Finite Element Analysis of Bone Remodeling:
Resident's Ridge Formation in Femoral Condyle
Yusuke TAKAHASHI, Shigehiro HASHIMOTO
Biomedical Engineering, Department of Mechanical Engineering,
Kogakuin University, Tokyo, 163-8677, Japan
shashimoto@cc.kogakuin.ac.jp http://www.mech.kogakuin.ac.jp/labs/bio/andHiromichi FUJIE
Human Mechatronic Systems, Faculty of System Design,
Tokyo Metropolitan University, Tokyo, Japanfujie@sd.tmu.ac.jp

ABSTRACTThe Resident’s ridge has been used as a landmark at surgicaloperations to reconstruct the anterior cruciate ligament,
although the mechanical background of the ridge has not beeninterpreted. The formation of Resident’s ridge on the human
femur has been analyzed under a hypothesis that the ridge isformed through interstitial fluid flow-induced bone remodelingin the present study. A two-dimensional analytical model has
been constructed with 228 x 20 cortical bone elements. A
tensile force of 485 N was applied to the surface of attachment
area of the ligament with an inclination angle of 7.6 degree tothe surface, while both the ends of the model were fixed.
Interstitial fluid flow rate and compressive strain in the model inresponse to the force application have been calculated with afinite element analysis software. Based on the flow rate orcompressive strain the bone shape near the ligament attachment
was remodeled until equilibrium state was attained. Results
revealed that high flow rate was observed at the end of ligament
attachment while almost negligible flow rate was observed at
the center of ligament attachment. Moreover, calculated bone
shape based on the flow rate distribution was similar to actualbone shape near the ligament attachment. It was, therefore,suggested that the Resident's ridge formation can be explainedby interstitial fluid flow-induced bone remodeling.

attachment of the ACL (Fig. 1) [1], has been used as a landmark
at surgical operations to reconstruct the ligament, although themechanical background of the ridge formation remains unclear.
To explain the ridge formation, we have proposed a hypothesisthat the ridge formation is occurred due to bone remodeling in
response to ACL force-induced interstitial fluid flow [2].
Following the hypothesis, the formation of the Resident’s ridge
has been analyzed with the finite element method in the presentstudy.

Keywords: Biomedical Engineering, Finite Element Analysis,
Bone Remodeling and Resident's Ridge Formation.

1. INTRODUCTION
The anterior cruciate ligament (ACL), which is one of four
major ligaments in the knee, is a crucial structure for knee
stability. Since the ACL is the most liable to failure andrupture in the four ligaments in daily and sports activities,
surgical reconstruction is often applied to restore the ligament
function. The Resident's ridge: a bony ridge near the femoralFig. 1: Resident's ridge (shown by red arrow) on theposterior-superior border of the lateral wall of the intercondylar
notch of the human femoral condyle [6].

2. METHODS
Finite Elements
A computational 2-D model of a cortical bone (22.8 mm × 2.0mm) near the ACL femoral attachment was created using
pixel-based finite elements in a FEM software (Abaqus 6.7,Simulia, USA) as shown in Fig.2. The size of each element
was of 0.10 mm × 0.10 mm. The bone was assumed to behomogeneous and isotropic material with Young’s modulus of
20 GPa [3] and Poisson’s ratio of 0.3. Moreover, the bone wasassumed to be permeable for water with the permeability of0.001 Pa s [4].
Calculation
A tensile force corresponding to 485 N of ACL force [5] hasbeen applied to the bone surface of 7.6 mm in width [6] at thecenter of the model with an inclination angle of 7.6 degree tothe surface [Matsuda], while both the lateral ends of the model
was fixed. Interstitial fluid flow rate and compressive strain in
the model in response to the force application was calculated.
Referring to a bone remodeling analysis by Tsubota et al. [2],bone surface movement was performed by adding a newelement on a surface if the flow rate in an element was higher
than 6.0 × 10-2 mm/s. Simultaneously, the element waseliminated if the flow rate was lower than 0.1 × 10-2 mm/s.
The procedure including the flow rate analysis and bone surface
movement was repeated until equilibrium state was attained.
For comparison, strain-induced bone remodeling analysis was
also performed under a condition that element addition wasperformed in response to compressive strain (> 2.0 × 105) andelement elimination was performed in response to tensile strain(> 3.5 × 105), referring to a previous study by Fujie [7].

Fig. 3: Interstitial fluid flow-induced bone remodeling withflow rate distribution (a: first step before remodeling, b; 5th stepof remodeling, c; 10th (final) step of remodeling)
1 mmFig. 4: Histological (HE) observation of the human femoral
ACL attachment.

3. RESULTS

Fig. 2: 3-D CT image of the human knee including the femoral
attachment of the ACL and 2-D model of the femoral corticalbone with the ACL force applied to the ACL attachment area.

