Simulation of Ridge Formation in Cortical Bone near theAnterior Cruciate Ligament Insertion: Bone Remodeling due toInterstitial Fluid FlowYusuke TAKAHASHI, Shigehiro HASHIMOTO
Biomedical Engineering Laboratory, 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
Biomechanics Laboratory, Faculty of System Design,
Tokyo Metropolitan University, Tokyo, 191-0065, Japanfujie@sd.tmu.ac.jp http://www.comp.sd.tmu.ac.jp/fujielab/ABSTRACT
The ridge formation in the cortical bone near the anterior
cruciate ligament (ACL) insertion has been simulated based onbone
remodelingduetointerstitial
fluidflow.
Three-dimensional (3-D) data of cortical bone at the distal endof the femur were obtained from a computer topography imageof a human knee joint, and were transformed to a 3-D voxel
model consisting of voxel elements of 500 × 500 × 500 μm insize. A finite element analysis software (ABAQUS) wasutilized to determine the interstitial fluid flow in the corticalbone in response to the application of ACL tensile force, tibialcompressive force, and patellar compressive force. Boneremodeling analysis was repeated until equilibrium in which anew voxel element was added on a surface where local flow rate
was higher than predefined thresholds. Results revealed thatridge formation occurred in response to the force application andthe ridge structure was dependent on the thresholds of interstitial
fluid flow rate.
Keywords: Biomedical Engineering, Finite Element Analysis,
Bone Remodeling, Resident's Ridge Formation Anterior
Cruciate Ligament and Interstitial fluid flow.

1. INTRODUCTION
Resident's ridge near the anterior cruciate ligament (ACL) on thefemoral condyle in the knee joint is clinically used as alandmark to find the bone tunnel position at the surgical ACL
reconstruction surgery. Numerous numbers of anatomical
researches have been reported as regard with the dimension andstructure of the ridge [2-6]. However, the analytical model offemur used in the studies was two dimensions, so it was difficult
to simulate to physiological condition. Therefore, we developeda three dimension femoral cortical bone model to perform aprecise bone remodeling analysis in the present study. To
biomechanically explain the Resident’s ridge formation, wehypothesized that due to interstitial fluid flow in response toexternal loads. The analysis was reported with a variety of thethreshold of flow rate. However, the mechanism of formation of
the ridge has not been well explained. A 3-D model of thedistal femur has been created with the cortical bone in thepresent study. Meanwhile, the structure of trabecular bone hasbeen biomechanically based on bone remodeling due tocompressive strass/strain [7] and interstitial fluid flow [8, 9].
Therefore, Fujie et al proposed that the Resident’s ridge
formation can be explained by bone remodeling due tocompressive strain [10] and interstitial fluid flow [11].

2. METHODS
Finite Elements Model
The cancellous bone of femur, the tibia and patella wereremoved from the CT image of the human knee joint with theimage editing software of GIMP (GNU Image Manipulation
Program) (Fig. 1). Finite element model was configured withvoxel elements using VOXELCON (QUINT, 2013). The sideof voxel was 500 μm. ABAQUS (6.13) was used for finite
element analysis in which each element was assumed to behomogeneous and isotropic with elastic modulus of 20 GPa [10]and Poisson’s ratio of 0.3. The permeability of the element
was 5.13 × 109 m2 [12] for the interstitial fluid of 0.001 Pas ofviscosity. The pore pressure elements (C3D8RP) were used tovisualize the interstitial fluid flow.

(a)

59.5N

300N
485 N
300N

RemodelingFig. 1: Three dimensional model of cortical bone at the distal
end of femur and forces applied to femur three external.

Calculation
The force applied from the patella to the femur (F3) wascalculated with the following equations,
F1 = F2 cosθ1 + F3 sinθ2F2 sinθ1 = F3 cosθ2(b)

(1)
(2)

where F1 is quadriceps force, while F2 is the force of patellar
ligament force, θ1 is acute angle between F1 and F2, and θ2 is thecomplementary angle between F1 and F3.
In the present simulation, F1 was set at 136 N, referred from
quadriceps using muscles analysis of quadriceps during gateusing Opensim. The direction of F1 was parallel with the boneaxis of the femur. θ1 is 0.43 rad that corresponds to the angle
between the bone axis and the patellar ligament. θ2 was 0.17
rad that corresponds to the flexion angle of the knee joint at theheel strike position in gate.
The point of application of F3 was referred from the previous
anatomical study by Tecklenburg et al. [13]. The position ofattachment of the ACL was determined with the previous
anatomical study by Andrew et al. [16] and Iriuchishima et al.
[17]. The proximal end of femur was fixed while, the force of
300 N was applied on head medical and lateral of the distal endof the femur (Fig. 1).
F1 was increased to 600 N while F3 was also increased to thetarget value for 1s. Subsequently, F2 was increased to the targetvalue, while F1 and F3 were kept constant (Fig.4).
Bone Remodeling Process
The bone remodeling process was started, when F2 reached tothe target value. A new voxel element was added on the element,
in which the flow rate exceeds the threshold value of either 0.75,
1.00, 1.25 or 1.50 μm/s, under an assumption that boneformation occurred where local flow rate exceeded the threshold.
This calculation process was repeated twice. Note that ACL
attachments were elevated to the surface of a remodeled bonevoxel (Fig.2).

