## 13 Mechanical Aspects of the Hip Joint

Healthy human beings take between one hundred thousand and several million steps per year, and peak values of the load on the hip joint, corresponding to a multiple of the weight of the whole body, occur in the heel-strike and toe-off phases of every one of them. The hip joint seems to be adapted to this high, repetitive loading. Even in old age, in the majority of people the function of the hip joint is only slightly restricted, if at all. This finding is not inconsistent with the regular finding of age-related alteration (*degeneration*) of the joint cartilage as well as changes in bone density and trabecular architecture. Severe alterations, leading to clinical symptoms and a restriction of joint function, are encountered in only a minority of individuals. However, in persons showing significant deviations from the normal geometric configuration of the femoral head and acetabulum, premature destruction of the joint may be observed. The magnitude and repetition rate of the load on the hip joint suggest that primary mechanical causes may be responsible for the development and progress of osteoarthritis.

Interest in the mechanical aspects of the hip joint has been substantially encouraged by the pioneering work of Pauwels. 1 This chapter outlines how to determine the load on the hip joint in the stance phase of slow gait by means of a biomechanical model calculation. Within the framework of this simplified model, the question of how the joint load may be influenced by pathologic gait, walking aids, or surgical interventions is discussed, with examples. Detailed information on hip joint loading is obtained from gait analysis as well as from direct measurements employing instrumented joint replacements. Knowledge of the joint load is a prerequisite for determining the pressure on the joint surface and to forming hypotheses on mechanical factors in the etiology of osteoarthritis of the joint.

### 13.1 Load on the Hip Joint in the Stance Phase of Slow Gait

The load on the hip joint is analyzed in the stance phase of slow gait on the basis that this phase may be regarded as typical of everyday activities. In the stance phase, one foot is on the floor while the other is lifted off the floor with the leg being swung forward through the frontal plane. The designation “slow” indicates that the inertial forces resulting from slowing down and accelerating the body segments during each step are assumed to be negligibly small.

The simplistic model calculation (** Fig. 13.1 **) takes into account only three forces acting on the pelvis in the frontal plane. **W** is the gravitational force (“weight”) of the body mass less the mass of the standing leg. The point of force application is the center of mass of the body less the standing leg: that is, the center of mass of the head, arms, trunk, and swinging leg. The gravitational force points vertically downwards. **F** is the force of the abductor muscles, which balance the moment of the gravitational force. The vector **F** represents the forces of all muscles that may effect an abduction of the standing leg. The direction of **F** is chosen along the direction of the gluteus medius muscle. The points of force application of **F** are the centers of the insertion areas of the gluteus medius at the iliac bone and at the major trochanter. All additional muscle forces that may be active in stabilizing the hip joint during the stance phase with respect to flexion and extension are disregarded. The hip joint is assumed to be a perfect, friction-free ball-and-socket joint. Thus, the joint force **H**, acting from the femoral head onto the acetabulum, runs through the center of the femoral head. (The rationale is as follows: In a state of static equilibrium a friction-free joint cannot transmit a moment. If the vector of the joint load did not pass through the center of the femoral head, it would generate a moment with respect to the center and the joint would start moving.)

With knowledge of the magnitude of **W**, its point of application (that is, the location of the center of mass of the body less the standing leg), and the direction and points of application of the muscle force **F**, the magnitude of **F** can be obtained from the equilibrium condition of moments. The equilibrium condition of forces requires the vector sum of **W**, **F**, and **H** to be equal to zero. As result the direction and magnitude of **H** can be determined.

To determine **H**, it is advantageous to determine the components **H** _{x} and **H** _{y} separately (** Figs. 13.2 and 13.3 **). The coordinate system is oriented so that the x-axis points in the horizontal direction and the y-axis in the vertical direction. Since the gravitational force **W** is aligned vertically and the muscle force **F** almost vertically, we expect the load on the hip joint to be determined essentially by the y-components of these forces; the x-components will make only a small additional contribution.

It is assumed that the mass of one leg equals approximately 20% of the body mass. Under this assumption, we obtain for the y-component of the gravitational force **W**

In good approximation, the center of mass of the whole body is positioned above the symphysis (as the architecture of our body is, broadly, right–left symmetrical). The center of mass of the body regardless of the standing leg is shifted to the side of the swinging leg. For the relationship between the moment arm D of the gravitational force and the moment arm L_{1} of the y-component of the muscle force we assume

Under these assumptions (and in accordance with the sign convention for moments) we obtain in equilibrium of moments

and for the y-coordinates of the forces

In static equilibrium it holds for the y-components of the forces that

and, for their y-coordinates when inserting F_{y} from Eq. 13.4

**W** _{y} points in the negative y-direction. W_{y} is thus equal to −0.8 · m · g. After insertion into Eq. 13.6 we obtain

In other words: the y-component of the force transmitted from the femoral head onto the acetabulum has a magnitude 2.4 times the weight of the whole body. The positive value of H_{y} indicates that this force points in the positive y-direction; the femoral head exerts a compressive force on the acetabulum.

