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Adouni, M.B.A. Multi-Domain Model of Anterior Cruciate Ligament. Encyclopedia. Available online: https://encyclopedia.pub/entry/14628 (accessed on 11 December 2023).
Adouni MBA. Multi-Domain Model of Anterior Cruciate Ligament. Encyclopedia. Available at: https://encyclopedia.pub/entry/14628. Accessed December 11, 2023.
Adouni, Malek Ben Ahmed. "Multi-Domain Model of Anterior Cruciate Ligament" Encyclopedia, https://encyclopedia.pub/entry/14628 (accessed December 11, 2023).
Adouni, M.B.A.(2021, September 27). Multi-Domain Model of Anterior Cruciate Ligament. In Encyclopedia. https://encyclopedia.pub/entry/14628
Adouni, Malek Ben Ahmed. "Multi-Domain Model of Anterior Cruciate Ligament." Encyclopedia. Web. 27 September, 2021.
Multi-Domain Model of Anterior Cruciate Ligament
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This entry is adapted from the peer-reviewed paper 10.3390/app11188580

The anterior cruciate ligament’s (ACL) mechanics is an important factor governing the ligament’s integrity and, hence, the knee joint’s response. Despite many investigations in this area, the cause and effect of injuries remain unclear or unknown. This may be due to the complexity of the direct link between macro- and micro-scale damage mechanisms. In the first part of this investigation, a three-dimensional coarse-grained model of collagen fibril (type I) was developed using a bottom-up approach to investigate deformation mechanisms under tensile testing. 

tropocollagen fibrils anterior cruciate ligament finite elements molecular dynamic

1. Introduction

Collagens type I that form fibrils are present as the main contributor to the integrity of the joint ligaments via a hierarchical extension over many length scales. Collagen is made up of amino-acid sequences organized in a polypeptide helix and combined into a set of three supercoils that produce a molecule of tropocollagen (TC) [1][2]. An X-ray diffraction experiment was employed to determine the topography of short peptide fragments representing the collagen molecules. This molecule was characterized by a weight of 300 KDa, length of 300 nm, and 1 to 2 nm diameter[3][4]. The TC molecules aggregate into fibrils via intermolecular adhesion and covalent crosslinks at their ends with respect to well-specified axial and center-to-center locations offset [5][6][7]. The mechanical behavior of the collagenous structures has received significant attention from molecular to aggregate level, either experimentally[8][9][10][11][12][13] or computationally via molecular dynamic (MD) simulation [14][15][16][17][18][19][20][21]. A clear agreement has been reported that these superstructures lead to helpful mechanical behavior characterized by high strength and extensibility of up to 100% strain before breakage [22]. However, most previous investigations were limited to nano- and micro-scales. The reasons behind this limitation were the intimate coupling between chemistry, biology, and mechanical deformation and their structural texture that involves specific implementation via different scales[22].
On the larger scale (millimeter and upscale), the soft tissues’ mechanical behavior was considered either elastic, basic hyperelastic, hyperelastic, or viscoelastic fiber-reinforced composite materials [23]. Most of these constitutive models were limited to the elastic behavior and have been able to reproduce the mechanical response of the ligaments measured during experimental tensile testing[23][24][25][26][27][28][29]. A very limited number of studies considered softening elasticity behavior yet restricted to the macro-mechanical scale [30][31]. On the side of the model application, the anterior cruciate ligament (ACL) was the focus of most of the developed computational frames since it is more prone to injury than any other knee soft tissue. Recent investigations have shown that around 50% of lower limb ligament injuries involve the ACL [32]. ACL damage’s pathogenesis and pathophysiological underpinnings were well connected to the molecular level [33][34]. This process of damage was described microscopely as collagen degradation [21]. Thereafter, exploring how molecular-level interactions combine, including micro-degradation mechanism, to create a tissue-level mechanical response of collagenous materials is a potential path for the advancement of ACL injury or trauma treatments.
The principal aim of this work was to highlight the link between ACL molecular structure and its aggregate mechanical behavior. At one extreme, such a link uses molecular dynamic simulation to characterize the fibril structure properties as a function of crosslink degradation. At the other extreme, the link uses a multilevel hyper-elastoplastic fibril-reinforced model to simultaneously investigate how changes in the fibril structure are manifested at the ligament level.

