New Concepts In Longitudinal Arch Biomechanics

Pages: 20 - 27
Author(s): 
Kevin A. Kirby, DPM
Topics: 

In order to promote a better understanding of the neurological and mechanical functions of the longitudinal arch, this author discusses the concept of the Longitudinal Arch Load-Sharing System (LALSS) and how the longitudinal arch plays an integral role in facilitating the flexibility and stability of daily weightbearing.

The longitudinal arch of the human foot is a unique structure within the animal kingdom. Dudley J. Morton, MD (1884-1960), who was a physician, anatomist and anthropologist, wrote one of the classic books on evolution of the human foot.1 He claimed that the development of the medial longitudinal arch was one of the most important factors that allowed humans to achieve bipedal locomotion.2

Other authors have claimed the prime reason for the development of the longitudinal arch was to stiffen the forefoot on the rearfoot so the strong calf muscles could more effectively push the body weight forward during walking and running.3–6 Other authors have suggested the longitudinal arch absorbs the extra shock, which was required by bearing weight on only two limbs.7,8

Whatever the reason for its development, the longitudinal arch creates a characteristic morphology to the human foot, which makes it distinct and separate from all other members of the animal kingdom.

Even though the extremes of longitudinal arch height, ranging from pes planus to pes cavus, have interested medical professionals for over 150 years, today’s podiatrists not only need to understand the mechanical effects of longitudinal arch height but they also need to understand the biomechanics of the longitudinal arch during weightbearing activities (see left illustration).9–11

Accordingly, I will detail a new concept in longitudinal arch biomechanics, the Longitudinal Arch Load-Sharing System (LALSS), in this article to help explain the neurological and mechanical function of the longitudinal arch, and how the longitudinal arch allows the foot to exhibit its exquisite balance of both flexibility and stability during our daily weightbearing activities.12,13

Essential Principles On The Mechanics Of Load-Sharing Systems

The LALSS is a type of “load-sharing system,” which is a common design in both mechanical and electrical systems. Load-sharing systems are often designed with redundancy by having multiple components performing the same operation so if one component fails, the other components in the system will still be able to perform the task. If all components work properly, the load on each component of the system decreases. However, if one component fails, the loads on the remaining components of the load-sharing system increase. Multi-engine aircraft, power stations with multiple generators and computers with multiple processors are all common examples of load-sharing systems.14,15

One familiar type of load-sharing system that is mechanically analogous to the longitudinal arch of the foot is present within the rear suspension of trucks, where both leaf springs and shock absorbers dampen vertical accelerations between the truck’s chassis and its rear axle. Both the leaf springs and shock absorbers work together to stiffen the rear suspension and help prevent the truck chassis from bottoming out while driving with heavy loads or when driving over uneven roads. If the shock absorbers fail in the rear suspension load-sharing system, the leaf springs will have an increased load. If the leaf springs fail, the shock absorbers will have an increased load. However, when each component of the rear suspension is working properly, the vehicle suspension functions optimally and both the leaf springs and shock absorbers have reduced loads.  

More recently, variable stiffness shock absorbers have become available for the suspensions of vehicles. Drivers can either manually adjust these variable stiffness shock absorbers during driving or microprocessors automatically adjust the shock absorbers in order to improve the comfort and handling characteristics of the vehicle.16,17 The control properties of these variable stiffness shock absorbers in vehicles are mechanically analogous to the control properties that the central nervous system (CNS) uses to regulate the stiffness of the longitudinal arch in order to optimize the comfort and mechanical efficiency of the individual during the multitude of weightbearing activities he or she performs on a daily basis.  

A Guide To The Compression Load-Bearing Elements Of The Longitudinal Arch Load-Sharing System

External forces, consisting of ground reaction force (GRF) acting on the plantar rearfoot and forefoot, exert large flattening moments on the longitudinal arch. No other body part is regularly subject to such large external forces as the plantar foot.18 During walking, peak loads acting on the plantar foot range from 1.1 to 1.5 times body weight whereas, during running, peak loads are double that of walking.19 During jumping activities, peak loads acting on the plantar foot can easily exceed over four times body weight.20 In addition, internal forces, consisting of tibial compression force acting on the dorsal talus and Achilles tendon tension force acting on the posterior calcaneus, add to the exceptionally large flattening moments that the longitudinal arch is subject to during our daily weightbearing activities (see right illustration).  

