1. 1
Increase in Tibial Stress Due to Pronation
Grace McConnochie, University of Portland, December 16th, 2015.
Abstract: A study was conducted to examine how the stress in a human tibia varied with increasing pronation usinga
finiteelement model with varyingtorsional load.MaximumVon Mises stress and strain in thetibia increased
significantly with a small increasein torsional load.This suggests thattibia is highly sensitiveto torsion and efforts to
limitpronation duringthe gaitcycleshould be encouraged to reduce tibial stressinjuries.
Introduction
Over pronation,via increased external rotation and
eversion of the subtalar jointduringthe gaitcycle,is
associated with a higher incidenceof medial tibial stress
fractures and medial tibial stresssyndrome.[1] However,
it is debatablewhether increased pronation is the cause
of increased tibial injuries.[2] Duringa normal gaitcycle,
as the foot progresses through pronation and supination
in the stance phaseof gait, the tibia typically rotates
through 15°.[3] When this angle is exceeded by 2-4
degrees, an increasein repetitive strain injuries areseen
to result.[4] An example of the pronation process can be
seen in figure1. It remains unanswered as to whether
injuries to the tibia aredue to increased stress in the bone
itself due to pronation,or other factors such as how
muscles exert forces on the bone. Little research has been
done to examine how pronation effects the stress within
the tibia,with most studies examining compressiveor
tensileloads.The mechanical properties of bone are
highly variableand depend on the direction and nature of
the loading.Duringrunning,the tibia is primarily subject
to an axial forceduringimpact,with this ground reaction
force reachingup to 3x body weight.[5] Pronation is
thought to inflictadditional stressvia torsion of the bone
which has been found to range from 8 to 24Nm.[6]
Consequently, the tibia is subjectto both normal and
shear stress. This projectaims to determine whether
pronation leads to a significantincreasein tibial stress
usinga finiteelement model that changes the extent of
tibial torsion to approximatethe degree of pronation.
Figure 1. Increasein tibial torsion with pronation.
Method
A model tibia was created usingSolidWorksCAD
modellingsoftware. Using3D photography, an image of a
solid model tibia was obtained.This image was then
converted to a stl fileand imported into SolidWorks.The
surfacewas used as a template from which to model the
tibia. A series of 18 cross sectional planes werecreated
perpendicular to the longitudinal axis. The intersection of
the template surfacewith each of these planes was
traced. Two guide curves were sketched alongthe
longitudinal axisof the tibia.A surfaceloft was then used
to join the cross sectional sketches,with the longitudinal
sketches actingas guidecurves. A flatsurfacewas
maintained at the proximal and distal ends in order to
maintain a simplesurfacefromwhich loads and boundary
conditions could beapplied.The surfaces were knitted
and thickened to 3.5mm which is approximately thatof
cortical bone.[7] The model was analyzed usingAutodesk
Mechanical Simulation software. The model tibia can be
seen in figure2.

2. 2
Figure 2: Tibia model compared with actual tibia.
The custom material was specified to be cortical bone
which provides the tibia with most of its strength and
mass.Sincecortical boneis anisotropic,material
properties were specified as given in table 1. A local
coordinatesystem was set up to allow the material
properties to be specified accordingly.
Table 1: Material properties of Cortical Bone.[8,9]
Plane Elastic
Modulus
(GPa)
Poisson’s
Ration
Density
g/cm3
Longitudinal 11.7 0.22 1.96
Transverse 8.2 0.21
The tibia was fixed over the proximal cross sectional
surface.Sincethe model tibia was of a small size,an axial
force of 1500N, equivalentto approximately 3x the body
weight of a small female,was applied axially atthe distal
end of the tibia to approximate the compressiveforce on
the tibia when running. A torsional load rangingfrom8 to
24Nm was applied distally in increasing increments of
4Nm. After the initial mesh was generated, the mesh was
further refined around the region of maximum Von Mises
stress.Maximal values for Von Mises stress and strain
were obtained for each loadingscenario. Astrain based
fatigue analysiswas also performed usingASM software.
The same axial load was applied with a 24Nm torsional
load to examine the fatigue lifewith the highest degree of
torsion.
Hand calculations wereperformed that approximated the
tibia as a hollowcylinder with the same axial and 24Nm
torsional load.Maximumnormal stress was determined in
order to verify the computational results.
The study was completed over a period of 3 weeks.
Results
Maximal Von Mises stress and strain increased with
increasingtorsional load.As seen in table 2, an 8Nm
torsional load resulted in a maximal Von Mises stress of
12MPa. This valueincreased to 29MPa for a 24Nm
torsional load. For maximum Von Mises strain,a torsion
of 8Nm resulted in 1920 microstrain which increased to
4790 for a 24Nm load. For the fatigue analysis,itwas
determined that failurewould occur after 5.83x1013
cycles.
Table 2: Results for maximal Von Mises Stress and Strain
for varyingtorsional load.
As shown in figure 3, both stress and strain showed a
linear relationship with increasingtorsional load.The
location of maximal stress and strain was in the lower
third of the tibia on the medial side.The Von Mises stress
distribution can beseen in figure 4.
Figure 3. Graph showing the linear increasein stress and
strain with increasingtorsional load.
Torsion
(Nm)
Max Von Mises
Stress (MPa)
Max von Mises
Strain (µɛ)
Cycles to
failure
8 12.10 1920 n/a
12 15.90 2550
16 20.30 3230
20 24.79 3970
24 29.36 4790 5.83x1013
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
0 5 10 15 20 25 30
VonMisesStrain
VonMisesStress(Mpa)
Torsion (Nm)
Maximal Von Mises Stress (Mpa) Max von Mises Strain

