gait cycle starting at heel strike of the right foot. The stance phase (time interval of floor contact) commences at heel strike; it ends at toe-off. This is followed by the swing phase, which again is terminated by heel strike. In normal walking the stance phase makes up about 60% and the swing phase about 40% of the gait cycle. In pathological gait, values different from these are seen. Differences in leg length, for example, result in a shortening of the stance phase of the shorter leg.

At the beginning and in the middle of the gait cycle, on each occasion for about 10% of the gait cycle, both feet are in contact with the floor at the same time. The duration of this double support phase decreases as the velocity of walking increases. In running, the double support phase disappears and the stance and swing phase both assume the value of about 50% of the gait cycle. Unlike during walking, in running there are short time intervals in which both feet are off the ground. During these time intervals, both legs “fly” forward with the body. Because of this, the stride length when running can be increased beyond the maximum that is possible during walking, which is restricted for reasons of anatomy.

With S as stride length and T as duration of a stride, the velocity v in the direction of the line of progression is

Normal walking speed is in the order of 1.3 m/s; slow and fast walking speeds are 0.8 m/s and 1.5 m/s, respectively.1,2 Stride frequency v is given by

The stride frequency of slow walking is around 0.6 Hz; the stride frequencies of normal and fast walking are 0.9 and 1.0 Hz, respectively. For a given walking speed, persons of shorter stature have higher stride frequencies. This compensates their smaller step length, which is typical of shorter people.1,2

If, for a given walking speed, people are asked to choose their most comfortable stride frequency, these self-selected frequencies are observed to vary by only a small amount. Holt et al 8 provide a formula by which the duration of a stride may be approximately predicted:

This empirical formula is derived from a pendulum model of the leg, modeling the whole leg as a rigid body and permitting no bending at the knee joint. In this formula g denotes the gravitational acceleration, I the moment of inertia of the leg about an axis through its center of mass perpendicular to the sagittal plane, m the mass of the leg, and d the distance from the greater trochanter to the center of mass.

### 18.3 Kinematics

**Fig. 18.3 **shows an example from the pioneering experiments of Braune and Fischer9 documenting the motion of the leg in the stance and swing phases. The locations and orientations of upper leg, lower leg, and foot were measured from a series of photographs by means of markers fixed on the skin; the contours of the bones shown in **Fig. 18.3 **are merely shown for the purpose of illustration. At heel strike the hip joint is flexed. In the stance phase the hip joint is first extended and then flexed in preparation for the swing phase. At heel strike, the knee is flexed as well. In the stance phase it is extended and flexed again toward toe-off. The ankle joint changes the angle of its position from dorsiflexion at heel strike to plantar flexion at toe-off.

Today, the motion in walking is documented by optoelectronic methods. Light-emitting or light-reflecting markers are affixed to the segments of the body. The markers are observed by a set of video cameras, allowing reconstruction of their movement in three dimensions over time. At each instant in time, the location of the set of markers provides information on the relative position and orientation of the trunk, upper leg, lower leg, and foot segments. The change in position and orientation seen after a time lapse Δt (commonly ranging between 1/20 s and 1/50 s) allows the linear and angular velocities of the segments to be computed. The change in the velocities from one time interval to the next permits computation of the linear and angular accelerations of the segments.

**Fig. 18.4 **shows the temporal course of the angles in the sagittal plane of the hip, knee, and ankle during walking. The authors, Kerrigan et al, observed healthy adults of both sexes.3 In the cohort investigated there were only minor differences between men and women. Strictly speaking, the motion of the segments of the lower extremity during walking is not confined to the sagittal plane; in reality it is three-dimensional, and in addition the leg may perform a rotation about its long axis. However, for many purposes the description of the motion of the leg as plane motion is an acceptable approximation.

Disease or injury can cause the angular motion to deviate from the healthy norm. For example, after reconstruction of an injured anterior cruciate ligament, some patients will avoid bending that knee in phases of high loading. In these patients, the reduced bending angle of the knee will be compensated by increased flexion of the hip. A bending deficit of the knee is also observed after partial excision of the meniscus. Weakness of the quadriceps, avoidance of its use, or inhibition of neuromuscular control have been suggested as possible causes.

During walking, a characteristic rotation of the trunk about a vertical axis can be observed. The anterior movement of the right leg in the swing phase is coupled with an anterior movement of the right hip. Seen from above, the pelvis is rotated anticlockwise (** Fig. 18.5 **). To maintain the dynamic equilibrium, the shoulder must simultaneously be rotated in the opposite direction. The magnitude of the angular motion is in the order of ±5°. 10 If for some reason the compensatory movement of the shoulder cannot be performed, a striking alteration of the gait results.