In order to resist these large external and internal forces during standing, walking, running, jumping and other weightbearing activities, the longitudinal arch must develop internal forces that resist deformation and flattening of the longitudinal arch. Accordingly, the longitudinal arch is comprised of two main types of elements: 1) the compression load-bearing elements, including the bones and joint cartilage of the longitudinal arch; and 2) the tension load-bearing elements, including the plantar fascia, plantar ligaments and plantar intrinsic and extrinsic muscles of the foot.21

The osseous structures along with the hyaline articular cartilage of the longitudinal arch and its joints comprise the compression load-bearing elements of the longitudinal arch. The bones of the longitudinal arch are excellent at resisting compression loads and also good at resisting bending and torsional loads.22 The hyaline articular cartilage covering the surfaces of the joints of the longitudinal arch serves not only as an interosseous shock absorber for the longitudinal arch but also provides for low-friction gliding and reduction of subchondral bone peak pressures within the pedal joints.23

The bones of the longitudinal arch also serve as points of attachment for the tension load-bearing elements of the LALSS and form the structural framework of the longitudinal arch. Just like the wooden rafters within the roof of a house resist compression, bending and torsional forces due to vertical and shearing loads acting on the roof from snow and wind, the bones of the longitudinal arch resist compression, bending and torsional forces due to vertical and shearing loads acting on the plantar foot. The loading and unloading cycles of the longitudinal arch result in the flattening and raising of the longitudinal arch, which normally occurs without injury to the individual, thousands of times every day, week after week, month after month, and year after year.

Understanding The Tension Load-Bearing Elements Of The Longitudinal Arch Load-Sharing System

The compression load-bearing elements (i.e. bones and articular cartilage) of the longitudinal arch cannot, by themselves, resist longitudinal arch flattening. They need internal supportive elements that can provide plantar tension forces to help resist arch flattening. These internal forces originate from the four layers of tension load-bearing elements of the LALSS: the plantar fascia, plantar intrinsic muscles, extrinsic muscles of the plantar longitudinal arch and plantar ligaments. These plantarly located tension load-bearing structures work synergistically to regulate the stiffness of the longitudinal arch so optimum longitudinal arch flattening occurs during all weightbearing activities.

The plantar fascia originates from the medial calcaneal tubercle proximally and inserts as five separate slips onto the bases of the proximal phalanges of all five digits, and is the most superficial layer of the LALSS tension load-bearing elements.24 The plantar fascia is an elastic structure that is subject to forces that authors have estimated to be 0.96 times body weight in simulated cadaver experiments.25,26 In addition, Hicks’ classic research on plantar fascia biomechanics demonstrated an arch-raising “windlass effect” with hallux dorsiflexion and an arch-lowering “reverse windlass” with hallux plantarflexion.27 Transection of the plantar fascia reduces longitudinal arch stiffness, which in turn produces longitudinal arch flattening and elongation.28–30 Like the plantar ligaments, tension within the plantar fascia is not under the direct control of the central nervous system but is regulated passively by alterations in longitudinal arch shape.13

The plantar intrinsic muscles form the next layer of the tension load-bearing elements of the LALSS, being just deep to the plantar fascia (see left illustration). The abductor hallucis, flexor digitorum brevis, abductor digiti quinti and quadratus plantae muscles are the most important plantar intrinsic muscles when it comes to preventing longitudinal arch flattening and elongation with the other plantar intrinsic muscles probably having a lesser role.31 Kelly and coworkers have shown in recent fine-wire electromyography (EMG) research that the central nervous system activates the plantar intrinsics to help stiffen the longitudinal arch to aid in balance, help prevent arch flattening with increasing vertical loading forces and stiffen the arch more during running than during walking.32–34

