patient-specific finite element analysis of chronic contact stress exposure after intraarticular...

$: Patient-specific finite element analysis of chronic contact stress exposure after intraarticular fracture of the tibial plafond$
Patient-Specific Finite Element Analysis of Chronic Contact StressExposure after Intraarticular Fracture of the Tibial Plafond

Wendy Li,1 Donald D. Anderson,1,2 Jane K. Goldsworthy,1 J. Lawrence Marsh,2 Thomas D. Brown1,2

1Department of Biomedical Engineering, The University of Iowa, 2181 Westlawn Building, Iowa City, Iowa 52242, 2Department of Orthopedics andRehabilitation, The University of Iowa, 2181 Westlawn Building, Iowa City, Iowa 52242

Received 21 September 2007; accepted 7 January 2008

Published online 10 April 2008 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jor.20642

ABSTRACT: The role of altered contact mechanics in the pathogenesis of posttraumatic osteoarthritis (PTOA) following intraarticularfracture remains poorly understood. One proposed etiology is that residual incongruities lead to altered joint contact stresses that, over time,predispose to PTOA. Prevailing joint contact stresses following surgical fracture reduction were quantified in this study using patient-specific contact finite element (FE) analysis. FE models were created for 11 ankle pairs from tibial plafond fracture patients. Both (reduced)fractured ankles and their intact contralaterals were modeled. A sequence of 13 loading instances was used to simulate the stance phase ofgait. Contact stresses were summed across loadings in the simulation, weighted by resident time in the gait cycle. This chronic exposuremeasure, a metric of degeneration propensity, was then compared between intact and fractured ankle pairs. Intact ankles had lower peakcontact stress exposures that were more uniform and centrally located. The series-average peak contact stress elevation for fractured ankleswas 38% (p¼ 0.0015; peak elevation was 82%). Fractured ankles had less area with low contact stress exposure than intact ankles and agreater area with high exposure. Chronic contact stress overexposures (stresses exceeding a damage threshold) ranged from near zero to ahigh of 18 times the matched intact value. The patient-specific FE models represent substantial progress toward elucidating the relationshipbetween altered contact stresses and the outcome of patients treated for intraarticular fractures. � 2008 Orthopaedic Research Society.

Published by Wiley Periodicals, Inc. J Orthop Res

Keywords: joint incongruity; finite element analysis; intraarticular; posttraumatic osteoarthritis

The pathogenesis of osteoarthritis (OA) is poorly under-stood. Rapid onset and progression of OA often followinjury to a joint, its surrounding ligaments, and/or thejoint capsule.1 A recent study2 estimated that 12% ofreported cases of symptomatic OA involving one of themajor joints of the lower extremity (hip, knee, or ankle)are posttraumatic. Posttraumatic osteoarthritis (PTOA)is an especially predictable outcome following displacedintraarticular fractures,2–4 particularly so for the tibialplafond fracture of the ankle. The mechanopathology ofPTOA has been linked to three causative factors: acuteinjury severity, chronic pathological loading due to re-sidual instability, and elevated stresses due to residualincongruity.5–7 To understand better the relative in-fluence of each factor on the progression of cartilagedegeneration leading to PTOA, it is desirable to quantifyeach factor independently and accurately and to cor-relate each with long-term patient outcome.

Displaced tibial plafond fractures are typically treat-ed with surgical reduction and fixation, with the goal ofdecreasing any deleterious mechanical consequences ofarticular incongruity. Unfortunately, the study of thesemechanical effects has been limited to animal andcadaveric experiments involving idealized representa-tions of fracture incongruity and joint loading.1,3,6,7

Altered joint mechanics in a series of intraarticularfracture patients has only been assessed indirectly, bycrude measures of the degree to which the articularsurface is restored.8 These measurements are imprecise,

and constitute an imperfect surrogate for the mechanicalenvironment to which the cartilage is exposed followingtreatment and fracture healing.

Patient-specific finite element (FE) stress analysisprovides a useful tool for assessing altered joint mechan-ics. To date, only a few FE models of the ankle joint havebeen developed, and few attempts have been made to usethem in simulating the entire sequence of load variationencountered during gait or other functional activities.Moreover, the majority of FE models of natural jointcontact stresses have simulated intact contact surfaces.The limited work with incongruity models has beenrestricted to simplified geometries such as step-offs andgaps.3 There have as yet been no FE models of articularirregular incongruities secondary to actual intraarticu-lar fractures in human patients.1

Our objective was to quantify joint contact stressalterations accompanying surgically reduced tibial pla-fond fractures using patient-specific FE analyses. Abetter understanding of altered contact stresses and thecorresponding patient clinical outcome with residualincongruity may help guide future fracture treatmentdecisions.