2. Research

Figure 1 shows the obtained stress–strain curve for a single molecule. The curve can be divided into three zones describing three different mechanisms. Zone I : in this phase, the molecule was stretched along its principal axis. The small resulting stress was due to the change of the angle energy. This phase is hardly visible on the stress–strain curve since it needed an extremely slow strain rate to allow for atoms to relax. Zone II : in this phase, the molecule was uniformly stretched. The elastic constant was ~7.9 GPa and resulted mainly from the bond stretching below the hyperelastic critical distance r1. Zone III : in this phase, a sharp change in strength occurred as the bond distance reached the hyperelastic critical distance r1 (elastic constant was ~47.1 GPa). The molecule continued to stretch uniformly until reaching the breaking point. The molecule broke when interatomic distances reached the breaking distance rb
.
Applsci 11 08580 g003 550
Figure 1. Current computed stress–strain variation in the single TC molecule along with Buehler et al. [42] model prediction.
Figure 2 shows the stress–strain curve for the collagen fibril for different crosslink densities. The overall trend of the curves is consistent with previous work: increasing crosslink densities increased both the ultimate tensile strength and the ultimate tensile strain of the fibril. Similar to the single molecule, the angles on the fibril were first straightened since the angle energy was much smaller than the bond and pairwise energies. Then, with increasing strain, the internal stress started building up in the structure up to a threshold where the pairwise forcefield could no longer resist the shear forces induced between molecules. As a result, the molecules started sliding and stress started to decrease. When crosslinks were present in the fibril, they provided additional resistance to the shearing between molecules and, therefore, retarded the sliding threshold, increasing the ultimate tensile strain and stress.
Applsci 11 08580 g004 550
Figure 2. Strain–stress curve of the collagen fibril as a function of the amount of crosslink (β) predicted using the coarse-grained model under axial tensile testing.
Nonlinear curve fitting of our data collected from molecular dynamics simulation was used to evaluate the material characteristics of the fibril for native and degraded tropocollagen crosslinks. The goodness-of-fit (GOF) value (coefficient of determination, given as mean, standard error (SE)) for the fitted data was 0.91 ± 0.04 for the crosslink failures. For all cases, the fitted curves provided satisfactory fits to the MDS data. Table 1 shows the average optimal input fibril parameters for degradation processes. The mechanical properties of the fibrils influenced the aggregate behavior of the ACL at full extension. Tropocollagen crosslinks degradation slightly influenced the elastic stress of the ACL as observed during the axial tension that ranged between 0 and 6%. The effect of this degradation became remarkable when the axial strain varied between 6 and 8% (Figure 5). However, the ACL yield stress was substantially influenced by tropocollagen crosslink failure. The yield stress was approximately reduced by 90% when β varied gradually from 100% to 0 (Figure 3 and Figure 4). However, a minimal variation was observed on the elastoplastic behavior of the ACL when the amount of crosslink failure was more than 80% (β = 20% or less). Under pre-yielding loading conditions (7.5% axial strain), ligaments stresses distributions were nonuniform at all degradation stages (Figure 5). The maximum axial stresses ranged from ~10MPa to ~20 MPa. The largest stress values were located at the posterolateral side near the tibial junction, and the smallest values were at the anteromedial area near the femoral junction (Figure 5).
Applsci 11 08580 g005 550
Figure 3. (a) Finite-element model of the ACL with the associated boundary conditions considered to simulate the uniaxial tensile test. (b) Computed axial maximum stress–strain behavior of the ACL.
Applsci 11 08580 g006 550
Figure 4. Computed ACL yield strength: (a) and strain; (b) as a function of the crosslink content (β).
Applsci 11 08580 g007 550
Figure 5. Stress distribution in the ACL at 7.5% axial strain (elastic zone).
Table 1. Material parameters of the fibril found via the data-fitting procedure.
Table 1. Mesoscopic structural properties.
Molecular Properties Fiber Properties
Parameter Value Parameter Value
Molecule number of atoms 3134 Gap [Å] 400
Molecule total mass [g/mol] 287,000 Overlap [Å] ~282
Number of beads per molecule 218 D-period [Å] ~682
Mass of each bead [g/mol] 1316 Length of fibril [Å] 3410
Length along principal axis [Å] 3011 Hex. lattice constant [Å] 16.52
 
Plastic elongation was used as a plastic-change indicator in this study (λp). This variable specified when and where the plastic change occurred. Damage propagation (plastic change) of ligament structures was restricted to the collagen fiber’s surface layers (Figure 6). The maximum stress distribution was typically related to damage initiations and distributions. In most cases, the damage began in the highest stressed element and spread in the same direction of the stress distribution (Figure 6). ACL damage started between 8 and 17% axial strain with an associated range of axial stress varying between 13 MPa and 58 MPa when tropocollagen crosslinks failure ranged from no crosslink to 100% crosslink. The maximum plastic elongation computed ranged from 29% (100%) to 34% (0%). The increase in the crosslink’s failure between the tropocollagen molecules significantly increased the area of damage.
Applsci 11 08580 g008 550
Figure 6. ACL-damage distribution (plastic change) at 3% post-yielding strain.

