Annotated Bibliography

This section is for internal MCLS lab use. It summarizes information gathered from the literature.

Continuum Ligaments

[DKB10] modeled four tibiofemoral ligaments (ACL, PCL, MCL, LCL), and four patellofemoral ligaments and tendons (MPL, LPL, quadriceps tendon, and patellar tendon). The figures also appear to show a medial patellar retinaculum, however the text does not describe structures or their material properties. The tibiofemoral ligaments, MPL, and LPL were modeled as fiber reinforces structures with a transversely isotropic hyperelastic material model. The quadriceps and patellar tendon were modeled with a neo-Hooken model.


[NBJvdG+17] modeled the ACL, PCL, MCL, LCL, and patellar tendon were modeled with a Holzapfel-Gesser-Ogden (HGO) hyperelastic material model. The fiber orientation of the ACL was split into two groups (anterior and posterior). Thermal loading was used to apply initial strain, with a negative expansion coefficient assigned to each ligament.

Cartilage

[PCMD06] modeled cartilage as a single phase linear elastic material
  • E = 5 Mpa
  • \(\nu = 0.46\)
[KwonOhRyongKangKyoungTakSonJuhyun+13] and [KKS+17] cited [PCMD06] in their methods, and use a stiffer Young’s modulus for the cartilage
  • E = 20 Mpa
  • \(\nu = 0.46\)

[KKS+17] modeled the interface between the cartilage and bone as fully bonded. A pressure-overclosure relationship was used to model articular contact.

[DKB10] modeled the cartilage as isioropic linearly elastic
  • E = 12 Mpa
  • \(\nu = 0.45\)
[DHRJ03] modeled the artilage as isotropic linear elastic. Frictionless contact was modeled. Thier convergence study showed that 4 layers of elements were needed to model the cartilage.
  • E = 15 Mpa
  • \(\nu = 0.475\)
[LKST15] modeled cartilage contact with a nonlinear elastic foundation formulation.
  • E = 5 Mpa
  • \(\nu = 0.45\)
  • 3 mm uniform thickness
[NBJvdG+17] modeled the cartilage as a nonlinear Neo-Hookean hyperelastic isotropic material.
  • \(C_{10} = 0.86\) MPa
  • \(D = 0.048 MPa^{-1}\)
\[\psi = C_{10}(I_1 - 3) + \frac{1}{2D}(J-1)^2\]

Meniscus

[PCMD06] modeled the meniscus as a single phase linear elastic material
  • E = 59 Mpa
  • \(\nu = 0.49\)

[KKS+17] modeled the meniscus as homogeneous linearly elastic and transversely isotropic. A hexahedral mesh was aligned to the circumferential direction of the model to define local element coordiante systems. Linear springs were used to attach meniscal horns to bone. A pressure-overclosure relationship was used to model articular contact.


[DKB10] modeled the menisci as transversely isotropic linearly elastic
  • \(E_{cir} = 120\) Mpa
  • \(\nu_{cir} = 0.45\)
  • \(E_{axial} = E_{transverse} = 20\) Mpa
  • \(\nu_{axial}=\nu_{transverse} = 0.3\)
[DKB10] modeled the meniscal horns as isotropic, linearly elastic, citing that their properties were poorly understood
  • E = 120 Mpa
  • \(\nu = 0.45\)

[NBJvdG+17] modeled the meniscus with a Holzapfel-Gesser-Ogden (HGO) hyperelastic model. Meniscal attachments were modeled as bundles of tension-only nonlinear springs

Table 11 Meniscal attachment properties [NBJvdG+17]
Attachment Name Stiffness (N/mm) Number of Springs
Horn 400 4
anterior transverse ligament Not reported 3
anterior and posterior meniscofemoral ligaments 49 1

[DHRJ03] performed a sensitivity study on how meniscal properties affect contact metrics. The meniscal horn attachments were modeled as linear springs. Frictionless contact was modeled. Thier convergence study showed that 4 layers of elements were needed to model the meniscus.

The experimental component of the study used pressure-sensitive film to measure contact under 400 N and 1200 N compressive loads at 0 and 15 degrees flexion. A finite element model was developed, and a simplified sampling technique was used to define how sensitive the contact metrics were to assigned material properties.

