Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Static analysis of the ankle joint

4,759 views

Published on

a simple static analysis of the ankle joint in stance and tip-toe, resulting joint reaction forces

Published in: Health & Medicine, Technology
  • Be the first to comment

Static analysis of the ankle joint

  1. 1. Cardiff School of EngineeringCoursework Cover SheetPersonal DetailsStudent No: 1056984Family Name: Divecha First Name: HirenPersonal Tutor: Prof Sam Davies Discipline: MMMModule DetailsModule Name: Engineering Theory 1 Module No: ENT536Coursework Title: Static analysis of the Ankle jointLecturer: Dr D M O’DohertySubmission Deadline: 30/10/2010DeclarationI hereby declare that, except where I have made clear and full reference to the work of others, thissubmission, and all the material (e.g. text, pictures, diagrams) contained in it, is my own work, hasnot previously been submitted for assessment, and I have not knowingly allowed it to be copied byanother student. In the case of group projects, the contribution of group members has beenappropriately quantified.I understand that deceiving, or attempting to deceive, examiners by passing off the work of anotheras my own is plagiarism. I also understand that plagiarising anothers work, or knowingly allowinganother student to plagiarise from my work, is against University Regulations and that doing so willresult in loss of marks and disciplinary proceedings. I understand and agree that the University’splagiarism software ‘Turnitin’ may be used to check the originality of the submitted coursework.Signed: …..…………………………………….………... Date: ……………………… 1
  2. 2. Static analysis of the Ankle jointHiren Maganlal DivechaCandidate Number: 1056984ENT536 – Engineering Theory 11. AbstractThe ankle joint plays an important role in supporting the body and allowing for propulsion. Theforces experienced vary greatly under different loading conditions and can reach up to 15 timesthe body weight whilst sprinting. Under static conditions, free body analysis has been used in thisreport to demonstrate the changes in joint reaction force from single leg stance (1.8 times bodyweight) to single leg tip-toe stance (2.5 times body weight). Finally, the biomechanical reason formaintaining non-weight-bearing status in conservatively managed small posterior malleolarfractures is discussed after demonstrating that the joint reaction force with the foot suspendedhorizontal in mid-air is only around 0.02 times the body weight acting in a near horizontaldirection. When compared to the near vertical direction and the magnitude of the joint reactionforce in single stance, it is clear to see how fracture displacement could occur if weight bearingwere allowed.(word count = 2787)Table of Contents 2
  3. 3. 1. Abstract ...................................................................................................................................... 22. Introduction ............................................................................................................................... 43. Basic Anatomy of the Tibio-talar Joint ....................................................................................... 54. Static Analyses of the Tibio-talar Joint ....................................................................................... 6 a) Single Leg Stance .................................................................................................................... 7 b) Single Leg Tip-toe Stance ..................................................................................................... 10 c) Foot Suspended in Mid-Air................................................................................................... 135. Conclusion ................................................................................................................................ 156. References ................................................................................................................................ 17 3
  4. 4. 2. IntroductionThe ankle joint is located between the leg and the foot. It is involved in supporting the bodyduring standing or the stance phase of gait, provides a lever arm for the push-off phase of gait(thus resulting in propulsion) and provides some amount of “shock absorption” during walkingand running activities. The ankle joint experiences loading of half the body weight during bipedalstanding. This can rise to 3 times body weight during walking and up to 15 times body weightduring sprinting. The ankle joint will be considered in certain positions (single leg stance, single legtip-toe stance and suspended horizontally in mid-air) with static analysis to estimate the jointreaction force as well as the muscle force exerted by either the gastrocnemius-soleus-plantarisgroup or the tibialis anterior muscle. 4