Results revealed that the flow rate was very high at both sidesof ligament attachment while it was almost negligible at thecenter of ligament attachment (Fig. 3a). The bone surface
structure near the ACL attachment was gradually remodeled
during the flow rate-induced remodeling calculation (Fig. 3b),and finally reached to an equilibrium state (Fig. 3c). Note thatthe anterior side of the ACL attachment (right circle in Fig. 3c)
was remodeled from a flat shape to a Resident's ridge-likestructure of 0.8 mm in height and 1.4 mm in width. Moreover,another ridge formation was observed at the other side of theACL attachment (left circle in Fig. 3c) while a bone resorption
was observed near the center of the ACL attachment (centercircle in Fig. 3c). In comparison, equilibrium state was not
attained in the strain-induced bone remodeling (Fig. 4). At the10th remodeling calculation, a broad but low ridge of 0.4 mm inheight and 4 mm in width was observed at the anterior side ofthe ACL attachment. Note that bone absorption was observedat the other side of the ACL attachment but was not observed
near the center of the attachment.

4. DISCUSSION

6. ACKNOWLEDGMENT

Calculation of the flow rate-induced bone remodeling wasreached to an equilibrium state that clearly indicates a
Resident's ridge-like bone structure. Moreover, another ridge
formation at the other side and bone resorption near the center
were observed within the ACL attachment. These remodeled
structures obtained in the bone remodeling analysis were similar
to actual bone structure. Note that the quantitative results
were dependent on the analytical condition, however, the trendof the obtained results as to ridge formation and bone resorption
were identical regardless of the condition. It was, therefore,suggested that the Resident's ridge formation and associatedbone structure changes can be explained by interstitial fluid
flow-induced bone remodeling. Although ridge-like boneformation was observed at not only anterior side but also
posterior side of the ACL attachment, flow direction wasdifferent; outlet flow in the anterior side versus inlet flow in theposterior side. This difference in flow direction may cause a
difference in bone formation. Moreover, the fluid flow rates ofremodeling condition were not based on experimental results.
Further and more detailed studies are required for the analysisof the Resident's ridge formation, including an in vitro study as
regard with osteocyte response to interstitial flow.

This work was supported by a Grant-in-Aid for Strategic
Research Foundation at Private Universities from the Japanese
Ministry of Education, Culture, Sports and Technology.

5. CONCLUSION
A two-dimensional analytical model has been constructed with
228 x 20 cortical bone elements. A tensile force of 485 N wasapplied to the surface of attachment area of the ligament with aninclination angle of 7.6 degree to the surface, while both theends of the model were fixed. Interstitial fluid flow rate andcompressive strain in the model in response to the force
application have been calculated with a finite element analysis
software. Based on the flow rate or compressive strain thebone shape near the ligament attachment was remodeled until
equilibrium state was attained. Results revealed that high flowrate was observed at the end of ligament attachment whilealmost negligible flow rate was observed at the center ofligament attachment.

REFERENCES[1] K. Shino, T. Suzuki, T. Iwahashi, T. Mae, N. Nakamura, K.
Nakata and S. Nakagawa, “The Resident’s Ridge as an
Arthroscopic Landmark for Anatomical Femoral Tunnel
Drilling in ACL Reconstruction”, Knee Surgery, Sports
Traumatology, Arthroscopy, Vol. 18, No. 9, 2010, pp.
1164-1168.
[2] K. Tsubota, T. Adachi and Y. Tomita, “Functional Adaptationof Cancellous Bone in Human Proximal Femur Predicted by
Trabecular Surface Remodeling Simulation Toward Uniform
Stress State”, Journal of Biomechanics, Vol. 35, No. 12,
2002, pp. 1541-1551.
[3] J.C. Lotz, T.N. Gerhart and Hayes WC, “MechanicalProperties of Metaphyseal Bone in the Proximal Femur”,
Journal of Biomechanical Engineering, Vol. 113, No. 4,1991, pp. 317-329.
[4] E.A. Nauman, K.E. Fong and T.M. Keaveny, “Dependenceof Intertrabecular Permeability on Flow Direction andAnatomic Site”, Annals Biomedical Engineering, Vol. 27,
No. 4, 1999, pp. 517-524.
[5] E.H. Chen and J. Black, “Materials Design Analysis of theProsthetic Anterior Cruciate Ligament”, Journal ofBiomedical Materials Research, Vol. 14, No. 5, 1980, pp.
567-586.
[6] M.L. Purnell, A.I. Larson and W. Clancy, “Relationships toCriticalBony
Landmarks
Using
High-resolution
Volume-rendering Computed Tomography”, American
Journal of Sports Medicine, Vol. 36, 2008, pp. 2083-2090.
[7] H. Fujie, K. Nakata and K. Shino, “Resident's Ridge
Formation Due To ACL Force-Induced Bone Remodeling”.
Japanese Clinical Biomechanics and Related Research,
ORS 2013 Annual Meeting, Poster No: 1383