17.1 The Kinematic Chain of the Foot

Drawing on general mechanical terminology, the foot and hand are also referred to as “branched open kinematic chains.” What this means is that they each consist of a series of different, distinct joints linked together from proximal to distal. The term is intended to suggest how a distal limb carries out a movement that is composed of the individual movements of the more proximal joints along the same branch.

Abduction and adduction of the foot, leading to external and internal rotation, originate in the hip and knee. The ankle, comprising the talocrural joint and the subtalar joint, allows movements around two different anatomical axes ( Fig. 17.2 ) and composite movements involving both axes. More distally, in the Chopart and Lisfranc joints the foot may perform small movements mainly to adapt to the conditions of the ground beneath it, though these movements are limited by the tension of the fasciae.

The kinematic properties of the foot are mainly due to the talocrural joint (sometimes also termed the ankle proper) and the subtalar joint. From various points of view the two joints can be regarded as a functional unit. This is due to the fact that the talus is involved in and connects the two joints. A particular feature of the talus is that no muscles are attached to it, and instead it is fixed by ligaments only. This means that it cannot be kept in position or moved specifically by muscular action. All the muscles involved in foot movements cross the talus, the ankle, and subtalar joint. Consequently, the forces from the forefoot, hindfoot, and tibia that act on the talus must compensate each other and no moment can be transmitted. In addition, the axes of the two joints differ in orientation but they intersect near the tarsal sinus, that is, in the region of the talus.5 It remains unclear whether the two axes do actually intersect or merely pass close to one another.

The relative positions of the axes of the talocrural and subtalar joints suggest comparison with a technical joint, for example a universal or Cardan joint. However, in contrast to an engineered universal joint, the two axes of the ankle joint are not orthogonal. The axis of the talocrural joint runs roughly transversely and it allows dorsiflexion and plantar flexion of the whole foot in the sagittal plane. The axis of the subtalar joint runs obliquely from the medial dorsal aspect of the navicular bone to the lateral plantar aspect. Rotatory movements about this axis lead to a coupled movement, in which an outward or inward movement of the tip of the foot occurs simultaneously with lowering and elevation of the medial border of the foot.

Unfortunately the nomenclature for these movements is not uniform. Only the movement about the axis of the talocrural joint is consistently named:plantar flexion and dorsiflexion. Kummer5 describes the movement around the subtalar joint axis as “pronation/supination,” while Mann 7 describes it as “inversion/eversion” (see Fig. 17.2 ). The International Society of Biomechanics 8 recommends the terms “inversion” and “eversion” to describe the composite rotation around the longitudinal axis of the foot, in contrast to the American Academy of Orthopaedic Surgeons (AAOS) 9 and various textbooks, 10 where “inversion/eversion”describes the movement around the axis of the subtalar joint and “supination/pronation” means movement around the longitudinal axis of the foot. A detailed discussion may be found in Debrunner and Jacob.6

The basic studies to measure the joint axes in the ankle joint complex were conducted by Isman and Inman 11 and Inman. 12 They performed measurements in cadaver specimens and determined the means and standard deviations for the position and orientation of the axes. The orientation of the talocrural axis is defined by reference to the axis of the shank and the longitudinal axis of the foot, which is itself defined by Inman as the line connecting the center of the heel to the gap between the second and third toes. The axis of the talocrural joint is nearly perpendicular to the plane spanned by these two axes. In the frontal plane it inclines approximately 10°, with the lateral end lower than the medial end. In the transverse plane the axis is inclined by approximately 6°, with the lateral end lying further back than the medial end. The lateral end of the axis of the subtalar joint lies behind and below the medial end. In the proximal view the axis forms an angle of 23 ± 11°, with the longitudinal axis of the foot, and in the lateral view it forms an angle of 41 ± 9° with the horizontal. The strikingly large standard deviations are due to the fact that interindividual variation is so great.

Measurements of the location and orientation of the axes of the ankle and subtalar joints are subject not only to individual variations but also to technical inaccuracies if measurements are not based on specimens or performed using imaging techniques or with intracortical bone pins. 13 As the talus is not directly accessible from outside, its position cannot be indicated by markers. Furthermore, the value of such measurements is limited by the fact that the position and orientation especially of the axis of the subtalar joint depend on the direction of movement (flexion or extension) and loading of the joint. 14 For clinical studies, individual modeling and description of the kinematics are necessary. Using X-ray stereophotogrammetry, Lundberg et al 15 confirmed the earlier results of Hicks, 16 who found that the orientation of the talocrural axis in the frontal plane changes depending on dorsiflexion and plantar flexion, but in the horizontal plane it remains stable; that is, it continues to pass through the malleoli.