In equilibrium of forces it holds for the x-components of the hip joint load and the muscle force (** Fig. 13.3 **) that

This equation contains only two addends as the x-component of the gravitational force equals zero. With β as the angle between the vertical and the direction of the muscle force **F**, we obtain for the x-coordinate **F** _{x} of the muscle force

and in equilibrium with F_{y} = 2.0 · W_{y} we obtain

The angle β is approximately 15°; the tangent of 15° is 0.27. Thus H_{x} is much smaller than H_{y}. With knowledge of H_{x} and H_{y} the magnitude of the total hip joint load H is calculated as

The angle β between the vector of the hip joint load **H** and the vertical is calculated as

### 13.2 Influence of Gait Technique, Walking Aids, or Surgical Intervention on the Hip Joint Load

The model calculation of the hip joint load in the stance phase of slow gait can be used to visualize the effects on the joint load of gait techniques, the use of walking aids, or changes to bone geometry through surgical intervention.

#### 13.2.1 Gait Technique

A gait anomaly termed “Duchenne limp” is illustrated in **Fig. 13.4 **. In this type of gait, the center of mass of the body is shifted to the side of the standing leg. This shift reduces the moment arm D_{1} of the gravitational force **W** with respect to the moment arm D during normal gait. Consequently the force **F** of the abductor muscles required for equilibrium will decrease. This results in a decrease of the load H on the hip joint. In the limiting case, when the center of mass of the body less the standing leg is positioned perpendicularly above the hip joint and the moment arm D_{1} assumes a value of zero, a very substantial load decrease results. The Duchenne limp is, however, unsuitable for long-term reduction of the load on the hip joint because the accompanying bending of the lumbar spine to the side cannot be tolerated over long periods.

In practice a Duchenne limp may indicate an attempt by an individual to reduce the load on an already impaired joint, or it may indicate weakness of the abductor muscles. The implications for therapy in these two cases would be quite different.

#### 13.2.2 Cane

**Fig. 13.5 **shows the pelvis again in the stance phase of slow gait. A cane is employed contralaterally to the standing leg. For brevity, we consider here only the y-components of the forces. **S** is the force from the cane onto the hand. **S** _{y} is the y-component of this force; it points in the positive y-direction. For calculation of the joint load, the assumptions on the moment arm of the body weight and the magnitude of the gravitational force are left unchanged:

In addition, we assume the moment arm E of the cane force **S** to amount to twice the moment arm D and thus to four times the moment arm of the of the abductor muscles:

With these assumptions we obtain from the equilibrium condition of moments (in accordance with the sign convention for moments)

Using the cane reduces the magnitude of the required muscle force **F** _{y} by an amount equal to four times the magnitude of the cane force **S** _{y}.

In equilibrium of forces it holds for the y-coordinates of the forces that

The addends in this equation can assume positive or negative values, depending on whether the forces point in the positive or the negative y-direction. For the coordinates of the forces **W** and **S** it holds in equilibrium of moments that

(Note: As Eq. 13.16 deals with the coordinates of the forces and not with their magnitudes, inserting F_{y} = 2.0 · W_{y} − 4.0 · S_{y} from Eq. 13.15 would be incorrect. It should be pointed out that W_{y} is a negative number and S_{y} a positive number. Eq. 13.17 implies that the magnitude of F_{y} is lessened by four times the magnitude of S_{y}.) It then follows for **H** that

and with insertion of W_{y} = −0.8 · m · g

Using a cane reduces the y-component of the load on the hip joint by an amount equal to five times the force between the cane and the hand. The effect can be illustrated with an example. Given a body mass of 60 kg, the gravitational force W amounts to approximately 600 N. The y-coordinate of the load on the hip joint then amounts to (Eq. 13.6)

Using a cane and assuming a force of S_{y} = +50 N between hand and cane, we obtain

Using the cane reduces the joint load by about 20%. It must be stressed that the reduction in joint load can be achieved only if the cane is used contralaterally to the hip joint in question. Using the cane ipsilaterally would increase the load on the hip joint. Alternatively, a reduction in body mass might be considered in order to decrease the hip joint load. In principle this is a valid idea as the joint load H_{y} depends directly on the body mass m. To achieve a reduction in load comparable to that when a cane is used, however, the body mass must be reduced by approximately 20%. In many cases this will probably be difficult to achieve.

