Beam Theory and Finite Element Approaches to Modelling the Stresses in the Second Metatarsal During Running

Stress fracture of the second metatarsal is a problematic injury amongst runners, requiring long recovery times. The physiological mechanisms by which a stress fracture may develop are reasonably well understood, however there is poorer understanding of the training variables which may lead to increased risk of injury. This is compounded by the difficulty of directly measuring metatarsal stress. The aims of this thesis were to develop both 2D beam theory and 3D finite element models with participant-specific parameters to investigate the stresses experienced by the second metatarsal during running. The models would be used to answer an applied question regarding the differences in second metatarsal stress between rearfoot (RF) runners and non-rearfoot (NRF) runners.

A single data set was collected consisting of 20 runners, including 12 habitual rearfoot and 8 habitual non-rearfoot strikers. Synchronised force, pressure and kinematic data were collected during barefoot running (3.6 ms^-1) in addition to three plane magnetic resonance data of the right second metatarsal of each participant.

The first modelling study developed and evaluated a 2D beam theory model incorporating vertical and horizontal ground reaction forces under the metatarsal head and toe and utilising participant-specific geometrical information from magnetic resonance images. Peak stress and input variables were compared between RF and NRF groups and statistical parametric mapping analysis allowed comparison of the stress time histories between groups. Results demonstrated that ground reaction forces under the metatarsal head were greater in the NRF group at the time of peak stress, but that peak stress did not differ between groups. The SPM analysis found greater stress in the NRF group during early stance.

The second modelling study developed and evaluated a 3D finite element model, incorporating distributed loading and soft tissue effects between the metatarsal head and the ground. A two-part metatarsal bone consisting of trabecular and cortical layers was reconstructed from magnetic resonance images, in addition to the soft tissues surrounding the metatarsal bone. Three time points during stance were analysed; maximum braking (minimum horizontal ground reaction forces), maximum vertical ground reaction force, and maximum propulsion (maximum horizontal ground reaction forces). Maximum von Mises stress and input variables were compared between groups at all three time points. Results showed that vertical ground reaction forces under the metatarsal head were greater in NRF runners at all time points, but stress did not differ between groups at any time.

When using the two models the same overall findings were observed, suggesting that external forces do not represent internal loading well. The magnitudes of stress were not different between groups at the time of peak stress (2D model) or the times of maximum braking, maximum vertical ground reaction force or maximum propulsion (3D model), suggesting that habitual foot strike modality does not affect the risk of stress fracture via this mechanism.