17.2 Statics of the Foot

Because of its longitudinal arch, the loading of the foot during standing occurs mainly in two anatomical regions: the heel region, with the calcaneus as one bony support, and the ball of the foot, with the metatarsal heads as the other bony support. The fifth ray contributes a minor degree of lateral support in the midfoot region, but this can be ignored for the purpose of calculations. To ensure a secure stance, the line of gravity—the line of action of the gravitational force W—must pass through the foot at a point between the supports in the forefoot and hindfoot. In doing so, it gives rise to two moment arms, one of the forefoot and one of the hindfoot, denoted by d_f and d_h respectively. The ground reaction forces acting on the forefoot and the hindfoot are denoted by R _f and R _h respectively. In equilibrium of moments ( Fig. 17.3 ) The sum of R _f and R _h is equal to the ground reaction force R. R is opposite and equal to the gravitational force W.

In relaxed stance the line of gravity runs through the foot near the Lisfranc joint and the distances d_f and d_h are in an approximate ratio of 2 : 3, so R _f and R _h amount to approximately 60% and 40% of the body weight respectively. The position of the line of gravity is variable, however, changing relative to the foot during the phases of gait and on changes in posture. The further forward it is, the greater the proportion of the reaction force acting below the forefoot. When the line of gravity runs through the ball of the foot, the magnitude of the reaction force R_f equals the body weight. In this position, compensatory movements to ensure stable stance are no longer possible without involving the toes.

17.2.1 Loading of the Ankle

In normal stance the left and right ankle each support half of the weight of the body less the weight of the respective foot, which amounts to 1.5% of body weight. However, loading of the ankle is increased if the line of gravity does not pass midway between the two ankles but is shifted forwards. The load on one foot— generated by half the body weight—can be estimated by a model calculation similar to the one used for the hip in Chapter 13 , though, in this case, the model is set up in the sagittal plane. The gravitational force W acts vertically, parallel to the y-coordinate, and is denoted below by W _y ( Fig. 17.4 ). The moment around the ankle joint produced by the gravitational force is compensated by the force A in the Achilles tendon. For simplicity, only the y-component will be considered and will be denoted as A _y. The resulting force R _y acts on the ankle. Its line of action must intersect the axis of the ankle joint, as otherwise it would produce a moment around the ankle in contradiction of the conditions of equilibrium. Limiting the discussion to these three forces means that antagonists such as the dorsal flexor muscles of the foot and toes are ignored, although their action is necessary for a stable stance and they further increase the actual load on the ankle.

The plantar flexion moment exerted by the triceps surae muscle through the Achilles tendon is

The opposing moment due to the gravitational force is

Because of their different directions of rotation, the two moments have opposite signs. In static equilibrium

Therefore the magnitude of force A _y in the Achilles tendon can be obtained from

According to the equilibrium condition, the three forces must add up to 0, that is,

After substitution the magnitude of the reaction force R _y acting on the subtalar joint is obtained:

The distances d_W and d_A are about the same and therefore R _y has about twice the magnitude of the gravitational force W. Quantitatively the distance d_A amounts to approximately 5 cm. 17 Therefore, for a person of 75 kg mass and standing on both feet the plantar flexion moment according to Eq.17.2 is

Measurements by Smith 18 yielded moments between 8.3 Nm and 25 Nm, thus confirming the order of magnitude of this estimate. One reason for the large variability of the results is postural sway, which is accompanied by swaying of the line of gravity and hence by variations in the moment arm d_W. If the line of gravity intersects the ball of the foot, d_W exceeds d_A by a factor of approximately 3. The load on the ankle then amounts to four times the body weight. This model can be extended to one-legged stance as well, so long as it is confined to the sagittal plane. In this case the whole body weight is supported by one foot alone, so the load is doubled.