#### 13.2.3 Surgical Intervention

Surgical interventions can alter the geometry of the bony skeleton and thus change the moment arms of muscles. **Fig. 13.6 **shows the example of a varisation osteotomy, where a bone wedge is excised from the intertrochanteric region. Geometrically this intervention effects a decrease in the angle between the femoral neck and the femur and lateralization of the greater trochanter. Postoperatively the moment arm L_{1} of the abductor muscle can be about 15% larger than the preoperative moment arm L. Because the moment arm is larger, the required muscle force becomes proportionally smaller (change from F to F_{1}), and accordingly so does the joint load. In addition, the psoas muscle has become shorter. The subsequent reduction in the stress of this muscle will induce a further reduction of the load on the hip joint. For a quantitative estimate of this effect, information on the passive stiffness of the muscle is required; this is not precisely known.

A further effect of the surgical intervention illustrated in **Fig. 13.6 **is the rotation of the femoral head with respect to the acetabulum. This results in relocation (relative to each other) of those parts of the surface areas of the head and acetabulum that are subjected to compressive stress.

### 13.3 Determination of Hip Joint Load by Gait Analysis

If accelerated linear or rotational motions of the body segments occur, influences of inertial forces and inertial moments must be taken into account when determining the load on the hip joint. To illustrate the effect of inertial forces, we start by discussing a simple, intuitively accessible example. The posture shown in **Fig. 13.7 **is not to be interpreted as the stance phase in slow gait but as the posture assumed when hitting the ground with the right foot after jumping from a low wall. On landing, the velocity of the body mass cranial to the hip joint must be slowed down (decelerated) from its initial value to zero. The variable a designates the magnitude of the acceleration involved. The magnitude of the inertial force **F** _{in} amounts to

Regarding the sign of the inertial force: when the person hits the ground, the velocity points in the negative y-direction; the change in velocity (the acceleration) points in the positive y-direction. The inertial force **F** _{in} is opposite to the acceleration and thus in the negative y-direction—that is, in the same direction as the gravitational force.

The load on the hip joint can now be estimated using formulae almost identical to those in the stance phase of slow gait. The only difference is that instead of the gravitational force **W** _{y} the sum of the gravitational and inertial forces has to be inserted. In **Fig. 13.7 **this sum is designated by **W***.

For the magnitude of the y-component of the hip joint load we obtain

In this example the inertial force acts as if the body weight were momentarily increased by an amount equal to 2.4 · m · a. The numerical value of this increase depends on the magnitude of the acceleration a. If the change from the initial velocity to zero takes place within a short time interval (for example, when landing with the legs straight), the acceleration will have a high value. If the change in velocity can be extended over a longer time interval (for example, by bending the knees and thus providing a soft impact), the acceleration will assume a lower value.

The load on the hip joint can be determined in a model calculation if a person’s anthropometric data (dimension and mass of body segments) are known and kinematic (motion) and kinetic data (forces between the feet and the ground) are measured in the course of a gait cycle. Gait analysis supplies important information on hip joint loading far beyond what can be obtained by looking at simple models such as the stance phase of slow gait. For the purpose of calculation, the standing leg is regarded as a free body (** Fig. 13.8 **). The masses, locations of the centers of mass, and moments of inertia about the centers of mass of the segments foot, lower leg, and thigh must be known. The course over time of the linear acceleration of the centers of mass of the segments, the angular acceleration of the segments about their centers of mass, and the force **R** _{F} from the floor onto the foot are measured during walking. Starting from the foot, one after another the forces and moments on the ankle joint, knee joint, and hip joint can now be calculated (see Chapter 12 ). To determine the load on the hip joint, a model of the joint must be established that accurately describes its geometry and the lines of action and moment arms of the muscles that cross the joint. If more than a single muscle is active at a particular instant in time, additional assumptions are required in order to obtain an unequivocal solution.

As an example, **Fig. 13.9 **shows a result from the pioneering experiments of Paul. 2 At that time, measurement and calculation could be performed only for the time interval when the foot was in contact with the floor. For this reason, the curves end at about 60% of the gait cycle. Maximum values of the hip joint load occur after heel-strike and before toe-off. These peak loads are caused by the deceleration and acceleration of the body mass. The peak loads rise with increasing gait velocity, because the accelerations increase and hence so do the inertial forces.

Fig. 13.10 illustrates the result of a gait analysis.3 It also shows the result of a direct measurement of hip joint loading employing an instrumented joint prosthesis (see below, Section 13.4). The agreement between the calculated and the measured magnitude of the peak loads and the time points at which they occur is excellent. (The “waviness” of the load curve computed from the gait analysis is due to the underlying algorithm, which takes several muscle groups into account; for details, see the original paper.)