MATERIALS AND METHODSAnalysis cases were drawn from an ongoing clinical series of36 patients with unilateral tibial plafond fractures. The anklesfrom 11 patients were successfully modeled, with poor CT scanquality being the primary reason for case exclusion. Patientage ranged from 20 to 57 years old (mean of 33.5 years;SD¼ 11.4 years). Fractures ranged in severity from a simpleB-1 through a highly comminuted C-3 by the AO/OTA clas-sification.9 Informed consent was obtained from each patientunder institutional review board approval. The fractures weretreated using articulated external fixation combined withlimited internal fixation.10 Plain radiographs (AP, lateral, andmortise views) and CT scans were taken of the patients’ ankles.

JOURNAL OF ORTHOPAEDIC RESEARCH AUGUST 2008 1039

Correspondence to: Donald D. Anderson (T: 335-8135; F: 319-335-7530; E-mail: [email protected])

This article includes Supplementary Material available via theInternet at http://www.interscience.wiley.com/jpages/0736-0266/suppmat.

� 2008 Orthopaedic Research Society. Published by Wiley Periodicals, Inc.

FE Model GenerationScans were taken of patients’ uninjured contralateral intactankles and of their fractured ankles within 12 h of surgicalreduction. Helical CT scan settings were either 2-mm slicethickness� 0.5-mm reconstruction or 0.63-mm thickness�0.3-mm reconstruction. Slices were 512� 512 pixels acquiredin the transverse plane with a field of view selected to providein-plane spatial resolutions from 0.25 to 0.5 mm.

Tibial and talar bony surfaces were extracted from the CTimage data using an iso-surfacing algorithm (OsiriX software;www.osirix-viewer.com).11 Surfaces were formed by subvoxelinterpolation of Hounsfield intensities, based on a user-specified threshold. The resulting surfaces were smoothedand further refined utilizing reverse engineering software(Geomagic Studio; Geomagic, Research Triangle Park, NC).These tools allow a user to smooth globally or alternatively tosmooth local regions of a surface interactively. The samemodest degree of global smoothing was applied to intact andfractured ankle surfaces, with fractured surfaces usuallyrequiring further interactive local smoothing, owing to focalsurface incongruities. The aim was to smooth features judi-ciously, balancing the smoothness requirements for successfulFE contact simulation versus the need to preserve local surfaceirregularities to capture associated stress aberrations. Becausesmoothing can substantially influence FE-predicted contactstresses (20 to 30% reduction in peak contact stress12), it waskept to the minimum amount necessary to obtain successfulFE solutions.

The average 3D deviation (across all processed ankles)between raw and smoothed surfaces was�0.32 mm (Fig. 1; also,see supplementary materials for full details of the surfacesmoothing). This average value represents the difference of thefinal smoothed surface from the raw iso-surface extracted fromCT data, rather than the difference of the smoothed surfacefrom true anatomic geometry (as the latter was unavailable).Smoothed surfaces were then extruded 1.7 mm along thesurface normal directions to define uniform thickness cartilagevolumes.13

CT data were acquired while patients lay supine with theirankle joints plantar-flexed and externally rotated. This relaxedankle posture was not a functionally neutral pose of the ankle atthe beginning of the stance phase of level walking. Therefore,working in an interactive medical data visualization environ-ment (Data Manager; B3C BioComputing Competence Center,Bologna, Italy),14 an experienced ankle surgeon prescribed

neutral weight-bearing apposition, using previously describedprocedures.15 For the 11 cases, reorientation of the jointranged from 8 to 358 of dorsiflexion and from 0 to 188 of internalrotation. A landmark-based local reference frame was definedas well, and the ankle was reoriented to align this local framewith a clinically appropriate global reference frame for sub-sequent ankle joint loading simulation.

