Bone microstructure in finite element modeling: the functional role of trabeculae in the femoral head of Sciurus vulgaris
Zoomorphologie - 2019
Tóm tắt
In arboreal habitats, animals encounter substrates of varying inclinations. Consequently, the external loads acting on the limb bones during arboreal locomotion are diverse in terms of magnitude and orientation. It is not well understood how limb bones are adapted to a broad range of loading directions and which functional role is adopted by the trabecular microstructure in particular. In this study, we conducted a finite element analysis of the proximal femur of the Eurasian red squirrel (Sciurus vulgaris) to assess the functional performance of the bone during horizontal (0° inclination) and uphill locomotion (30° and 60° inclination). To elucidate the functional significance of the femoral trabecular microstructure in particular, we compared a model using a realistic geometry that included trabecular bone with two models using hypothetical geometries, one being solid inside and the other being hollow inside (cortical bone only). We report that the von Mises stress in the proximal femur increases with increasing substrate inclination. The reason for that is the higher percentage of body mass acting on the hind limbs during uphill locomotion rather than architectural limitations of the microstructure. Furthermore, the model using a realistic geometry shows a high similarity in its functional performance to the hypothetical solid model by avoiding high peak loads in the cortex equally well. These findings highlight the exceptional ability of trabecular bone to maintain stability under external loading of varying directions while at the same time facilitating mineral exchange and bone (re)modeling.
Từ khóa
Tài liệu tham khảo
Aerts P (1998) Vertical jumping in Galago senegalensis: the quest for an obligate mechanical power amplifier. Philos Trans R Soc B Biol Sci 353(1375):1607–1620
Andrada E, Mämpel J, Schmidt A, Fischer M, Karguth A, Witte H (2013) From biomechanics of rats’ inclined locomotion to a climbing robot. Int J Des Nat Ecodyn 8(3):192–212
Barak MM, Lieberman DE, Hublin J-J (2011) A wolff in sheep’s clothing: trabecular bone adaptation in response to changes in joint loading orientation. Bone 49(6):1141–1151
Bishop PJ, Hocknull SA, Clemente CJ, Hutchinson JR, Barret RS, Lloyd DG (2018) Cancellous bone and theropod dinosaur locomotion. Part II—a new approach to inferring posture and locomotor biomechanics in extinct tetrapod vertebrates. PeerJ 6:e5779. https://doi.org/10.7717/peerj.5779
Bloomfield S, Allen M, Hogan H, Delp M (2002a) Site-and compartment-specific changes in bone with hindlimb unloading in mature adult rats. Bone 31(1):149–157
Bloomfield SA, Hogan HA, Delp MD (2002b) Decreases in bone blood flow and bone material properties in aging fischer-344 rats. Clin Orthop Relat Res 396:248–257
Brassey CA, Margetts L, Kitchener AC, Withers PJ, Manning PL, Sellers WI (2013) Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones. J R Soc Interface 10(79):20120823
Bright JA (2014) A review of paleontological finite element models and their validity. J Paleontol 88(4):760–769
Bright JA, Rayfield EJ (2011) The response of cranial biomechanical finite element models to variations in mesh density. Anat Rec 294(4):610–620
Burkhart TA, Andrews DM, Dunning CE (2013) Finite element modeling mesh quality, energy balance and validation methods: a review with recommendations associated with the modeling of bone tissue. J Biomech 46(9):1477–1488
Carter D, Orr T, Fyhrie D (1989) Relationships between loading history and femoral cancellous bone architecture. J Biomech 22(3):231–244
Chadwick KP, Shefelbine SJ, Pitsillides AA, Hutchinson JR (2017) Finite-element modelling of mechanobiological factors influencing sesamoid tissue morphology in the patellar tendon of an ostrich. R Soc Open Sci 4(6):170133
Cody DD, Hou FJ, Divine GW, Fyhrie DP (2000) Short term in vivo precision of proximal femoral finite element modeling. Ann Biomed Eng 28(4):408–414
David V, Laroche N, Boudignon B, Lafage-Proust M-H, Alexandre C, Rüegsegger P, Vico L (2003) Noninvasive in vivo monitoring of bone architecture alterations in hindlimb-unloaded female rats using novel three-dimensional microcomputed tomography. J Bone Miner Res 18(9):1622–1631
Demes B, Fleagle JG, Jungers WL (1999) Takeoff and landing forces of leaping strepsirhine primates. J Hum Evol 37:279–292
Doube M, Klosowski MM, Wiktorowicz-Conroy AM, Hutchinson JR, Shefelbine SJ (2011) Trabecular bone scales allometrically in mammals and birds. Proc R Soc B Biol Sci 278(1721):3067–3073