Table 12 Meniscal sensitivity parameters from [DHRJ03]
Parameter Initial Value Lower Bound Upper Bound
Shear modulus \(G_{r\theta}=G_{rz}\) (MPa) 57.5 22.7 77.7
Transverse ligament stiffness (N/mm) 200 50 900
Total stiffness of horn attachment (N/mm) 2000 500 30000
Poisson’s ratio \(\nu_{r\theta}=\nu_{z\theta}\) 0.3 0.1 0.35
Poisson’s ratio \(\nu_{rz}\) 0.2 0.1 0.4
\(E_r=E_z\) (MPa) 20 15 60
\(E_\theta\) (MPa) 150 100 200

This study concluded that the contact metrics were sensitive to the meniscal circumferential modulus (\(E_\theta\)), axial/radial modulus (\(E_r=E_z\)), and the total horn stiffness.


[DKB10](1, 2, 3, 4) Yasin Y. Dhaher, Tae-Hyun Kwon, and Megan Barry. The effect of connective tissue material uncertainties on knee joint mechanics under isolated loading conditions. Journal of Biomechanics, 43(16):3118–3125, December 2010. URL: http://www.sciencedirect.com/science/article/pii/S0021929010004380, doi:10.1016/j.jbiomech.2010.08.005.
[DHRJ03](1, 2, 3) Tammy L. Haut Donahue, M. L. Hull, Mark M. Rashid, and Christopher R. Jacobs. How the stiffness of meniscal attachments and meniscal material properties affect tibio-femoral contact pressure computed using a validated finite element model of the human knee joint. Journal of Biomechanics, 36(1):19–34, January 2003. URL: http://www.jbiomech.com/article/S0021-9290(02)00305-6/abstract, doi:10.1016/S0021-9290(02)00305-6.
[KKS+17](1, 2, 3) Kyoung-Tak Kang, Sung-Hwan Kim, Juhyun Son, Young Han Lee, Shinil Kim, and Heoung-Jae Chun. Probabilistic evaluation of the material properties of the in vivo subject-specific articular surface using a computational model. Journal of Biomedical Materials Research Part B: Applied Biomaterials, 105(6):1390–1400, August 2017. URL: http://onlinelibrary.wiley.com/doi/10.1002/jbm.b.33666/abstract, doi:10.1002/jbm.b.33666.
[LKST15]Rachel L. Lenhart, Jarred Kaiser, Colin R. Smith, and Darryl G. Thelen. Prediction and Validation of Load-Dependent Behavior of the Tibiofemoral and Patellofemoral Joints During Movement. Annals of Biomedical Engineering, 43(11):2675–2685, April 2015. URL: http://link.springer.com/article/10.1007/s10439-015-1326-3, doi:10.1007/s10439-015-1326-3.
[NBJvdG+17](1, 2, 3, 4) Hamid Naghibi Beidokhti, Dennis Janssen, Sebastiaan van de Groes, Javad Hazrati, Ton Van den Boogaard, and Nico Verdonschot. The influence of ligament modelling strategies on the predictive capability of finite element models of the human knee joint. Journal of Biomechanics, 65:1–11, December 2017. URL: http://linkinghub.elsevier.com/retrieve/pii/S0021929017304529, doi:10.1016/j.jbiomech.2017.08.030.
[PCMD06](1, 2, 3) E. Peña, B. Calvo, M. A. Martínez, and M. Doblaré. A three-dimensional finite element analysis of the combined behavior of ligaments and menisci in the healthy human knee joint. Journal of Biomechanics, 39(9):1686–1701, January 2006. URL: http://www.jbiomech.com/article/S0021-9290(05)00211-3/abstract, doi:10.1016/j.jbiomech.2005.04.030.
[KwonOhRyongKangKyoungTakSonJuhyun+13]Kwon Oh‐Ryong, Kang Kyoung‐Tak, Son Juhyun, Kwon Sae‐Kwang, Jo Seung‐Bae, Suh Dong‐Suk, Choi Yun‐Jin, Kim Ho‐Joong, and Koh Yong‐Gon. Biomechanical comparison of fixed‐ and mobile‐bearing for unicomparmental knee arthroplasty using finite element analysis. Journal of Orthopaedic Research, 32(2):338–345, October 2013. URL: https://onlinelibrary.wiley.com/doi/full/10.1002/jor.22499, doi:10.1002/jor.22499.