3. 3
Figure 4: Depiction of Von Mises stress distribution.
For the hand calculations,maximumnormal stress was
found to be 20.8MPa. The calculationsareattached in
appendix A.
Discussion
This analysisprovided an approximation for the change in
Von Mises stress and strain in a human tibia with torsion
as a resultof pronation during running.The location of
maximal stress and strain was themedial distal region of
the tibia.(Figure4) Since the majority of tibial stress
injuries occur in this region of minimal crosssectional
area,this location seems appropriate.
Both Von Mises stress and strain increased with torsion.It
would be expected that an increasein load would
increasethe amount of stress experienced by the
material.The extent to which the stress and strain
increased with a small increasein torsional load
compared to the largeaxial load was significant.
Increasingthetorsional load from8Nm to 24Nm
increased the maximal Von Mises stress by a factor close
to 3. Torsion generates shear stress and human bone is
much weaker in shear than it is in compression.Itis
therefore reasonablethatthe tibia bone is more sensitive
to stress as a resultof torsion.As a result, pronation
should be minimized to reduce tibial stressinjuries.
The maximum Von Mises stress obtained was 29.4MPa.
This valueseems a reasonableresultgivingthe yield
strength of cortical bonehas been estimated at 129MPa.
[10] This indicates thatthe tibia is notbeingsignificantly
stressed duringone step of the gait cycle when running
with excessivepronation.For confirmation,additional
hand calculationsapproximatingthetibia as a hollow
25mm diameter cylinder with a 24Nm and 1500N
torsional and axial load respectively resulted in a maximal
stress of 20.8MPa usingmaximal normal stress theory.
(See appendix A) Since the tibia varies in cross sectional
area,a stress of 20.8MPa would be expected to be slightly
lower than the maximal Von Mises stress of 29.4MPa
found usingthe finiteelement method.
The results obtained for maximal Von Mises strain are
also comparableto other studies. Mean strain during
running has been found to range from 3805 to 4864
microstrain.[11] Sincethe values obtained in this study
were maximum rather than average strain,itis
reasonablethatthe results of this study would be of
greater magnitude.
What should be recognized is that the loadingof the tibia
duringrunningor walking is repeated. If this load were
applied repeatedly is itpossiblefailurewould result.A
96mm3 specimen of cortical bonehas a probability of
failureof 0.63 at 86MPa for a stress endurancetest of
100,000 cycles till failure.[12] Another study has found
cortical bonefatigue strength is approximately 190Mpa
for 10 cycles or 160MPa at 1 million cycles.[13] Since
these stress values area lotlarger than the results
obtained, this suggests that a force of 3x bodyweight and
torsional load of 24Nm does not does resultin a
potentially damaginglevel of tibial stress.Astrain based
fatigue lifeanalysisfound that failurewould occur after
5.83x1013 cycles.This resultis significantly higher than
1million cycles till failureestimated for a stress of 160Mpa
and is also longer than the human lifespan. Given that the
maximum Von Mises stress found was lower than
160MPa,it seems reasonablethat failurewould occur ata
much later stage. It should be acknowledged that this
fatigue analysiscannottakeinto accountthe biological
nature of bone. If the loadingwere repeated to the extent