FE meshes, representing the cartilage volume bounded bythe subchondral plate, were then generated using commercialmeshing software (TrueGrid; XYZ Scientific Applications,Livermore, CA). The number of elements used was determinedin a mesh convergence study. About 30,000 eight-noded linearhexahedral elements sufficed to represent the tibial and talarcartilage. Each cartilage volume consisted of four elementlayers. The cartilage was backed with, and fixed to, a layer ofrigid, four-noded quadrilateral shell elements, simulating themuch stiffer subchondral plate. Simulations of the stance phasewere performed using commercial FE software (ABAQUSStandard v.6.5; ABAQUS, Pawtucket, RI). The FE modelformulation was previously detailed.15 Briefly, the cartilagevolumes were modeled as homogeneous, isotropic and linearlyelastic, with a Young’s modulus of 12.0 MPa and a Poisson’sratio of 0.42.16,17 The coefficient of friction was set at 0.01.18

The FE analyses included several provisional loading steps(to bring the joint into a seated apposition as governed bythe articular surfaces), followed by 13 steps spanning the stancephase of gait. All rotational movements and compressiveloadings were applied to reference nodes (one for each bone)defined on the (rigid) tibial and talar subchondral surfaces.Reference node locations were selected to be coincident along aprovisional ankle plantar/dorsiflexion axis at the midpoint ofthe talar condyles when the ankle was first loaded. The tibiawas incrementally rotated through a sequence of angles rang-ing from 58 plantar to 98 dorsiflexion, while loaded with aconcentrated follower load of a magnitude scaled from thepatient’s body weight19 (Fig. 2). An arthritic loading history wasused because arthritic patients tend to exhibit decreasedloading; the maximum applied load was scaled to 320% bodyweight, rather than the normal 470% body weight. The taluswas allowed to reorient relative to the tibia as it was loaded,constrained by articular geometry and a light medial/lateralspring (linear stiffness¼ 100 N/mm) included as a surrogate forfibular support.

This FE model formulation was previously validated bycomparing computed contact stresses to those measured in twocadaveric ankles using a thin-film pressure sensor.20 Theexperimental data from that physical validation enabled sys-tematic selection of key model parameters, such as degree ofsurface smoothing and mesh refinement.

PostprocessingContact areas were calculated for the instant of peak loading,which occurred at about 60% of the stance phase. Area data atthat instant were then binned according to their prevailingcontact stress magnitudes. The contact area bin totals wereplotted against the contact stress magnitudes as area engage-ment histograms.

Contact stress data from the 13 incremental solutions wereused to calculate cumulative chronic contact stress exposureand overexposure. Exposure is a measure of the joint’s contactstress history over a specified time period, whereas over-exposure is a measure of deleterious mechanical insult. Thesemetrics were defined similarly to those used in an earlier studyof patients with congenital hip dislocation, in which a positivecorrelation was found between elevated cumulative contact

Figure 1. The process for generating patient-specific models.Inferior views of intact and fractured (reduced) source CT images,raw tibial bone surfaces from CT, smoothed tibial bone surfaces, andFE meshes of the cartilage volumes. (Data for patient #4.) [Colorfigure can be viewed in the online issue, which is available at http://www.interscience.wiley.com]

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JOURNAL OF ORTHOPAEDIC RESEARCH AUGUST 2008

stress overexposure and long-term patient outcome (incidenceand progression of OA).21 Cumulative chronic contact stressexposures were calculated over the tibial articulating surfaceon a step-by-step basis:

Pcumulative ¼X13

i¼1

ððPi � PdÞ � DtiÞ ð1Þ

where Pcumulative is the per-gait cycle cumulative contact stressexposure distribution (in MPa-s); Pi are the FE-computednodal contact stresses at a given increment in the gait cycle, i,varying across the 13 load increments; Pd is a contact stressdamage threshold (remaining to be established); and Dti is theresident time (seconds) associated with a given increment inthe gait cycle (assuming a cadence of 58 steps/minute19). WhenPd is taken to be zero, Pcumulative provides a raw exposure value.

For computing a cumulative chronic contact stress overex-posure, the contact stress damage threshold, Pd, was set to6 MPa, based upon an assumption that in intact ankles, onewould not expect OA to develop, and therefore a nominal over-exposure value below the tolerance of the joint (here assumedto be nearly zero, but another value remaining to be esta-blished) would be expected.

Statistical AnalysesBecause the differences between intact and fractured resultswere not normally distributed, the Wilcoxon’s signed-rankstest was used to compare results between the intact andfractured cases instead of the traditional Student’s pairedt-test. The chi-squared (w2) test of homogeneity for comparisonof two histograms was applied to compare the average areaengagement histograms.22 Significance was set at p< 0.05.