If this calculation is used to model joint loading during the push-off phase of gait, account must be taken of dynamic forces that increase the ground reaction force during toe-off in normal walking to 120% of body weight. Moments are then generated in excess of 100 Nm. 19 However, this model reaches its limits when detailed analyses are required, and more complex models become necessary, involving dynamic analysis, the action of agonists and antagonists in different phases of gait, and the changes in the moment arms during the stance phase. 20

17.2.2 Internal Forces in the Arch

The vertical reaction force R _y exerted by the talus on the tibia is generated by the supporting forces under the forefoot and under the heel and by the tension in the Achilles tendon. The vertical forces acting on the calcaneus produce a moment which is compensated by horizontal forces generated by the tension of the fasciae. The same is true for the forefoot, where the vertical force which supports the forefoot and toes produces an oppositely directed moment, which in turn is compensated by the moment generated by the fasciae. For simplicity the following assumptions are made: it is assumed that, in contrast to the plantar aponeurosis, the force exerted by the long plantar ligament on the calcaneus and forefoot can be neglected because of its weaker structure and less efficient moment arm. It is also assumed that the plantar aponeurosis runs approximately horizontally.

The vertical forces acting on the forefoot and hindfoot produce a moment of the same magnitude but in opposite directions. The same is true of the horizontal components. Therefore, in equilibrium it is sufficient to consider either the forefoot or the hindfoot alone to determine the force P in the plantar aponeurosis. The moment arms of the hindfoot can be taken from the center of the ankle joint ( Fig. 17.5 ). In equilibrium of moments

Therefore the plantar aponeurosis stabilizes the calcaneus with force P, whose magnitude is given by

As the plantar aponeurosis is countersupported by the metatarsal heads, the horizontal component of the force in the forefoot is equal to –P. The magnitude of P depends implicitly on the location of the line of gravity. If the foot is supported only under the hindfoot, the Achilles tendon relaxes and in the term

A_y becomes zero, thus minimizing the force in the plantar aponeurosis, which then can be written

with the index h indicating loading of the hindfoot. W is the magnitude of the gravitational force. As d_h and d_P are roughly equal, P_h is roughly equivalent to the body weight. If, on the other hand, the foot is supported only under the forefoot, the ground reaction force R_h under the heel vanishes. Instead, the Achilles tendon is activated. As described above, on forefoot loading the force of the Achilles tendon is approximately three times the weight of the body and its moment arm d_A is roughly the same size as d_P. The resulting magnitude of tension P _f in the plantar aponeurosis is therefore

where the index f indicates forefoot support. P_f amounts to about three times the gravitational force—in agreement with corresponding measurements 21 and finite element calculations. 22

The variation of tension in the fascia of the plantar aponeurosis therefore depends on the location of the line of gravity, with important consequences for the behavior of the foot during the stance phase. When the heel comes into contact with the ground, the tension in the Achilles tendon and in the plantar fascia is relatively low. Thus the ability of the foot to deform due to the irregular joint surfaces of the Lisfranc and Chopart joint is not inhibited and the foot can adjust to the form of the ground. However, as the line of gravity moves forwards, the tension in the plantar aponeurosis increases and mobility reduces as the joint surfaces become wedged together. In this way the foot becomes stiff and acts as a rigid lever for push-off.

The windlass mechanism as described by Hicks 23 acts to reinforce this effect. Because the plantar aponeurosis inserts into the joint capsules of the metatarsophalangeal joints and extends functionally beyond them, the aponeurosis can be tensed by lifting the toes. The same happens during roll-off over the toes, which flexes the metatarsophalangeal joints and thus further tenses the aponeurosis ( Fig. 17.6 ).

A further important aspect is the height d_P of the ankle above the ground. Eq. 17.10 shows that P is inversely proportional to this height, that is, P increases when d_P decreases. Under normal conditions, brief vertical loading of the ankle causes the arch to give elastically and then recover. The descent of the talus is limited by the increase of tension in the fascia. A finite element calculation quantifies this effect. 24 However, severe overloading with increased descent of the talus increases the tension in the bones so greatly that microfractures and partial destruction of the trabecular structure may lead to shortening of the bones involved, with consequent irreversible reduction of the height of the arch. This in turn increases the tension in the plantar aponeurosis, risking bone damage. This risk is especially raised where bone strength is compromised, for instance, as a result of metabolic disorders such as diabetes. This may lead to accelerated repetition of the overload injuries and eventually to collapse of the longitudinal arch and fragmentation of the involved bones as in Charcot arthropathy. 25

17.2.3 Internal Forces in the Forefoot

The internal forces in the forefoot between the talus and the metatarsophalangeal joints are determined primarily by the tension of the plantar aponeurosis, which inserts in the metatarsophalangeal joint capsules. However, the anterior ground reaction force R _f beneath the forefoot can be displaced forwards beyond the ball of the foot by using the toes. This affects the internal forces in the forefoot and hindfoot: involvement of the toes transmits forces to the ankle and lower leg through the forefoot, while the lengthened forefoot lever requires an increased compensating force in the Achilles tendon.