4. 4
which the rate of bone repair and remodeling was
exceeded by the micro damage created as a resultof
loading,bone injury is much more likely.Consequently,
the fatigue analysisdoes not give an accurateindication
of cycles till failure.
Although this model accurately depicted the geometric
shapeof the tibia,there were some limitations evidentin
the design. The thickness of cortical boneis not uniform
throughout the tibia.Sincethe design model could not
show the interior of the tibia,the cortical bonethickness
could only be approximated as an average value.As a
result,it is likely thatthe stress results obtained may
differ from the actual values.
Additionally,bonematerial properties areanisotropic,
and highly variable,dependent on other factors such as
mineral distribution, density and loadingenvironment.
[14] Although it was possibleto specify different material
properties in the transverseand longitudinal planes,this
cannot accountfor individual variations in bonedensity
and properties throughout the tibia. As result, the
maximum stress found should only be taken as an
indicativevalue.
It should also beacknowledged that the tibia is supported
by the fibula which was not modelled in this study.
Although itdoes not providesignificantsupport,the
fibular is still a weight bearingbone that would alter the
forces experiences by the tibia. Additionally,external
forces exerted on the tibia due to muscle contraction
would also beexpected to influence the resultingstress
distribution.
Conclusion
A finiteelement model was used to examine the stress
incurred in a human tibia duringthe gait cycle.From this
study, it can be shown that a torsional load significantly
increases the stress experienced in a human tibia.Since
pronation can placeadditional torsional loadingon the
tibia duringthe gaitcycle, this suggests that pronation is a
significantcontributor to medial tibial stress injuries.
Although the maximal stresses incurred froman axial load
of 1500N and a torsional load up to 24Nm were below
those thought to resultin failure,repeating loadingover
time could still lead to injury,particularly if excessive
pronation was not controlled,due to the biological
remodeling properties of bone in response to load.
Due to the limitationsin modellingtheexact bone
geometry, properties and loadingconditions, theresults
of this study should only be taken as indicativeof the
change in stress due to pronation. Future analysiscould
take into accountthe variablematerial properties and
thickness of cortical boneas well as examine other
potential loads due to bending and forces at sites of
muscleattachment.
Works Cited
1. Yates B, White S. The Incidenceand Risk
Factors in the Development of Medial Tibial
Stress Syndrome Among Naval Recruits
American Journal of Sports Med. April 2004.
32 (3)772-80;
doi:10.1177/0095399703258776
2. Maggs K. The DefinitiveGuide to Pronation:
Clinicians Version - RunningReform.
Running Reform. Accessed November 16,
2015.Availableat:
http://runningreform.com/the-definitive-
guide-to-pronation-clinicians-version/
3. Basic Biomechanics.Wefixfeet; Accessed
November 16, 2015. Availableat:
http://www.wefixfeet.ca/clinical.
4. Wesley, R. A. Investigation of Biomechanical
Risk Factors of Medial Tibial Stress
Syndrome through FiniteElement Analysis.
North Carolina Agricultural and Technical
State University; 2015.
5. Nilsson J,Thorstensson A. Ground reaction
forces at different speeds of human walking
and running. Acta Physiologic Scandinavica.
1989 Jun;136(2):217-27.
6. Kawamoto R, IshigeY, Watarai K,Fukashiro
S. QuantitativeInvestigation of Torsional
Loading of the Tibia duringQuick Changeof
Running Direction. International Journal of
Sport and Health Science. 2003;1(1):24-33.
doi:10.5432/ijshs.1.24.
7. Treece GM, Gee AH, Mayhew PM, Poole
KES. High resolution cortical bonethickness
measurement from clinical CTdata. Medical
Image Analysis. 2010;14(3):276-290.
doi:10.1016/j.media.2010.01.003.
8. Kulkarni MS,Sathe SR Experimental
determination of material properties of
cortical cadeveric femur bone. Trends in

5. 5
Biomaterials and Artificial Organs 2008;
22(1):9–15
9. Gaynor, E. Mechanical Properties and
Histology of Cortical Bonefrom Younger
and Older Men. Department of Anatomy,
The University of Michigan Medical School,
Ann Arbor, Michigan.
10. Carter DR, Caler WE, Spengler DM, Frankel
VH. Fatigue behavior of adultcortical bone:
the influenceof mean strain and strain
range. Acta Physiologic Scandinavica. 1981
Oct;52(5):481-90.
11. Edwards, W. B. Internal structural loadingof
the lower extremity during running:
Implicationsfor skeletal injury.Iowa State
University. 2010. Ames, Iowa.
12. Zioupos P, X TW, Currey JD. The
accumulation of fatiguemicrodamage in
human cortical boneof two different ages
in vitro. Clinical Biomechanics (Bristol,
Avon). 1996;11:365–75.
13. Black J, Ong K, Lovald S. Orthopaedic
Biomaterials in Research and Practice. New
York: Churchill Livingstone;113.
14. Edwards WB, Schnitzer TJ, Troy KL.
Torsional stiffnessand strength of the
proximal tibia arebetter predicted by finite
element models than DXA or QCT. Journal
of Biomechancis. 2013 Jun 21; 46(10):1655-
62. doi: 10.1016/j.jbiomech.2013.04.016.

6. i
Appendix A: Hand Calculations
Cortical bone was approximated as a cylinder with outer diameter 25mm and thickness 3.5mm.
Maximum Shear Stress
τ = T r / J
Where
τ = shear stress (Pa)
T = twistingmoment =24Nm
r = distancefrom center to stressed surfacein the given position d=.0125m
J = Polar Moment of Inertia of an Area J = π (D4 - d4) / 32 = π (.0254 - .02154) / 32 = 1.74e-8 m4
Gives T= 17.2MPa
Normal Stress
σ = Fn / A
Where
σ = normal stress (Pa)
Fn = normal component force =1500N
A = area = π (.0252 - .02152)/4 = 1.28e-4m2
Gives σ =11.7MPa
Sincebone is a brittlematerial usemaximum normal stress theory
σ1= √(11.72 + 17.22) = 20.8𝑀𝑃𝑎