  5. 5. 3. Basic Anatomy of the Tibio-talar JointThe ankle joint or, more specifically, the tibio-talar joint is formed by the articulation between thedistal tibia, distal fibula and the trochlea of the talus. The distal tibia and fibula form a mortiseinto which the talus fits. This forms a uni-planar, hinged synovial joint. The joint is stabilized by itsbony congruency, which is tightest in dorsiflexion as the wider anterior part of the talus engageswithin the mortise. This in part explains why injuries are more likely to occur in the plantar-flexedfoot when there is some relative “looseness” of the talus in the ankle mortise. Furthermore,ligamentous structures stabilize the tibio-talar joint. These include the lateral ligamentouscomplex (anterior talo-fibular, posterior talo-fibular and calcaneo-fibular ligaments) and thestronger medial deltoid ligament, as well as the syndesmotic structures.The axis of rotation of the tibio-talar joint has been determined to run from just inferior andanterior to the tip of the lateral malleolus to just inferior to the tip of the medial malleolus (Isman& Inman 1969). This allows dorsiflexion of 10° - 30° and plantar-flexion of 20° - 50°. Dorsi-flexionis produced by contraction of the tibialis anterior muscle, which is weakly assisted by the extensordigitorum longus, extensor hallucis longus and peroneus tertius muscles. Plantar-flexion isproduced by the contraction of the gastrocnemius, soleus and to a lesser extent the plantarismuscle. These muscles have a common tendon, the Achilles tendon, which inserts into thecalcaneal tuberosity. It has been shown that in the normal tibio-talar joint during walking, theaverage dorsi-flexion is 10.2° and plantar-flexion 14.2° (Stauffer et al 1977). 5
  6. 6. 4. Static Analyses of the Tibio-talar JointFor the purposes of the following static analyses of the tibio-talar joint, the following assumptionshave been made: 1. The ankle – foot is considered as a free body 2. The sagittal plane is only considered 3. The foot is taken as being a rigid structure. Only movements about the tibio-talar joint centre of rotation are considered (i.e.: dorsi-plantar-flexion) 4. The tibio-talar joint is frictionless 5. The subject’s mass is 70 kg 6. The acceleration due to gravity (g) is 9.81 m.s-2Electromyographic studies of standing subjects have shown that the gastrocnemius and soleus areactive whereas the tibialis anterior is not (Joseph & Nightingale 1952 & 1956). Thus, the tibialisanterior shall be excluded from these analyses. More specifically, the tibialis anterior is activeduring two specific points in the gait cycle. Firstly, for the first 10% of the stride at the point ofheel contact to mid-stance when its dorsiflexion action prevents foot slap and decelerates thefoot into stance. Secondly, for the latter 40% of the stride corresponding to the “swing phase”from toe-off to heel strike when its function is to ensure clearance of the foot from the groundthroughout the swing phase. This pattern of activation has been confirmed by dynamicelectromyographic studies of the gait cycle in normal walking (Winter & Yack 1987; Ounpuu &Winter 1989). 6
  7. 7. A combination of sources have been referred to for specific measurements and angles in the footand ankle (Sammarco & Hockenbury 2001; Snijders 2001; Winter 2009). The length of the footfrom heel to metatarsals is 21 cm. The centre of rotation of the tibio-talar joint lies 5 cm anteriorand 4 cm superior to the point of action of the Achilles tendon (AT) on the calcaneum. TheAchilles tendon acts at an angle of 87° to the horizontal axis (Procter & Paul 1982). The groundreaction force (GRF) is equivalent to the weight of the body minus the weight of the foot and acts4 cm anterior to the centre of rotation of the tibio-talar joint (Hellebrandt et al 1938). The centreof mass of the foot lies 6 cm anterior to and 2 cm below the centre of rotation of the tibio-talarjoint. The mass of the foot (mfoot) is taken as 1.5% of the total body mass i.e. 1.05 kg.a) Single Leg StanceThe following static analysis will determine the force exerted by the Achilles tendon whilst asubject performs a single leg stance with the