The most important contributor to the forces in the toes is the first ray. Cadaver measurements by Jacob 26 reveal the ratio of moment arms L₁ and L₂ ( Fig. 17.7 ) to be

so that

gives the magnitude of the force F _hl acting along the tendon of the flexor hallucis longus:

The magnitude of force F _hl therefore is 2.2 times the magnitude of ground reaction force F. From the vector sum of the two forces (taking into account an inclination of the flexor hallucis tendon of 15° to the horizontal), the magnitude of the resultant force across the joint can be calculated as 2.6 times the ground reaction force. The force F, by which the toe pushes off from the ground, cannot be estimated on the basis of a model but has to be measured. Plantar pressure distribution measurement during push-off shows the magnitude of F to be approximately 25% of body weight. 27 As the loading of the joint is 2.6 times the ground reaction force, the resultant joint loading is 65% of body weight. Similar calculations for the more proximal metatarsophalangeal joint reveal higher loading because the moment arm of the ground reaction force is longer. The loads on the toes of the other rays are smaller and are calculated in the same way, with anatomic and geometric parameters modified as appropriate.

17.3 Posturography

In normal stance on both legs the bodyʹs center of mass is located a few centimeters anterior to the lumbar spine at about the level of the fourth lumbar vertebra. It is not possible to give a generalized, anatomically precise localization, since the bodyʹs center of mass depends on the positions of the centers of mass of the different body segments, which in turn vary according to the segments’ distribution of mass and their position. To ensure stable stance and prevent falling, the base of support (the area beneath and between the feet) must be below the center of mass. As this condition must also be met during changes of loading, a complex regulatory (sensing and controlling) mechanism is needed to keep the center of mass over the base of support and allow dynamic balance. Measuring this postural control by measuring the ground reaction forces is termed posturography.

In biomechanics the dynamics of balance is commonly described by reference to the model of the inverted pendulum. A simple example of this is balancing a stick on the fingertip and keeping it vertical. If the center of mass of the stick is not kept exactly above its base, the stick starts to lean over to one side or the other and it falls over. To avoid this, the finger must follow the stick, moving the point of application of the reaction force. This model cannot be applied directly to the analysis of posture as the supporting base cannot be moved, but the point of application of the ground reaction force can be shifted by changing the load distribution in the feet.

Fig. 17.8 is a schematic lateral diagram of the foot based on Winter 30 with the aim of describing the fundamental mechanisms involved in maintaining dynamic balance. The x-coordinate axis, with its origin below the ankle, runs in the support plane. The foot is supported in the forefoot and hindfoot regions where the reaction forces R _f and R _h act. For reasons of simplicity only the vertical components are considered below. The line of action of the ground reaction force R crosses the base line at X_R. The center of mass of the body is located at height h_c above the ankle joints. The trunk is inclined by the angle θ so that the center of mass and consequently the line of action of the gravitational force W are displaced by X_W with reference to the ankle joint.

As θ is very small, a good approximation is

The two forces R and W acting in opposite directions exert a moment that rotates the trunk around the ankle joint. The angular acceleration θ is derived from the angular momentum equation

where I denotes the moment of inertia of the trunk relative to the axis of the ankle. To simplify the calculation, the difference between the magnitudes of the gravitational force W and ground reaction force R is ignored by setting

Furthermore, by using Eq. 17.18 the angular acceleration can be replaced so that the acceleration in x-direction x_W of the center of mass can be written

This means that the distance (x_W − X_R) between the two lines of action of the gravitational force and the ground reaction force is decisive for the tilting movement. Whether this pair of forces acts more posteriorly or more anteriorly is unimportant, but they must act within the support area. This is evident for the ground reaction force, as it can be generated only inside the support area. This means that the line of gravity must be restricted to this area. If it moves beyond these limits, the ground reaction force can no longer follow, and falling can be avoided only by either moving the center of mass (for instance, by moving the arms or trunk) or by expanding the area of support (for instance by a step forwards or backwards).