Dumont ER, Piccirillo J, Grosse IR (2005) Finite-element analysis of biting behaviour and bone stress in the facial skeletons of bats. Anat Rec 283(2):319–330
Farke AA (2008) Frontal sinuses and head-butting in goats: a finite element analysis. J Exp Biol 211(19):3085–3094
Gefen A, Seliktar R (2004) Comparison of the trabecular architecture and the isostatic stress flow in the human calcaneus. Med Eng Phys 26(2):119–129
Gil L, Marcé-Nogué J, Sánchez M (2015) Insights into the controversy over materials data for the comparison of biomechanical performance in vertebrates. Palaeontol Electron 18.1.10A:1–24
Hart K, Shaw J, Vajda E, Hegsted M, Miller S (2001) Swim-trained rats have greater bone mass, density, strength, and dynamics. J Appl Physiol 91(4):1663–1668
Hesse B, Nyakatura JA, Fischer MS, Schmidt M (2015) Adjustments of limb mechanics in cotton-top tamarins to moderate and steep support orientations: significance for the understanding of early primate evolution. J Mamm Evol 22(3):435–450
Joo Y-I, Sone T, Fukunaga M, Lim S-G, Onodera S (2003) Effects of endurance exercise on three-dimensional trabecular bone microarchitecture in young growing rats. Bone 33(4):485–493
Kabel J, van Rietbergen B, Dalstra M, Odgaard A, Huiskes R (1999) The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone. J Biomech 32(7):673–680
Keyak J, Meagher J, Skinner H, Mote C Jr (1990) Automated three-dimensional finite element modelling of bone: a new method. J Biomed Eng 12(5):389–397
Kupczik K, Dobson C, Fagan M, Crompton R, Oxnard C, O’Higgins P (2007) Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of finite element models. J Anat 210(1):41–53
Lammers AR (2007) Locomotor kinetics on sloped arboreal and terrestrial substrates in a small quadrupedal mammal. Zoology 110(2):93–103
Lammers AR, Zurcher U (2011) Torque around the center of mass: dynamic stability during quadrupedal arboreal locomotion in the Siberian chipmunk (Tamias sibiricus). Zoology 114(2):95–103
Lammers AR, Earls KD, Biknevicius AR (2006) Locomotor kinetics and kinematics on inclines and declines in the gray short-tailed opossum Monodelphis domestica. J Exp Biol 209(20):4154–4166
Lieser B (2003) Morphologische und biomechanische Eigenschaften des Hüftgelenks (Articulatio coxae) des Hundes (Canis familiaris). PhD thesis, Ludwig-Maximilians-Universität München
Maas SA, Ellis BJ, Ateshian GA, Weiss JA (2012) FEBio: finite elements for biomechanics. J Biomech Eng 134(1):011005
MacLatchy L, Müller R (2002) A comparison of the femoral head and neck trabecular architecture of Galago and Perodicticus using micro-computed tomography (μCT). J Hum Evol 43(1):89–105
Marcé-Nogué J, de Esteban-Trivigno S, Escrig C, Gil L (2016) Accounting for differences in element size and homogeneity when comparing finite element models: armadillos as a case study. Palaeontol Electron 19.2.2T:1–22
Mielke M, Wölfer J, Arnold P, van Heteren AH, Amson E, Nyakatura JA (2018) Trabecular architecture in the sciuromorph femoral head: allometry and functional adaptation. Zool Lett 4(1):10
Milne N (2016) Curved bones: an adaptation to habitual loading. J Theor Biol 407:18–24
Murray P (1936) Bones: a study of the development of structure in the vertebrate skeleton. Cambridge University Press, London
Niebur GL, Feldstein MJ, Yuen JC, Chen TJ, Keaveny TM (2000) High resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone. J Biomech 33(12):1575–1583
Nishiyama KK, Gilchrist S, Guy P, Cripton P, Boyd SK (2013) Proximal femur bone strength estimated by a computationally fast finite element analysis in a sideways fall configuration. J Biomech 46(7):1231–1236
O’Higgins P, Milne N (2013) Applying geometric morphometrics to compare changes in size and shape arising from finite elements analyses. Hystrix Ital J Mammal 24(1):126–132
Parr W, Wroe S, Chamoli U, Richards H, McCurry M, Clausen P, McHenry C (2012) Toward integration of geometric morphometrics and computational biomechanics: new methods for 3D virtual reconstruction and quantitative analysis of Finite Element Models. J Theor Biol 301:1–14
Polly PD, Stayton CT, Dumont ER, Pierce SE, Rayfield EJ, Angielczyk KD (2016) Combining geometric morphometrics and finite element analysis with evolutionary modeling: towards a synthesis. J Vertebr Paleontol 36(4):e1111225
Pontzer H, Lieberman D, Momin E, Devlin MJ, Polk J, Hallgrimsson B, Cooper D (2006) Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation. J Exp Biol 209(1):57–65