Fig. 2: Upward movement of the ACL insertion to adding
elements where the flow rate exceeds thresholds value.

3. RESULTS
Fig. 3 shows the distribution of the flow rate before remodelingcalculation started. The direction of interstitial flow rate wasalmost perpendicular to the surface of the cortical bone (Fig. 4).
The high flow rate occurred in the anterior distal area ofattachment of the ligament. Figs. 5-8 show the first and secondsteps of remodeling with the threshold of the flow rate of 0.75μm/s, 1.00 μm/s, 1.25 μm/s and 1.50 μm/s, respectively.
The area of bone formation decreased as the increase of thethreshold of flow rate. Resident’s ridge-like bone formation
occurred at the thresholds of the flow rate of 0.75 μm/s and of
1.00 μm/s (Figs. 9(A) and 9(B)). On the other hand, suchformation did not occurred at the threshold of the flow rate of
1.25 μm/s.

Fig. 4(B): Flow rate distribution at the first step of remodelingcalculation

Fig. 3: Distribution of flow rate before the start of remodelingcalculation.

Fig. 5(A): Interstitial fluid flow-induced bone remodeling at thefirst step of remodeling calculation with a threshold of flow rateof 0.75 μm/s.

Fig. 4(A): Interstitial fluid flow before the start remodelingcalculation at cortical bone surface.

Fig. 5(B): Interstitial fluid flow-induced bone remodeling at thesecond step of remodeling calculation with a threshold of flowrate of 0.75 μm/s.

Fig. 6(A): Interstitial fluid flow-induced bone remodeling at thefirst step of remodeling calculation with a threshold of flow rateof 1.00 μm/s.

Fig. 7(B): Interstitial fluid flow-induced bone remodeling at thesecond step of remodeling calculation with a threshold of flowrate of 1.25 μm/s.

Fig. 6(B): Interstitial fluid flow-induced bone remodeling at thesecond step of remodeling calculation with a threshold of flowrate of 1.00 μm/s.

Fig. 8(A): Interstitial fluid flow-induced bone remodeling at thefirst step of remodeling calculation with a threshold of flow rateof 1.50 μm/s.

Fig. 7(A): Interstitial fluid flow-induced bone at the first step ofremodeling calculation with a threshold of flow rate of 1.25
μm/s.

Fig. 8(B): Interstitial fluid flow-induced bone remodeling at thesecond step of remodeling calculation with a threshold of flowrate of 1.50 μm/s.

Fig. 9(A): Remodeled bone with a threshold of flow rate of 0.75
μm/s.

Fig. 9(D): Bone remodeling with a threshold of flow rate of 1.50
μm/s.
4. DISCUSSION
In the present study, the cortical bone remodeling analysis wasperformed around the ACL insertion site of the femur based on ahypothesis that bone remodeling was caused by interstitial fluidflow. The interstitial fluid flow rate was analyzed in response to
three external forces to femur, tibial compressive force, patellacompressive force and ACL tensile force. For the analysis, themagnitude and direction of the forces and mechanical propertiesof the femur were referred from previous literatures. As a result,
we succeeded to complete the 3-D analysis as regard with theinterstitial fluid rate in the distal femur.

Fig. 9(B): Bone remodeling with a threshold of flow rate of 1.00μm/s.

Results revealed that Resident’s ridge-liked bone formation
occurred at the threshold of relatively low flow rates (0.75 μm/s
and 1.00 μm/s) while it did not occur at the threshold of
relatively high flow rate (1.25 μm/s and 1.50 μm/s). Weinbaum
et al. indicated that osteoblast is stimulated for bone formation
when the fluid flow-induced shear stress to the cell exceeds 1 Pa
[19]. Although detailed analysis has not been performed,flow-induced shear stress may be adequate for bone remodelingat the flow rate between 0.75 μm/s and 1.00 μm/s.
It is well known that many ridges can be observed near ligament
and tendon insertions, such as the tibial tuberosity near tibial
insertion of the patella tendon. Further studies possibly explain
the mechanism of the formation of three ridges.

5. CONCLUSION
We developed a detailed 3-D model of the distal femur andperformed a bone remodeling analysis due to interstitial fluid
flow for the explanation of the formation of the Resident’s ridge.
It was suggested that the Resident’s ridge-like bone formationoccur at relatively low thresholds of flow rate.
Fig. 9(C): Bone remodeling with a threshold of flow rate of 1.25μm/s.

6. ACKNOWLEDGMENT
The present study was supported in part by the Grant-In-Aid forscientific Research B (#25282134) from the MEXT, Japan, thePriority Research Found from Tokyo Metropolitan University,and the MEXT-Supported Program for the Strategic Research
Foundation at Private Universities, 2008-2012 (BERC,Kogakuin University) and 2013-2017 (FMS, Kogakuin
University).

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