RESULTSThe tibial articulating surfaces for the intact and(surgically reduced) fractured ankles are shown inFigure 3 (ankles mirrored, as necessary, to simplifyvisualization). The surfaces of the reduced ankles showdistinct fracture lines and fragment displacement. Ingeneral, the intact ankles had lower peak exposurevalues and more uniform, centrally positioned exposurepatches, than the (reduced) fractured ankles (Fig. 4).

FE-based scalar metrics included peak contact stress,contact area, and contact stress overexposure. The peakcontact stress and contact area values were reported forthe instant in the gait cycle with maximal joint load-ing, roughly 61% through the stance phase, in a 7.58dorsiflexed position. Series-wide, computed peak contactstress values of intact and fractured cases were 10.1�1.8(mean�SD) and 13.8�1.8 MPa, respectively, a signifi-cant difference (p¼ 0.0015). However, the ranges of peakvalues overlapped substantially: 7.4 to 12.9 MPa forintact cases and 11.0 to 16.5 MPa for fractured cases. Thegreatest difference in peak contact stress betweenmatched intact and fractured ankles was 82%; the smal-lest was 6%.

The average contact areas for intact and fractured caseswere 705.5�102.9 and 636.4�122.4 mm2, respectively(not significant, p¼0.051). In general, the intact caseshad a greater amount of area with low exposure valuesand a smaller amount of area with high exposure values,compared to the fractured cases (Fig. 5). The two areaengagement histograms had significantly different dis-tributions (p¼0.011).

The series-wide average, peak per-gait cycle over-exposure values for intact and fractured cases were0.6� 0.4 MPa-s and 1.5�0.5 MPa-s, respectively(Fig. 6). For some patients, the difference in stress over-exposure between intact and fractured ankles wasrelatively minor, while for others, the difference wasdramatic (from 1.5-fold to 18-fold).

DISCUSSIONClinical experience has shown that residual articularincongruity is poorly tolerated and is implicated in the

Figure 2. Anterosuperior (subchondral) view of the contactstress distributions of the 13 instants of the stance phase of gaitfor the intact and fractured ankles of patient #4. [Color figure can beviewed in the online issue, which is available at http://www.interscience.wiley.com]

CHRONIC CONTACT STRESS EXPOSURE AFTER INTRAARTICULAR FRACTURE 1041


progression of joint degeneration. A better understand-ing of the mechanopathology of PTOA is required toguide treatment decisions that may forestall or preventdisease progression. The present patient-specific FEmodels represent an advance in assessing elevated con-tact stresses due to residual articular incongruity, a

Figure 3. Anteroinferior view of thepatient-specific tibial articulating surfacesfor intact and (reduced) fractured ankles of all11 patients. Patient and fracture character-istics were as shown.

Figure 4. Inferior view of the contact stress exposure distributionon the tibial articulating surfaces for the intact and (reduced) fractur-ed ankles of all 11 patients. [Color figure can be viewed in the onlineissue, which is available at http://www.interscience.wiley.com]

Figure 5. Series-wide average, area engagement histograms forthe intact and fractured ankles. [Color figure can be viewed in theonline issue, which is available at http://www.interscience.wiley.com]

1042 LI ET AL.


factor influencing the clinical outcome of patients treat-ed for intraarticular tibial plafond fractures. To ourknowledge, this is the first FE comparison of contactstress of fractured versus intact joints in a clinicalseries. Moreover, the formulation addresses not just asingle isolated loading instant, but rather loadingsthroughout the stance phase.

Our FE results are consistent with experimentalvalues in the literature. Despite different test setups anddifferent applied loads, the contact area values reportedfor the normal ankle joint are surprisingly consistent,with average values of 558� 122 mm2.23–26 The averageintact contact area from our study (in neutral apposition)is 578�83 mm2.

The peak contact stress and range for the intact casesin neutral agree reasonably well with values measuredby Vrahas et al.,23 who reported a series-average peakstress value of 6.7 MPa (range of 2–12 MPa) in cadavericankles statically loaded to 1360 N. Our computationallypredicted series-average peak contact stress value forneutral apposition, at a mean of 1492 N load, was6.8 MPa (range of 5–9 MPa). A cadaveric study of theeffect of increasing degrees of residual incongruity in theform of step-offs in the knee joint was evaluated byBrown et al.6 They found that the cartilage contactstresses generally increased with greater step-off size,and that at 3-mm step-off level, contact stresses in-creased approximately 75%.