Püschel TA, Marcé-Nogué J, Gladman JT, Bobe R, Sellers WI (2018) Inferring locomotor behaviours in miocene new world monkeys using finite element analysis, geometric morphometrics and machine-learning classification techniques applied to talar morphology. J R Soc Interface 15:20180520
Rayfield EJ (2004) Cranial mechanics and feeding in Tyrannosaurus rex. Proc R Soc Lond B Biol Sci 271(1547):1451–1459
Rayfield EJ (2007) Finite element analysis and understanding the biomechanics and evolution of living and fossil organisms. Annu Rev Earth Planet Sci 35:541–576
Rayfield EJ, Norman DB, Horner CC, Horner JR, Smith PM, Thomason JJ, Upchurch P (2001) Cranial design and function in a large theropod dinosaur. Nature 409(6823):1033
Rho JY, Ashman RB, Turner CH (1993) Young’s modulus of trabecular and cortical bone material: ultrasonic and microtensile measurements. J Biomech 26(2):111–119
Rho J-Y, Tsui TY, Pharr GM (1997) Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation. Biomaterials 18(20):1325–1330
Richmond BG, Wright BW, Grosse I, Dechow PC, Ross CF, Spencer MA, Strait DS (2005) Finite element analysis in functional morphology. Anat Rec 283(2):259–274
Ryan TM, Ketcham RA (2002) The three-dimensional structure of trabecular bone in the femoral head of strepsirrhine primates. J Hum Evol 43(1):1–26
Ryan TM, Ketcham RA (2005) Angular orientation of trabecular bone in the femoral head and its relationship to hip joint loads in leaping primates. J Morphol 265(3):249–263
Ryan TM, van Rietbergen B (2005) Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models. Am J Phys Anthropol 126(1):82–96
Schindelin J, Arganda-Carreras I, Frise E, Kaynig V, Longair M, Pietzsch T, Preibisch S, Rueden C, Saalfeld S, Schmid B et al (2012) Fiji: an open- source platform for biological-image analysis. Nat Methods 9(7):676–682
Schmidt A, Fischer MS (2011) The kinematic consequences of locomotion on sloped arboreal substrates in a generalized (Rattus norvegicus) and a specialized (Sciurus vulgaris) rodent. J Exp Biol 214(15):2544–2559
Schneider CA, Rasband WS, Eliceiri KW (2012) NIH Image to ImageJ: 25 years of image analysis. Nat Methods 9(7):671
Si H (2015) Tetgen, a delaunay-based quality tetrahedral mesh generator. ACM Trans Math Softw 41(2):11
Silva MJ, Brodt MD, Fan Z, Rho J-Y (2004) Nanoindentation and whole- bone bending estimates of material properties in bones from the senescence accelerated mouse SAMP6. J Biomech 37(11):1639–1646
Søgaard CH, Danielsen CC, Thorling EB, Mosekilde L (1994) Long-term exercise of young and adult female rats: effect on femoral neck biomechanical competence and bone structure. J Bone Miner Res 9(3):409–416
Sugiyama T, Meakin LB, Browne WJ, Galea GL, Price JS, Lanyon LE (2012) Bones’ adaptive response to mechanical loading is essentially linear between the low strains associated with disuse and the high strains associated with the lamellar/woven bone transition. J Bone Miner Res 27(8):1784–1793
Turner CH, Rho J, Takano Y, Tsui TY, Pharr GM (1999) The elastic properties of trabecular and cortical bone tissues are similar: results from two microscopic measurement techniques. J Biomech 32(4):437–441
van Lenthe GH, Müller R (2006) Prediction of failure load using micro-finite element analysis models: toward in vivo strength assessment. Drug Discov Today Technol 3(2):221–229
Van Rietbergen B, Huiskes R, Eckstein F, Rüegsegger P (2003) Trabecular bone tissue strains in the healthy and osteoporotic human femur. J Bone Miner Res 18(10):1781–1788
Wauters L, Dhondt AA (1989) Body weight, longevity and reproductive success in red squirrels (Sciurus vulgaris). J Anim Ecol pp 637–651
Wei X, Dong Y, Zhang Z (2019) Finite element analysis of the femur of japanese quail (Coturnix coturnix japonica). Int J Morphol 37(2):641–646
Wirtz DC, Schiffers N, Pandorf T, Radermacher K, Weichert D, Forst R (2000) Critical evaluation of known bone material properties to realize anisotropic FE-simulation of the proximal femur. J Biomech 33(10):1325–1330
Wölfer J, Amson E, Arnold P, Botton-Divet L, Fabre A-C, van Heteren AH, Nyakatura JA (2019) Femoral morphology of scuiromorph rodents in light of scaling and locomotor ecology. J Anat. https://doi.org/10.1111/joa.12980
Yosibash Z, Padan R, Joskowicz L, Milgrom C (2007) A CT-based high- order finite element analysis of the human proximal femur compared to in vitro experiments. J Biomech Eng 129(3):297–309
Youlatos D, Samaras A (2011) Arboreal locomotor and postural behaviour of European red squirrels (Sciurus vulgaris L.) in northern Greece. J Ethol 29(2):235–242
Zauel R, Yeni Y, Bay B, Dong X, Fyhrie D (2006) Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements. J Biomech Eng 128(1):1–6