### 18.4 Muscle Activity

EMG measurements show which muscles are activated in the course of the gait cycle. As an example **Fig. 18.6 **shows the “on–off” pattern of the muscles at the hip. 11 The “on” time is defined as that time interval during which the EMG signal exceeds a particular threshold value. The threshold chosen could be, for example, 10% of the signal amplitude measured at peak activation of the muscle. In pathological gait the EMG pattern may differ markedly from normal: the activity of individual muscles may be increased, decreased, or vanishingly small. The time course of the activation may be modified, or unusual antagonistic activation may occur. Another important element in walking is the activation of the muscles of the trunk, especially of the back extensors and the oblique muscles. For example, the back extensors are always activated prior to heel strike. This prevents the trunk from tipping forwards upon heel strike.

### 18.5 Moment and Power of the Muscles

The moment and the power of the muscles that move a joint, and the force transmitted from one bone to another in that joint, cannot be measured directly. However, with knowledge of the kinematics and employing biomechanical models, it is possible to compute these parameters using the inverse dynamics approach (see Chapter 12 ). To explain the principle of this procedure in an accessible way, the following remarks are confined to the two-dimensional case. Modern, commercially available optoelectronic instrumentation measures and calculates in three dimensions.

For the purpose of calculation, the leg is modeled as consisting of three segments (upper leg, lower leg, and foot) connected by hinge joints (** Fig. 18.7 **). The equations of motion state that the translational and rotational motion of each segment is effected by the sum of the forces and moments acting. Forces effecting an accelerated translation, and moments effecting an accelerated rotation, can be transmitted to any segment only from its adjoining segments. In addition, the gravitational force acts at the center of mass of each segment; this force is directed vertically downwards.

Let us assume the mass of the lower leg, the location of its center of mass, and the moment of inertia about its center of mass to be known. If the translational acceleration of the center of mass and the rotational acceleration are measured, it would be possible to calculate the sum of the forces and moments that effected the observed motion. It would, however, make little sense to perform such a measurement and calculation for the lower leg in isolation, for in that case then we would know only the sums of the forces and moments acting. What fraction of these sums were transmitted from the upper leg (across the knee) or from the foot (across the ankle) would remain unknown. For this reason, the calculation of the forces and moments always starts at one end of the kinematic chain of the segments, preferably at the foot segment. The force and moment transmitted to the foot from the floor can be measured using a force platform. If the sums of all forces and moments acting are determined from the motion data employing the method of inverse dynamics, the force and moment transmitted from the lower leg to the foot can be determined by subtraction. The procedure is now repeated for the lower leg segment. With knowledge of the motion data and of the force and moment transmitted from the foot, the force and moment transmitted from the upper leg via the knee can be specified. In the next step, the force and moment transmitted from the trunk to the upper leg via the hip joint are obtained.

In principle, the determination of forces and moments could equally well start at the other end of the kinematic chain of body segments. To do this, one would start at the head and arm segments, proceed to the trunk segment, and then to the leg segments. Apart from the gravitational force, no external forces act on the head, arms, and trunk, and thus no force measuring equipment would have to be employed. Because of the comparatively large mass of the trunk, however, and the fact that its description as a rigid body is only a rough approximation, the results of this measurement and calculation would be less precise.

In detail, the procedure is as follows:

**Step 1.** In the stance phase of the gait cycle, a force platform measures the vector **R** _{1} with components **R** _{1x} and **R** _{1y} of the force (ground reaction force) between floor and foot (** Fig. 18.7 **). Since only compressive forces (but no tensile forces) are transmitted between the floor and the foot, the moment M_{1} transmitted from the floor on the foot is zero. With knowledge of the linear acceleration of the center of mass of the foot, the angular acceleration about the center of mass, the mass, and the moment of inertia, the net force and moment acting on the foot are calculated. If the vector **R** _{1} and the gravitational force are subtracted from the net force, the force **R** _{2} and the moment M_{2} acting on the foot from the lower leg are obtained.