Year	Entry
1987	Ker RF, Bennett MB, Bibby SR, Kester RC, Alexander RM. The spring in the arch of the human foot. Nature. January 8, 1987;325(6100):147-149.
1989	Schaffler MB, Radin EL, Burr DB. Mechanical and morphological effects of strain rate on fatigue of compact bone. Bone. 1989;10(3):207-214.
2005	Erdemir A, Saucerman JJ, Lemmon D, Loppnow B, Turso B, Ulbrecht JS, Cavanagh PR. Local plantar pressure relief in therapeutic footwear: design guidelines from finite element models. J Biomech. September 2005;38(9):1798-1806.
2008	Hsu Y-C, Gung Y-W, Shih S-L, Feng C-K, Wei S-H, Yu C-h, Chen C-S. Using an optimization approach to design an insole for lowering plantar fascia stress: a finite element study. Ann Biomed Eng. 2008;36(8):1345-1352.
2008	Yu J, Cheung JT-M, Fan Y, Zhang Y, Leung AK-L, Zhang M. Development of a finite element model of female foot for high-heeled shoe design. Clin Biomech (Bristol, Avon). 2008;23(suppl 1):S31-S38.
2006	Cheung JT-M, An K-N, Zhang M. Consequences of partial and total plantar fascia release: a finite element study. Foot Ankle Int. 2006;27(2):125-132.
2004	Cheung JT-M, Zhang M, An K-N. Effects of plantar fascia stiffness on the biomechanical responses of the ankle–foot complex. Clin Biomech (Bristol, Avon). October 2004;19(8):839-846.
2005	Cheung JT-M, Zhang M, Leung AK-L, Fan Y-B. Three-dimensional finite element analysis of the foot during standing: a material sensitivity study. J Biomech. May 2005;38(5):1045-1054.
2009	García-Aznar JM, Bayod J, Rosas A, Larrainzar R, García-Bógalo R, Doblaré M, Llanos LF. Load transfer mechanism for different metatarsal geometries: a finite element study. J Biomech Eng. 2009;131(2):021011.
1992	Martin B. A theory of fatigue damage accumulation and repair in cortical bone. J Orthop Res. November 1992;10(6):818-825.
2003	Gefen A. The in vivo elastic properties of the plantar fascia during the contact phase of walking. Foot Ankle Int. March 2003;24(3):238-244.
2001	Williams DS III, McClay IS, Hamill J. Arch structure and injury patterns in runners. Clin Biomech (Bristol, Avon). May 2001;16(4):341-347.
2001	Chen W-P, Tang F-T, Ju C-W. Stress distribution of the foot during mid-stance to push-off in barefoot gait: a 3-D finite element analysis. Clin Biomech (Bristol, Avon). August 2001;16(7):614-620.
1990	Yeadon MR, Atha J, Hales FD. The simulation of aerial movement, IV: a computer simulation model. J Biomech. 1990;23(1):85-89.
2010	Natali AN, Forestiero A, Carniel EL, Pavan PG, Zovo CD. Investigation of foot plantar pressure: experimental and numerical analysis. Med Biol Eng Comput. 2010;48(12):1167-1174.
2008	Actis RL, Ventura LB, Lott DJ, Smith KE, Commean PK, Hastings MK, Mueller MJ. Multi-plug insole design to reduce peak plantar pressure on the diabetic foot during walking. Med Biol Eng Comput. 2008;46(4):363-371.
2007	van Gent RN, Siem D, van Middelkoop M, van Os AG, Bierma-Zeinstra SMA, Koes BW. Incidence and determinants of lower extremity running injuries in long distance runners: a systematic review. Br J Sports Med. August 2007;41(8):469-480.
1997	Lemmon D, Shiang TY, Hashmi A, Ulbrecht JS, Cavanagh PR. The effect of insoles in therapeutic footwear: a finite element approach. J Biomech. June 1997;30(6):615-620.
2001	Carson MC, Harrington ME, Thompson N, O’Connor JJ, Theologis TN. Kinematic analysis of a multi-segment foot model for research and clinical applications: a repeatability analysis. J Biomech. October 2001;34(10):1299-1307.
1996	Bennell KL, Malcolm SA, Thomas SA, Wark JD, Brukner PD. The incidence and distribution of stress fractures in competitive track and field athletes: a twelve-month prospective study. Am J Sports Med. March–April 1996;24(2):211-217.
2006	Actis RL, Ventura LB, Smith KE, Commean PK, Lott DJ, Pilgram TK, Mueller MJ. Numerical simulation of the plantar pressure distribution in the diabetic foot during the push-off stance. Med Biol Eng Comput. 2006;44(8):653-663.
2012	Chen W-M, Park J, Park S-B, Shim VP-W, Lee T. Role of gastrocnemius–soleus muscle in forefoot force transmission at heel rise: a 3D finite element analysis. J Biomech. June 26, 2012;45(10):1783-1789.
1987	Matheson GO, Clement DB, Mckenzie DC, Taunton JE, Lloyd-Smith DR, Macintyre JG. Stress fractures in athletes: a study of 320 cases. Am J Sports Med. January–February 1987;15(1):46-58.
2012	Isvilanonda V, Dengler E, Iaquinto JM, Sangeorzan BJ, Ledoux WR. Finite element analysis of the foot: model validation and comparison between two common treatments of the clawed hallux deformity. Clin Biomech (Bristol, Avon). October 2012;27(8):837-844.
1990	Scott SH, Winter DA. Internal forces at chronic running injury sites. Med Sci Sports Exer. June 1990;22(3):357-369.
1979	Stokes IAF, Hutton WC, Stott JRR. Forces acting on the metatarsals during normal walking. J Anat. 1979;129(pt 3):579-590.
1987	Frost HM. Bone "mass" and the "mechanostat": a proposal. Anat Rec. September 1987;219(1):1-9.
2010	Gu YD, Ren XJ, Li JS, Lake MJ, Zhang QY, Zeng YJ. Computer simulation of stress distribution in the metatarsals at different inversion landing angles using the finite element method. Int Orthop. June 2010;34(5):669-676.