The extrinsic muscles of the plantar longitudinal arch form the next layer of tension load-bearing elements of the LALSS, just deep to the plantar intrinsic muscles (see right illustration). These extrinsic muscles include the posterior tibial, flexor digitorum longus, flexor hallucis longus and peroneus longus muscles. The posterior tibial and peroneus longus tendons cross plantarly across the arch and cause a forefoot plantarflexion moment, which helps resist longitudinal arch flattening. The flexor hallucis longus and flexor digitorum longus both insert distal to the metatarsophalangeal joints (MPJs) so their contractile activity generates a forefoot plantarflexion moment due to the increased proximally directed compression force acting on the distal metatarsal heads.21

The plantar ligaments form the deepest layer of the tension load-bearing elements of the LALSS and, like the plantar fascia, are passive structures that will have increased tension forces only when the longitudinal arch is elongated and flattened. Crary and coworkers found the strain in the spring ligament increased by 52 percent and strain in the long plantar ligament increased by 94 percent after plantar fasciotomy in cadaver feet.35 Therefore, even without central nervous system activity, the plantar fascia and plantar ligaments can help prevent longitudinal arch flattening using only passive mechanisms.

How The Longitudinal Arch Load-Sharing System Works

The longitudinal arch has multiple functions during weightbearing activities. The arch must be able to flatten to dampen vertical impact forces and it must alter its shape when the plantar foot encounters uneven terrain. In addition, the longitudinal arch must be able to resist flattening deformation during propulsive activities so muscular forces from the powerful gastrocnemius and soleus muscles transfer to the plantar forefoot with maximum mechanical efficiency. The central nervous system controls longitudinal arch stiffness by continually monitoring sensory input from the peripheral nervous system and subsequently sending motor output to the intrinsic and extrinsic muscles of the LALSS in order to optimize the weightbearing function of the foot, lower extremity and whole individual.12

The aforementioned four layers of tension load-bearing elements of the LALSS are divided into both passive and active elements. Since the central nervous system does not control the passive elements, the plantar fascia and plantar ligaments, they will be subject to increased tension forces only when the longitudinal arch flattens and elongates. However, as the central nervous system does control the active elements, the intrinsic and extrinsic plantar arch muscles, these can be activated or deactivated when the central nervous system determines that increased or decreased stiffening of the longitudinal arch is required. Therefore, the plantar ligaments and plantar fascia provide a baseline level of longitudinal arch stiffness while the central nervous system activation of the plantar intrinsic and extrinsic muscles increases longitudinal arch stiffness over this baseline level in order to optimize weightbearing function of the foot and individual.12

One of the most important mechanical design features of the LALSS is that, as with any other load-sharing system, if one element of the LALSS fails, the longitudinal arch will still function, resisting flattening deformation. However, with failure of one supporting element of the LALSS, increased tension demands on the remaining elements of the LALSS will occur. For example, with a plantar fascial rupture or plantar fasciotomy, the longitudinal arch does not totally collapse, but the plantar ligaments and the plantar intrinsic and extrinsic muscles develop increased tension forces to maintain longitudinal stiffness and prevent excessive longitudinal arch flattening (see left illustration). Without this unique and synergistic load-sharing system within the foot, the longitudinal arch would likely not have the stiffness or strength to maintain its shape and function properly on a daily basis throughout the lifetime of the bipedal human.12
    
A Quick Overview On The Dynamics Of Passive Longitudinal Arch Load-Sharing System Control

As I noted earlier, the central nervous system does not directly control the passive elements of the LALSS, the plantar fascia and plantar ligaments. As such, these passive elements can only exert tension forces when the forefoot dorsiflexes on the rearfoot or, in other words, when the longitudinal arch flattens and lengthens. Thus, when the plantar fascia and plantar ligaments are elongated with arch flattening, the longitudinal arch will continue to flatten until there are sufficient internal forefoot plantarflexion moments to prevent further longitudinal arch flattening and elongation, allowing the longitudinal arch to become stable on the ground.

Researchers have shown a direct mechanical relationship between Achilles tendon tension and plantar fascia tension.26,36 During walking or running gait, as the center of mass of the body moves more anterior relative to the foot and the ground reaction force increases on the plantar forefoot, the increased Achilles tendon force that occurs will also cause increased tension force within the plantar fascia and plantar ligaments. Thus, increases in ground reaction force acting on the plantar forefoot that cause an increase in passive tension within the plantar fascia and plantar ligaments have a profound biomechanical effect on the ability of the midtarsal and midfoot joints to resist dorsiflexion during late midstance and propulsion.