foot flat on the floor. As the centre of gravity of thebody during standing acts in front of the tibio-talar axis of rotation, there is a moment acting torotate the body forwards around the tibio-talar joint (Smith 1957). This is balanced by the plantarflexor muscle group (gastro-soleus-plantaris complex) acting via the Achilles tendon. Figure 1shows the free body diagram of the ankle and foot with the relevant forces acting on it.The joint reaction force is denoted by J and is shown to have orthogonal components Jx and Jy. Itacts at an angle β to the horizontal. The Achilles tendon force has orthogonal components ATx andATy and has a moment arm (p) from the centre of rotation of the tibio-talar joint. 7
  8. 8. y Jy J ATx AT ATy β x p Jx 4 cm 87° α 6 cm 2 cm 5 cm 4 cm mfoot x g 21 cm GRF Figure 1: Free body diagram of static forces acting on ankle joint in single leg flat stance1.2.3. 8
  9. 9. 4.5.6.Thus, when performing a single leg stance with the foot flat on the ground, the Achilles tendonforce in this simplified model is found to be 551 N with an overall joint reaction force of 1 217 N(1.8 times the body weight) acting at an angle of 88.6° to the horizontal axis. 9
  10. 10. b) Single Leg Tip-toe StanceWhen performing a single leg tip-toe, the foot – ankle behaves as a class 2 lever i.e. the load islocated between the effort and the pivot. The ground reaction force now acts at the pivot point,which is the plantar surface of the metatarsal heads. The plantar surface of the foot in thisexample is inclined at 45° to the horizontal. The angle of action of the Achilles tendon is taken toremain constant. The free body diagram of this scenario is shown in Figure 2 and the moment armof the weight of the foot (q) is calculated in Figure 3. y ATx Jy J AT ATy p x β Jx γ r q 2 cm 87° α 6 cm 5 cm mfoot x g 16 cm 45° GRF Figure 2: Free body diagram of static forces acting on ankle joint in single leg tip-toe stance 10
  11. 11. q r 2 cm ε 6 cm δ μ κ mfoot x g 45° Figure 3: Calculation of moment arm of weight of foot (q)1.2.3. 11
  12. 12. 4.5.6.7.Thus, when performing a single leg tip-toe stance, the Achilles tendon force in this simplifiedmodel is found to be 1 192 N with a resulting joint reaction force of 1 711 N (2.5 times bodyweight) acting at an angle of 58.8° to the horizontal axis. 12
  13. 13. c) Foot Suspended in Mid-AirWith the foot suspended in mid-air in a horizontal position, the tibialis anterior (TA) muscle isactive in generating a dorsiflexion moment to counteract the plantar-flexing moment generatedby the weight of the foot around the centre of rotation of the tibio-talar joint. The gastrocnemius-soleus-plantaris complex is presumed not be active in this situation, and this is certainly found tobe the case in electromyographic studies which show no activity during the latter 40% of the gaitcycle, corresponding to the “swing” phase when the foot is off the ground (Joseph & Nightingale1952 & 1956; Winter & Yack 1987; Ounpuu & Winter 1989). The tibialis anterior muscle force istaken to act at 30° to the horizontal (Procter & Paul 1982) with a perpendicular moment arm of3.5 cm from the centre of rotation of the tibio-talar joint (Maganaris et al 1999). Figure 4demonstrates the free body diagram for this scenario. y Jy J TAy x 3.5 cm β TA Jx 30° 4 cm TAx 6 cm 5 cm mfoot x g 21 cmFigure 4: Free body diagram of static forces acting on ankle joint in mid-air horizontal suspension 13
  14. 14. 1.2.3.4.Thus in the suspended horizontal foot, the tibialis anterior force is calculated to be 18N with aresulting joint reaction force of 15N (0.02 times body weight) acting at 5.5° to the horizontal. 14
  15. 15. 5. ConclusionFree body static analyses are useful in mathematically modelling joints and limbs under variousloading situations. However, because of the nature of the assumptions made, they only give us anestimate of muscle and joint reaction forces. The in vivo situation is much more complicated. Theankle – foot region has 33 articulations, which each experience some amount of friction and threedimensional joint movement and muscle action. Furthermore, joints are never truly static (ratherquasi-static with very small torques experienced which are corrected under subconscious controlto maintain balance and posture). In the examples demonstrated above, the joint reaction forcehas been shown to increase from 1.8 times body weight in single leg flat stance to 2.5 times bodyweight when performing a single leg tip-toe stance with the foot at 45°. This