1997	Burr DB. Bone, exercise, and stress fractures. Exerc Sport Sci Rev. January 1997;25(1):171-194.
1995	Duncan RL, Turner CH. Mechanotransduction and the functional response of bone to mechanical strain. Calcif Tiss Int. December 1995;57(5):344-358.
2008	Flavin R, Halpin T, O'Sullivan R, FitzPatrick D, Ivankovic A, Stephens MM. A finite-element analysis study of the metatarsophalangeal joint of the hallux rigidus. J Bone Joint Surg. 2008;90B(10):1334-1340.
2007	Wu L. Nonlinear finite element analysis for musculoskeletal biomechanics of medial and lateral plantar longitudinal arch of Virtual Chinese Human after plantar ligamentous structure failures. Clin Biomech (Bristol, Avon). 2007;22(2):221-229.
2000	Gefen A, Megido-Ravid M, Itzchak Y, Arcan M. Biomechanical analysis of the three-dimensional foot structure during gait: a basic tool for clinical applications. J Biomech Eng. December 2000;122(6):630-639.
2002	Gefen A. Stress analysis of the standing foot following surgical plantar fascia release. J Biomech. 2002;35(5):629-637.
2003	Gefen A. Plantar soft tissue loading under the medial metatarsals in the standing diabetic foot. Med Eng Phys. 2003;25(6):491-499.
2002	Arndt A, Ekenman I, Westblad P, Lundberg A. Effects of fatigue and load variation on metatarsal deformation measured in vivo during barefoot walking. J Biomech. May 2002;35(5):621-628.
2007	Budhabhatti SP, Erdemir A, Petre M, Sferra J, Donley B, Cavanagh PR. Finite element modeling of the first ray of the foot: a tool for the design of interventions. J Biomech Eng. 2007;129(5):750-756.
1946	Manter JT. Distribution of compression forces in the joints of the human foot. Anat Rec. November 1946;96(3):313-321.
1981	Nakamura S, Crowninshield RD, Cooper RR. An analysis of soft tissue loading in the foot: a preliminary report. Bull Prosthet Res. 1981;18(1):27-34.
2008	Cheng H-YK, Lin C-L, Wang H-W, Chou S-W. Finite element analysis of plantar fascia under stretch: the relative contribution of windlass mechanism and Achilles tendon force. J Biomech. 2008;41(9):1937-1944.
2010	Qian Z, Ren L, Ren L. A coupling analysis of the biomechanical functions of human foot complex during locomotion. J Bionic Eng. 2010;7(suppl 1):S150-S157.
1981	Carter DR, Caler WE, Spengler DM, Frankel VH. Fatigue behavior of adult cortical bone: the influence of mean strain and strain range. Acta Orthop Scand. 1981;52(5):481-490.
1985	Milgrom C, Giladi M, Stein M, Kashtan H, Margulies JY, Chisin R, Steinberg R, Aharonson Z. Stress fractures in military recruits: a prospective study showing an unusually high incidence. J Bone Joint Surg. November 1985;67B(5):732-735.
1980	Cavanagh PR, Lafortune MA. Ground reaction forces in distance running. J Biomech. 1980;13(5):397-406.
2010	Lieberman DE, Venkadesan M, Werbel WA, Daoud AI, D’Andrea S, Davis IS, Mang’Eni RO, Pitsiladis Y. Foot strike patterns and collision forces in habitually barefoot versus shod runners. Nature. January 28, 2010;463(7280):531-535.
1998	Qin Y, Rubin CT, McLeod KJ. Nonlinear dependence of loading intensity and cycle number in the maintenance of bone mass and morphology. J Orthop Res. July 1998;16(4):482-489.
2010	Qian Z-h, Ren L, Ren L-q, Boonpratatong A. A three-dimensional finite element musculoskeletal model of the human foot complex. In: Lim CT, Goh JCH, eds. 6th World Congress of Biomechanics (WCB 2010). August 1-6, 2010; Singapore. Heidelberg, Germany: Springer:297-300. IFMBE Proceedings; vol 31.
1998	Mosley JR, Lanyon LE. Strain rate as a controlling influence on adaptive modeling in response to dynamic loading of the ulna in growing male rats. Bone. October 1998;23(4):313-318.
2002	Camacho DLA, Ledoux WR, Rohr ES, Sangeorzan BJ, Ching RP. A three-dimensional, anatomically detailed foot model: a foundation for a finite element simulation and means of quantifying foot-bone position. J Rehab Res Dev. 2002;39(3):401-410.
2001	Jacob HAC. Forces acting in the forefoot during normal gait: an estimate. Clin Biomech (Bristol, Avon). 2001;16(9):783-792.

Year

Entry

1987

Ker RF, Bennett MB, Bibby SR, Kester RC, Alexander RM. The spring in the arch of the human foot. Nature. January 8, 1987;325(6100):147-149.

1989

Schaffler MB, Radin EL, Burr DB. Mechanical and morphological effects of strain rate on fatigue of compact bone. Bone. 1989;10(3):207-214.

2005

Erdemir A, Saucerman JJ, Lemmon D, Loppnow B, Turso B, Ulbrecht JS, Cavanagh PR. Local plantar pressure relief in therapeutic footwear: design guidelines from finite element models. J Biomech. September 2005;38(9):1798-1806.

2008

Hsu Y-C, Gung Y-W, Shih S-L, Feng C-K, Wei S-H, Yu C-h, Chen C-S. Using an optimization approach to design an insole for lowering plantar fascia stress: a finite element study. Ann Biomed Eng. 2008;36(8):1345-1352.

2008

Yu J, Cheung JT-M, Fan Y, Zhang Y, Leung AK-L, Zhang M. Development of a finite element model of female foot for high-heeled shoe design. Clin Biomech (Bristol, Avon). 2008;23(suppl 1):S31-S38.