Elevated contact stresses have been implicated in thehigh incidence of unsatisfactory outcome in intraarticu-lar fracture series.1,8 Elevated stresses attributed toresidual incongruity have been well documentedthrough in vitro studies, but the degree of elevation hasbeen postulated to be within the range tolerated byarticular cartilage.6 Simply assessing the magnitude ofcontact stress elevation, without accounting for theeffects of exposure time, did not correlate well withlong-term outcome in a study of congenital hip disloca-tion.21 However, contact stress overexposure correlated

with outcome with 82% reliability, suggesting that thecumulative effect of loading over time may influencelong-term joint health more than does loading magni-tude at any one instant.

The area engagement histograms showed that frac-tured ankles had a larger area with higher contact stresscompared to intact ankles. A larger contact area ex-periencing higher than normal loading over time mayinitiate cartilage degeneration, as maintenance of cartil-age structure is dependent on appropriate mechanicalloading.27–29 The question arises: at what level arestresses pathological? Although first-estimate data existfor the hip,21 the answer may well be joint-specific. Thevalue of 6 MPa for the ankle that we used must be viewedas provisional, based on an assumption that normalankles operate near the margin of tolerance.

The use of FE modeling necessarily involves simplify-ing assumptions. Although articular cartilage is struc-turally biphasic and exhibits viscoelastic behavior undercertain conditions, experimental testing has demon-strated that its stress–strain response under physiolog-ical loading rates is nearly linear.30 Recent theoreticalwork has further established the equivalence of short-time biphasic and incompressible elastic responses forarbitrary deformations and constitutive relations, fromfirst principles.31 Thus, a linear elastic cartilage modelseems reasonable for simulating level walking. Smooth-ing of the segmented subchondral bone surfaces wasnecessary for FE modeling, and articular cartilagethickness variations not included in the models wouldaffect stress loading patterns. A recent study with highaccuracy (�2 mm) found that ankle cartilage thickness isrelatively homogeneous throughout the weight-bearingareas of the joint.25 Given substantial earlier agreementbetween the intact FE model formulation and thevalidation cases, these simplifications therefore seemreasonable, especially for the intact joints.

For the fractured ankles, a constant uniform cartilagethickness of 1.7 mm was used, extruded from subchon-dral bone surfaces segmented from CT scans (as cartilagewas not well visualized). As the ankles were imagedshortly following surgical fracture reduction, the use ofCT arthrography or MRI to provide a mapping ofcartilage thickness was deemed unethical, as well asunlikely to yield accurate measures. Another limitationis that the scans were obtained prior to definitive weight-bearing, so there could be some shifting of reconstructedfragments in the unstable fracture configurations, aswell as further bone remodeling as the fractures heal.

Subchondral bone compressive modulus is almost twoorders of magnitude stiffer than articular cartilage.16,32

Treating subchondral bone as rigid therefore seems anacceptable assumption. The ligaments and fibula werenot explicitly included in the FE models because of theirrelatively minor contributions to stability and loadbearing of normal ankles. However, a medial/laterallinear spring was attached to the talus to provide amodest degree of fibular support. The dominant role thatarticular geometry plays in ankle stabilization within

Figure 6. Plot of peak contact stress overexposure (damagethreshold Pd¼ 6 MPa; see Equation 1) for the intact and (reduced)fractured ankles of 11 patients. [Color figure can be viewed in theonline issue, which is available at http://www.interscience.wiley.com]



normal ranges of motion has been experimentallydocumented in cadaveric testing.33 Other experimentalstudies show that the fibula transmits less than 20% ofthe ankle load.34

Orthopedic surgeons and researchers generally agreethat it is important to ascertain the factors that influencejoint injury outcome.8 To our knowledge, the presentankle contact FE analysis is the first to incorporate case-specific ankle geometry from a series of patients treatedfor intraarticular ankle fractures, to simulate the entirestance phase of gait, and to utilize summary metrics(cumulative exposure) intuitively relevant to PTOAonset. As such, it constitutes a step forward towardassessing chronic cumulative contact stress overexpo-sure dosages on a patient-specific basis and towardestablishing joint-specific tolerance levels for PTOA. Aslonger term follow-up of the present series of patientsbecomes available, it will provide the type of outcome/validation data required for these purposes.

ACKNOWLEDGMENTSFinancial support was provided by grants from the NIH(AR46601, AR48939, and AR55533). Ms. Valerie Muehling andMr. Andrew Pick helped collect clinical case data, and Dr. YukiTochigi assisted with the manual posing of the ankle models.Dr. Fulvia Taddei and Dr. Marco Viceconti (Istituti OrtopediciRizzoli) kindly provided assistance with the Data Managersoftware.

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