**Step 2.** The same algorithm is now applied to the lower leg segment. In mechanical equilibrium, the force and moment transmitted from the foot to the lower leg are opposite and equal to the force and moment transmitted from the lower leg to the foot; that is, they are **R** _{2} and M_{2}. With knowledge of the linear acceleration of the center of mass of the lower leg, the angular acceleration about the center of mass, the mass, and the moment of inertia, the net force and moment acting on the lower leg are calculated. If the vector −**R** _{2} and the gravitational force are subtracted from the net force, and the moment −M_{2} is subtracted from the net moment, the force **R** _{3} and the moment M_{3} acting on the lower leg from the upper leg via the knee joint are obtained.

**Step 3.** The same algorithm is now applied to the upper leg segment. The input data for the calculation are the force −**R** _{3} and the moment −M_{3} transmitted from the lower leg to the upper leg as determined in step 2, the mass of the upper leg, its moment of inertia, and the linear and rotational acceleration measured. The result of this calculation gives the force **R** _{4} and the moment M_{4} transmitted from the trunk via the hip joint to the upper leg.

The moments determined thus are the net moments generated by all the individual muscles and tendons spanning a joint. If more than a single muscle is active at the same time, the contribution of specific muscles to the net moment can only be determined if additional information is available (from EMG measurements, for example) or model assumptions are employed. For example, a small net moment may be a result of a low activity in the muscles involved, or, alternatively, it may mean that muscles have been activated antagonistically so that their moments partially compensate each other.

The power of muscles spanning a joint is equal to the product of moment and angular velocity:

Power is measured in watts [W]. The power of a muscle is counted positive if the muscle shortens in the course of the motion; it is counted negative if the muscle elongates in the course of the motion.

To simplify comparisons between individuals, the moment and power of the muscles can be adjusted for body mass and stature and be quoted in Nm/(kg · m) and W/(kg · m), respectively. **Figs. 18.8 **and **18.9 **show the adjusted moment and power of the muscles of the hip, knee, and ankle during walking, measured in a cohort of adults of both sexes.3 The course over time of moment and that of power look very different because the angular velocity changes in the course of the gait cycle. At those time points where either the moment or the velocity is zero, by definition the power is also zero. In the cohort investigated, the power of the muscles of the knee joint assumed a maximum value of approximately 0.4 W/(kg · m). For a person of 1.75 m body height and 65 kg mass, this corresponds to a power of 0.4 · 1.75 · 65 = 45.5 W. The power of muscles during particular phases or throughout the whole of the gait cycle is a sensitive indicator of the progress of healing after injury.

The joint force **R** between segments determined in gait analysis is the (net) sum of the compressive force between the articulating bones and the tensile force of the muscles, tendons, and ligaments that cross the joint. To calculate the compressive force acting on the articular surface, an anatomical model of the joint is needed. The model specifies the location of the center of rotation and the moment arms of the muscles. If more than one muscle is activated at a time, assumptions are required on how much of the total moment is generated by each of the different muscles (see Chapter 12 ). Examples of the compressive force on the articular surface of the hip and the femorotibial joint obtained from gait analysis are given in Chapters 13 and 14 .

The concept of determining the forces and moments transmitted from one segment of the leg to the next using the inverse dynamics approach appears basically simple. In practice, however, intricate problems are encountered in both measurement and calculation. Sources of error and uncertainty include the following:

The mass, location of the center of mass, and moment of inertia of the segments of the lower leg are known only imprecisely. The published reference data are derived from studies of small, unrepresentative groups.

Against the assumptions made for the purposes of calculation, segments composed of bones and soft tissue are not rigid bodies but change their shape in the course of the gait cycle.

Centers of mass and axes of rotation can be located only indirectly, by reference to external anatomical landmarks.

The motion of segments is measured using markers fixed to the skin. Due to movement of the skin or the activation of muscles, these markers can move relative to the joints in an uncontrollable fashion.

Some studies simplify the determination of the moment exerted on the hip or the knee by including only the vector **R** _{1} of the ground reaction force in the calculation. The moments are then expressed as products of the magnitude of the ground reaction force and the perpendicular distance from the center of rotation of hip or knee to the line of action of this force (** Fig. 18.10 **). However, this makes sense only for static or quasi-static applications where the inertial forces and moments of the segments can be neglected. In the dynamic case, moment and force depend not only on the vector of the ground reaction force, but also on the linear and angular accelerations of foot, lower leg, and upper leg. 12 Winter12 illustrated this with an example: If the simplified concept were to be applied to the cervical spine, the moment on the cervical spine would amount to L_{c} · |**R** _{1}|. No sensible investigator would accept that a moment of this magnitude acts on the cervical spine during walking.