3. Discussion

Researchers presents a comprehensive work incorporating the degradation mechanism of the type I collagen on the nano-scale into a description of the mechanical behavior of the ACL. The developed framework connects a meso-scale molecular dynamics-simulation model to a continuum fibril-reinforced hyper-elastoplastic model. The degradation mechanism was presented by the elimination of the enzymatical crosslinks. This was later well documented as a key element in the collagen's integrity and thereafter expressing a significant role in the yielding tissue level, and serves as an internal control for the integrity of our modeling approach. The proposed engineering frame was validated at two levels, molecular and continuum, by comparing the predictions with reported results in the literature. At the micro-level, the degradation in the enzymatical crosslinks affected the elastic stiffness of the second and third deformation regimes and the collagen failure strain. A higher crosslink density generated a well-connected structure of the collagen fibril. On the macro-scale and by means of the hierarchical model, a limited zone of the elastic and the complete plastic responses were influenced by the degradation of enzymatical crosslinks.

References

  1. Kadler, K.E.; Holmes, D.F.; Trotter, J.A.; Chapman, J.A. Collagen fibril formation. Biochem. J. 1996, 316, 1–11. [Google Scholar] [CrossRef] [PubMed]
  2. Parry, D.A. The molecular fibrillar structure of collagen and its relationship to the mechanical properties of connective tissue. Biophys. Chem. 1988, 29, 195–209. [Google Scholar] [CrossRef]
  3. Kramer, R.Z.; Venugopal, M.G.; Bella, J.; Mayville, P.; Brodsky, B.; Berman, H. Staggered molecular packing in crystals of a collagen-like peptide with a single charged pair. J. Mol. Biol. 2000, 301, 1191–1205. [Google Scholar] [CrossRef]
  4. Bella, J.; Eaton, M.; Brodsky, B.; Berman, H. Crystal and molecular structure of a collagen-like peptide at 1.9 A resolution. Science 1994, 266, 75–81. [Google Scholar] [CrossRef] [PubMed]
  5. Alberts, B.; Johnson, A.; Lewis, J.; Raff, M.; Walter, P.; Roberts, K. Cell Chemistry and Biosynthesis. In Molecular Biology of the Cell; Garland Science: New York, NY, USA, 2002. [Google Scholar]
  6. Alberts, B.; Johnson, A.; Lewis, J.; Raff, M.; Walter, P.; Roberts, K. Cell Junctions, Cell Adhesion, and the Extracellular Matrix. In Molecular Biology of the Cell, 4th ed.; Garland Science: New York, NY, USA, 2002. [Google Scholar]
  7. Bailey, A.J. Molecular mechanisms of ageing in connective tissues. Mech. Ageing Dev. 2001, 122, 735–755. [Google Scholar] [CrossRef]
  8. Catanese III, J.; Iverson, E.P.; Ng, R.K.; Keaveny, T.M. Heterogeneity of the mechanical properties of demineralized bone. J. Biomech. 1999, 32, 1365–1369. [Google Scholar] [CrossRef]
  9. Akizuki, S.; Mow, V.C.; Muller, F.; Pita, J.C.; Howell, D.S.; Manicourt, D.H. Tensile properties of human knee joint cartilage: I. Influence of ionic conditions, weight bearing, and fibrillation on the tensile modulus. J. Orthop. Res. 1986, 4, 379–392. [Google Scholar] [CrossRef] [PubMed]
  10. Diamant, J.; Keller, A.; Baer, E.; Litt, M.; Arridge, R.G.C. Collagen; ultrastructure and its relation to mechanical properties as a function of ageing. Proc. R. Soc. Ser. B Boil. Sci. 1972, 180, 293–315. [Google Scholar] [CrossRef]
  11. Abrahams, M. Mechanical behaviour of tendonIn vitro. Med. Biol. Eng. Comput. 1967, 5, 433–443. [Google Scholar] [CrossRef]
  12. Shen, Z.L.; Dodge, M.R.; Kahn, H.; Ballarini, R.; Eppell, S. Stress-strain Experiments on Individual Collagen Fibrils. Biophys. J. 2008, 95, 3956–3963. [Google Scholar] [CrossRef]
  13. Shen, Z.L.; Kahn, H.; Ballarini, R.; Eppell, S.J. Viscoelastic Properties of Isolated Collagen Fibrils. Biophys. J. 2011, 100, 3008–3015. [Google Scholar] [CrossRef]
  14. Lorenzo, A.C.; Caffarena, E.R. Elastic properties, Young’s modulus determination and structural stability of the tropocollagen molecule: A computational study by steered molecular dynamics. J. Biomech. 2004, 38, 1527–1533. [Google Scholar] [CrossRef] [PubMed]