Pertinent Insights On The Longitudinal Arch Auto-Stiffening Mechanism

A quarter-century ago, Dananberg described a “locking wedge and truss effect,” which he attributed to tightening of the plantar fascia during gait and described as an “auto-support mechanism.”37 More recently, Kirby described another automatic function of the foot, the Longitudinal Arch Auto-Stiffening Mechanism, which allows automatic stiffening of the whole longitudinal arch as the foot progresses from the beginning to the end of the midstance phase of gait (see right illustration).38

The Longitudinal Arch Auto-Stiffening Mechanism is a product of the integral mechanical link that exists among the Achilles tendon, plantar ligaments and plantar fascia. The effect of this passive increase in plantar fascia and plantar ligament tension with increasing ground reaction force on the plantar forefoot is an automatic stiffening of the longitudinal arch. This automatic longitudinal arch stiffening not only helps to limit further longitudinal arch flattening and elongation during late midstance, but also occurs without any direct central nervous system activation of the plantar fascia and plantar ligaments.12,13

The Longitudinal Arch Auto-Stiffening Mechanism is directly due to the unique construction of the human foot, ankle and lower extremity. First, the osseous elements of the longitudinal arch form a unique arched structure, which has the support of the two plantarly located, tension load-bearing elements of the LALSS, the plantar fascia and plantar ligaments. Second, the Achilles tendon, by attaching to the posterior calcaneus and being posterior to the ankle joint axis, exerts both a simultaneous ankle joint plantarflexion moment and a rearfoot plantarflexion moment with increases in its tension forces. This increase in rearfoot plantarflexion moment due to increased Achilles tendon tension during late midstance tends to cause longitudinal arch flattening, automatically increasing longitudinal arch stiffness.38

The Longitudinal Arch Auto-Stiffening Mechanism first became evident to me in 2004. At that time, two other biomechanics researchers and I performed experiments at the Pennsylvania State University Biomechanics Laboratory with fresh-frozen cadaver foot-leg specimens.39 These specimens’ Achilles tendons were tethered to a steel cable so that, even in these lifeless feet with no active central nervous system muscle control, the longitudinal arch became stiffer with increased plantar forefoot loads. These experimental observations suggested that no extra metabolic energy was required to produce longitudinal arch stiffening and only an increase in Achilles tendon tension was required to resist the ankle joint dorsiflexion moments that occur due to ground reaction force acting on the plantar forefoot. Therefore, due to the mechanical linkage between the Achilles tendon, plantar fascia and plantar ligaments, the Longitudinal Arch Auto-Stiffening Mechanism has likely greatly enhanced the locomotion abilities of the bipedal human over the millennia by decreasing the metabolic cost of walking and running.38

What You Should Know About Active Longitudinal Arch Load-Sharing System Control

The active elements of the LALSS, the plantar intrinsic muscles and the posterior tibial, flexor digitorum longus, flexor hallucis longus and peroneus longus muscles, all work together under central nervous system control to make the foot a more mechanically efficient and stable weightbearing organ for the human body. The central nervous system has the ability to make either the medial or lateral longitudinal arches stiffer if the central nervous system determines that these increases in arch stiffness will optimize the weightbearing activities of the individual.12

For example, in order for the foot to stay plantigrade in rapid side to side maneuvers or to conform to a sloped surface, the central nervous system may increase the stiffness of the medial longitudinal arch while not altering lateral longitudinal arch stiffness. As I mentioned earlier, this central control mechanism of the LALSS by the central nervous system is mechanically analogous to a microprocessor-controlled shock absorber in an advanced vehicle suspension that can increase the mechanical efficiency, safety and comfort of driving. Likewise, the ability of the central nervous system to use the unique design of the LALSS to continually and precisely regulate longitudinal arch stiffness provides for more mechanically efficient function of the foot, which in turn allows the individual to help avoid injury during the multitude of weightbearing activities he or she performs during a lifetime.12