explains whypatients with significant tibio-talar joint osteoarthritis experience increased pain when attemptingto stand up on their tip-toes.The scenario of a small posterior malleolar (posterior segment of the distal tibial articular surface)fracture is a good example of the clinical application of comparing free body analyses of the tibio-talar joint in different weight-bearing situations. Undisplaced fractures involving less than 25% ofthe distal tibial articular surface are usually managed without internal fixation and are treated incast immobilisation with a period of non weight-bearing (usually 6 – 8 weeks). The risk of post-traumatic arthritis has been estimated at around 30% and initially this was felt to be related tothe increased overall contact stress on the joint surface due to a reduced contact area (Macko etal 1991). However, recent studies have shown that the contact stresses with simulated posteriormalleolar fractures are not increased. Rather, the centre of stress distribution over the remainingjoint surface shifts more anteriorly. This anterior region does not normally experience much 15
  16. 16. loading under physiological conditions, which may explain the higher incidence of degenerativechanges seen in patients with these types of injuries (Fitzpatrick et al 2004).From the simplified model of a horizontal suspended foot, the joint reaction force is low (0.02times body weight; this does not include the weight of a below knee cast) compared to the jointreaction force expected with weight-bearing stance (1.8 times body weight). Furthermore, thejoint reaction force has been calculated to act at a near vertical angle (88°) in single leg stancecompared to the near horizontal joint reaction force (5.5°) when the foot is suspendedhorizontally. The risk of fracture displacement is obvious if weight-bearing mobilisation in thisscenario were to be permitted before significant fracture healing had commenced. 16
  17. 17. 6. ReferencesFitzpatrick, D. C., et al. 2004. Kinematic and Contact Stress Analysis of Posterior MalleolusFractures of The Ankle. Journal of Orthopaedic Trauma 18 (5), pp. 271-278.Hellebrandt, F. A., et al. 1938. The Location of The Cardinal Anatomical Orientation Planes PassingThrough The Center of Weight in Young Adult Women. American Journal of Physiology, pp. 465-470.Isman, R. E., & Inman, V. T. 1969. Anthropometric Studies of The Human Foot and Ankle. Bulletinof Prosthetics Research , pp. 97-129.Joseph, J., & Nightingale, A. 1956. Electromyography of Muscles of Posture: Leg and ThighMuscles In Women, Including The Effects of High Heels. Journal of American Physiology 132 (3),pp. 465-468.Joseph, J., & Nightingale, A. 1952. Electromyography of Muscles of Posture: Leg Muscles in Males.Journal of Physiology 117 (4), pp. 484-491.Macko, V. W., et al. 1991. The Joint-Contact Area of The Ankle. The Contribution of the PosteriorMalleolus. The Journal of Bone and Joint Surgery 73, pp. 347-351.Maganaris, C. M., et al. 1999. Changes in The Tibialis Anterior Tendon Moment Arm from Rest toMaximum Isometric Dorsiflexion: In Vivo Observations in Man. Clinical Biomechanics 14, pp. 661-666.Ounpuu, S., & Winter, D. A. 1989. Bilateral Electromyographical Aanalysis of The Lower LimbsDuring Walking in Normal Adults. Electroencephalography and Clinical Neurophysiology 72, pp.429-438. 17
  18. 18. Procter, P., & Paul, J. P. 1982. Ankle Joint Biomechanics. Journal of Biomechanics 15 (9), pp. 627-634.Sammarco, G. J., & Hockenbury, R. T. 2001. Biomechanics of the Foot and Ankle. In: M. Nordin, &V. H. Frankel, Basic Biomechanics of The Musculoskeletal System. 3rd ed. Lippincott Williams &Wilkins, pp. 223-255.Smith, J. W. 1957. The Forces Operating at The Human Ankle Joint During Standing. Journal ofAnatomy 91 (4), pp. 545-564.Snijders, C. J. 2001. Engineering Approaches to Standing, Sitting, and Lying. In: M. Nordin, & V. H.Frankel, Basic Biomechanics of The Musculoskeletal System. 3rd ed. Lippincott Williams & Wilkins,pp. 421-424.Stauffer, R. N., et al. 1977. Force and Motion Analysis of the Normal, Diseased and ProstheticAnkle Joints. Clinical Orthopaedics and Related Research 127, pp. 189-196.Winter, D. A., & Yack, H. J. 1987. EMG Profiles During Normal Human Walking: Stride-to-Strideand Inter-subject Variability. Electroencephalography and Clinical Neurophysiology 67, pp. 402-411.Winter, D. A. 2009. Kinetics: Forces and Moments of Force. In: Biomechanics and Motor Control ofHuman Movement. 4th ed. John Wiley & Sons, pp. 107-138. 18

×