  15. Nikolov, S.; Raabe, D. Hierarchical modeling of the elastic properties of bone at submicron scales: The role of extrafibrillar mineralization. Biophys. J. 2008, 94, 4220–4232. [Google Scholar] [CrossRef] [PubMed]
  16. Veld, P.J.I.; Stevens, M.J. Simulation of the Mechanical Strength of a Single Collagen Molecule. Biophys. J. 2008, 95, 33–39. [Google Scholar] [CrossRef]
  17. Buehler, M.J. Nature designs tough collagen: Explaining the nanostructure of collagen fibrils. Proc. Natl. Acad. Sci. USA 2006, 103, 12285–12290. [Google Scholar] [CrossRef]
  18. Chang, S.-W.; Shefelbine, S.J.; Buehler, M.J. Structural and Mechanical Differences between Collagen Homo-and Heterotrimers: Relevance for the Molecular Origin of Brittle Bone Disease. Biophys. J. 2012, 102, 640–648. [Google Scholar] [CrossRef] [PubMed]
  19. Depalle, B.; Qin, Z.; Shefelbine, S.J.; Buehler, M.J. Large Deformation Mechanisms, Plasticity, and Failure of an Individual Collagen Fibril with Different Mineral Content. J. Bone Miner. Res. 2015, 31, 380–390. [Google Scholar] [CrossRef]
  20. Liu, Y.; Thomopoulos, S.; Chen, C.; Birman, V.; Buehler, M.; Genin, G.M. Modelling the mechanics of partially mineralized collagen fibrils, fibres and tissue. J. R. Soc. Interface 2014, 11, 20130835. [Google Scholar] [CrossRef]
  21. Tang, Y.; Ballarini, R.; Buehler, M.J.; Eppell, S. Deformation micromechanisms of collagen fibrils under uniaxial tension. J. R. Soc. Interface 2009, 7, 839–850. [Google Scholar] [CrossRef]
  22. Buehler, M.J.; Ballarini, R. Microelectromechanical Systems (MEMS) Platforms for Testing the Mechanical Properties of Collagen Fibrils. Materiomics: Multiscale Mechanics of Biological Materials and Structures; Springer: Berlin, Germany, 2013. [Google Scholar]
  23. Weiss, J.A.; Gardiner, J.C. Computational Modeling of Ligament Mechanics. Crit. Rev. Biomed. Eng. 2001, 29, 303–371. [Google Scholar] [CrossRef]
  24. Ateshian, G.A.; Ellis, B.J.; Weiss, J.A. Equivalence Between Short-Time Biphasic and Incompressible Elastic Material Responses. J. Biomech. Eng. 2006, 129, 405–412. [Google Scholar] [CrossRef]
  25. Gardiner, J.C.; Weiss, J.A. Subject-specific finite element analysis of the human medial collateral ligament during valgus knee loading. J. Orthop. Res. 2003, 21, 1098–1106. [Google Scholar] [CrossRef]
  26. Gardiner, J.C.; Weiss, J.A.; Rosenberg, T.D. Strain in the Human Medial Collateral Ligament During Valgus Loading of the Knee. Clin. Orthop. Relat. Res. 2001, 391, 266–274. [Google Scholar] [CrossRef] [PubMed]
  27. Quapp, K.M.; Weiss, J.A. Material Characterization of Human Medial Collateral Ligament. J. Biomech. Eng. 1998, 120, 757–763. [Google Scholar] [CrossRef]
  28. Limbert, G.; Middleton, J. A transversely isotropic viscohyperelastic material—Application to the modeling of biological soft connective tissues. Int. J. Solids Struct. 2004, 41, 4237–4260. [Google Scholar] [CrossRef]
  29. Limbert, G.; Taylor, M.; Middleton, J. Three-dimensional finite element modelling of the human ACL: Simulation of passive knee flexion with a stressed and stress-free ACL. J. Biomech. 2004, 37, 1723–1731. [Google Scholar] [CrossRef]
  30. Adouni, M.; Mbarki, R.; Al Khatib, F.; Eilaghi, A. Multiscale modeling of knee ligament biomechanics. Int. J. Numer. Methods Biomed. Eng. 2021, 37, e3413. [Google Scholar] [CrossRef] [PubMed]
  31. Fratzl, P. Collagen: Structure and Mechanics; Springer Science & Business Media: Berlin, Germany, 2008. [Google Scholar]
  32. Nessler, T.; Denney, L.; Sampley, J. ACL Injury Prevention: What Does Research Tell Us? Curr. Rev. Musculoskelet. Med. 2017, 10, 281–288. [Google Scholar] [CrossRef]
  33. Kiapour, A.M.; Murray, M.M. Basic science of anterior cruciate ligament injury and repair. Bone Jt. Res. 2014, 3, 20–31. [Google Scholar] [CrossRef]
  34. Boorman, R.S.; Thornton, G.M.; Shrive, N.G.; Frank, C.B. Ligament grafts become more susceptible to creep within days after surgery: Evidence for early enzymatic deg-radation of a ligament graft in a rabbit model. Acta Orthop. Scand. 2002, 73, 568–574. [Google Scholar] [CrossRef] [PubMed]
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