In Conclusion

Over six centuries ago, after his extensive studies of the anatomy of the human body, Leonardo Da Vinci wrote that “the human foot is a masterpiece of engineering and a work of art.”40 The longitudinal arch of the human foot is one of those engineering marvels that is unique within the animal kingdom. With a combination of passive elements that provide a baseline stiffness to the longitudinal arch and active elements that allow continual regulation of longitudinal arch stiffness over this baseline, the bipedal human undoubtedly benefits significantly from this precisely-tuned mechanism within the weightbearing appendage, the foot. By fully appreciating the elegant engineering complexity of the longitudinal arch of the foot, the podiatrist will greatly enhance his or her ability to understand foot function and, thereby, design more therapeutically effective conservative and surgical treatments for patients.

Dr. Kirby is an Adjunct Associate Professor within the Department of Applied Biomechanics at the California School of Podiatric Medicine at Samuel Merritt University in Oakland, Calif. He is in private practice in Sacramento, Calif.

References
1.     Morton DJ. The Human Foot: Its Evolution, Physiology and Functional Disorders. Columbia University Press, Morningside Heights, New York, 1935.  
2.     Morton DJ. Evolution of the longitudinal arch of the human foot. J Bone Joint Surg. 1924;6:56-90.
3.     Elftman H, Manter. The evolution of the human foot, with especial reference to the joints. J Anat. 1935; 70(Pt 1):56-67.
4.     Bojsen-Møller F. Calcaneocuboid joint and stability of the longitudinal arch of the foot at high and low gear push off. J Anat. 1979; 129(Pt 1):165-176.
5.     Susman RL, Stern JT. Functional morphology of Homo habilis. Science. 1982; 217(4563):931-934.
6.     DeSilva JM. Revisiting the “midtarsal break.” Am J Phys Anthropol. 2010; 141(2):245-258.
7.     Saltzman CL, Nawoczenski DA, Talbot KD. Measurement of the medial longitudinal arch. Arch Phys Med Rehabil. 1995; 1;76(1):45-29.
8.     Ker RF, Bennett MB, Bibby SR, et al. The spring in the arch of the human foot. Nature. 1987; 325(7000):147-149.
9.    Whitman R. A study of the weak foot, with reference to its causes, its diagnosis, and its cure; with an analysis of a thousand cases of so-called flat-foot. J Bone Joint Surg. 1896; 8:42-77.
10.     Smith TF, Green DR. Pes cavus. In (Southerland JT, Boberg JS, Downey MS, eds.) McGlamry’s Comprehensive Textbook of Foot and Ankle Surgery, 3rd Edition, Vol. 1. Lippincott, Williams & Wilkins, Philadelphia, 2001, p. 761.
11.     Parkin A. The causation and mode of production of pes cavus. Med Chir Trans. 1891; 74:485-495.
12.     Kirby KA. Foot and Lower Extremity Biomechanics IV: Precision Intricast Newsletters, 2009-2013. Precision Intricast, Inc., Payson, AZ, 2014, pp. 31-34.
13.     Kirby KA. Longitudinal arch load-sharing system of the foot. Revista Española de Podología. 2017; 28(2):e18–26.
14.     Ye Z, Revie M, Walls L. A load sharing system reliability model with managed component degradation. IEEE Transactions on Reliability. 2014; 63(3):721-730.
15.     Taghipour S, Kassaei ML. Periodic inspection optimization of a k-out-of-n load-sharing system. IEEE Transactions on Reliability. 2015; 64(3):1116-1127.
16.     Warczek J, Burdzik R, Peruń G. The method for identification of damping coefficient of the trucks suspension. Key Engineering Materials. 2014; 588:281-289.
17.     Sun S, Deng H, Du H, Li W, Yang J, Liu G, Alici G, Yan T. A compact variable stiffness and damping shock absorber for vehicle suspension. IEEE/ASME Transactions on Mechatronics. 2015; 20(5):2621-2629.