In Fig. 17.8 X_W is greater than x_R, so that is positive, meaning that the center of mass is accelerating its forward tilting movement. This means that the application point of the ground reaction force (coordinate x_R) has to be moved forward beyond the line of gravity (coordinate x_w) by activation of the plantar flexors— the triceps surae, for example—so that the sign of angular acceleration is reversed and the center of mass starts moving backward. This produces the opposing reaction, namely to move the ground reaction force backward by relaxing the triceps surae and activating foot extensors such as the tibialis anterior muscle. These actions alternate, producing dynamic balance control.

Fig. 17.9 presents a typical time course of the two coordinates X_W and X_R. They are usually labeled COM (center of mass) and COP (center of pressure). The COP is equivalent to the point of force application in the support surface. The center of mass is a point in three-dimensional space, but here “COM” indicates the two-dimensional projection of the center of mass in the base of support. The COP is by definition bound to this plane. It can be seen that the two coordinates oscillate around a state of equilibrium approximately 55 mm in front of the ankle joint, the COP at a higher frequency and with a wider range than the COM. The higher frequency is required to ensure rapid regulatory reaction, while the larger amplitude is necessary to enable the COP to “capture” the COM. The amplitude of the COP is limited by the length of the foot; of necessity, that of the COM must be somewhat smaller.

Regulation of balance by shifting the COM by flexion and extension of the ankle is called ankle strategy. Another technique known as hip strategy can also be used; in this, the hip flexors and extensors move the COM relative to the COP. At the same time, other body segments may also be accelerated and their reaction forces may aid stabilization. This is most evident if the arms are also involved in balancing. However, the hip strategy is not often employed by healthy people. 31

In the frontal plane, the situation is different. Dynamic balance must be established here as well, and the projection of the center of mass must fall within the base of support. During standing on both feet the hip strategy is employed, essentially consisting of elevation or lowering of the pelvis on one side. The resulting redistribution of load from one side to the other causes displacement of the COP along the z-axis. The ankle strategy plays only a small part in this, by rotating one foot inward about its longitudinal axis and the other foot outward so that the COP shifts medially in the one case and laterally in the other. However, because the foot is narrow, this strategy is of minor importance for balance.

This complexity means that a great variety of regulatory mechanisms are involved in successfully keeping the center of mass above the base of support. These include vision, the sense of balance, proprioception regarding the position of the ankles, perception of the loading of the feet, together with neuromuscular control of posture. Impairments of one or more of these sensory systems interfere with the regulatory mechanisms. As a consequence, the amplitude of oscillations may increase or their frequency may decrease. This has led to a wealth of different posturographic measurement and analysis techniques used to quantify disturbances of balance and of its regulation.

As the above considerations show, the movements of both COP and COM provide important information about the mechanisms of balance regulation, so measuring both of them is desirable. Measuring COP is comparatively simple. A force measurement platform (forceplate) working with a frequency of at least 50 Hz can deliver worthwhile results. For better temporal resolution, a sampling rate of 100 Hz or more should be used. Fig. 17.10 shows two different images of a typical measurement of the COP oscillation in a healthy person. Measuring COM is a more elaborate undertaking. Direct measurement is not possible; instead all body segments must be recorded separately and the location of the COM is calculated from these. This can be done using optical techniques. An alternative is to measure the oscillations of the trunk alone, if the arms do not move against the trunk, so that only the movements of the trunk need to be captured. This can be achieved using accelerometric techniques allowing the COM to be determined according to Eq. 17.21, if the COP is measured simultaneously.

In clinical practice two measurements taken under different conditions are often compared, such as “eyes open” and “eyes closed.” For example, in patients with a diabetic foot, where sensory impairment due to neuropathy can be assumed, measurements taken with the eyes open and then closed are compared to discover how dependent the patient’s balance regulation is on visual feedback. These investigations can be extended by integrating deliberate or random disturbances, such as changes in the slope of the support. 32 Characterization and quantitative analysis of COP oscillations are based on statistical methods. 33 The most important parameters record the length of the trajectory recorded in a given time, the mean frequency and frequency distribution, and the direction of the largest and smallest oscillations. The posturographic method is limited to analysis of the location and movement of the COP; it does not provide a detailed investigation of the plantar supporting forces. That is provided by plantar pressure distribution measurement.