18.     Kirby KA. Foot and Lower Extremity Biomechanics IV: Precision Intricast Newsletters, 2009-2013. Precision Intricast, Inc., Payson, AZ, 2014, p. 69.
19.     Keller TS, Weisberger AM, Ray JL, Hasan SS, Shiavi RG, Spengler DM. Relationship between vertical ground reaction force and speed during walking, slow jogging, and running. Clin Biomech. 1996; 11(5):253-259.
20.     McNair PJ, Prapavessis H. Normative data of vertical ground reaction forces during landing from a jump. J Science Medicine Sport. 1999; 2(1):86-88.
21.     Kirby KA. Foot and Lower Extremity Biomechanics III: Precision Intricast Newsletters, 2002-2008. Precision Intricast, Inc., Payson, AZ, 2009, pp. 53-54.
22.     Bronner F, Farach-Carson MC, Roach HI (eds): Bone and Development. Springer, New York, 2010, p. 286.
23.     Bhosale AM, Richardson JB. Articular cartilage: structure, injuries and review of management. Br Med Bull. 2008; 87(1):77-95.
24.     Kelikian AS, Sarrafian SK. Sarrafian’s Anatomy of the Foot and Ankle: Descriptive, Topographic, Functional, 3rd ed. Wolters Kluwer Health/Lippincott Williams & Wilkins, Philadelphia, 2011, pp.144-154.
25.     Wright DG, Rennels DC. A study of the elastic properties of plantar fascia. J Bone Joint Surg. 1964; 46(A):482-492.
26.     Erdimir A, Hamel AJ, Fauth AR, Piazza SJ, Sharkey NA. Dynamic loading of the plantar aponeurosis in walking. J Bone Joint Surg. 2004; 86A:546-552.
27.     Hicks JH. The mechanics of the foot. II. The plantar aponeurosis and the arch. J Anatomy. 1954; 88(1):24-31.
28.     Ker RF, Bennett MB, Bibby SR, et al. The spring in the arch of the human foot. Nature. 1987; 325(7000):147-149.
29.     Sharkey NA, Ferris L, Donahue SW. Biomechanical consequences of plantar fascial release or rupture during gait: Part I – Disruptions in longitudinal arch conformation. Foot Ankle Int. 1998; 19(12):812-820.
30.     Murphy GA, Pneumaticos SG, Kamaric E, et al. Biomechanical consequences of sequential plantar fascia release. Foot Ankle Int. 1998; 19(3):149-152.
31.     Kelikian AS, Sarrafian SK. Sarrafian’s Anatomy of the Foot and Ankle: Descriptive, Topographic, Functional, 3rd ed. Wolters Kluwer Health/Lippincott Williams & Wilkins, Philadelphia, 2011, pp. 257-290.
32.     Kelly LA, Kuitunen S, Racinais S, Cresswell AG. Recruitment of the plantar intrinsic foot muscles with increasing postural demand. Clin Biomech. 2012; 27(1):46-51.
33.     Kelly LA, Cresswell AG, Racinais S, et al. Intrinsic foot muscles have the capacity to control deformation of the longitudinal arch. J R Soc Interface. 2014; 11(93):20131188.
34.     Kelly LA, Lichtwark G, Cresswell AG. Active regulation of longitudinal arch compression and recoil during walking and running. JR Soc Interface. 2015; 12(102):1-8.
35.     Crary JL, Hollis M, Manoli A. The effect of plantar fascia release on strain in spring and long plantar ligaments. Foot Ankle. 2003; 24(3):245-50.
36.     Carlson RE, Fleming LL, Hutton WC. The biomechanical relationship between the tendoachilles, plantar fascia and metatarsophalangeal joint dorsiflexion angle. Foot Ankle Int. 2000; 21(1):18-25.
37.     Dananberg HJ. Gait style as an etiology to chronic postural pain. Part I. Functional hallux limitus. J Am Podiatr Med Assoc. 1993; 83(11):433-441.
38.     Kirby KA. Foot and Lower Extremity Biomechanics IV: Precision Intricast Newsletters, 2009-2013. Precision Intricast, Inc., Payson, AZ, 2014, pp. 35-36.
39.     Lewis GS, Kirby KA, Piazza SJ. Determination of subtalar joint axis location by restriction of talocrural joint motion. Gait Posture. 2007; 25(1):63-69.
40.     Valderrabano V, Easle M (eds): Foot and Ankle Sports Orthopaedics. Springer, New York, 2016, p. 25.

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