Skip to main content
SpringerLink
Log in

Bone microstructure in finite element modeling: the functional role of trabeculae in the femoral head of Sciurus vulgaris

  • Original Paper
  • Published:
Zoomorphology Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Abbreviations

CT:

Computed tomography

deg:

Degrees

FEA:

Finite element analysis

m :

Body mass

m fh :

Effective body mass that is supported by one hind limb (fh = femoral head)

wotb:

Without trabeculae

wtb:

With trabeculae

α :

Angle between femur and substrate

β :

Angle defining the substrate inclination

γ :

Angle between femur and gravitational pull

ε :

Strain

σ :

Stress

3D:

Three dimensional

lβ :

Models with increasing magnitude of load depending on inclination

l0:

Models with same magnitude of load for all inclinations

References

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    Article  PubMed  PubMed Central  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    PubMed  PubMed Central  Google Scholar 

  • Bright JA (2014) A review of paleontological finite element models and their validity. J Paleontol 88(4):760–769

    Google Scholar 

  • Bright JA, Rayfield EJ (2011) The response of cranial biomechanical finite element models to variations in mesh density. Anat Rec 294(4):610–620

    Google Scholar 

  • 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

    PubMed  Google Scholar 

  • Carter D, Orr T, Fyhrie D (1989) Relationships between loading history and femoral cancellous bone architecture. J Biomech 22(3):231–244

    CAS  PubMed  Google Scholar 

  • 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

    PubMed  PubMed Central  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • Demes B, Fleagle JG, Jungers WL (1999) Takeoff and landing forces of leaping strepsirhine primates. J Hum Evol 37:279–292

    CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    Google Scholar 

  • Farke AA (2008) Frontal sinuses and head-butting in goats: a finite element analysis. J Exp Biol 211(19):3085–3094

    PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    CAS  PubMed  PubMed Central  Google Scholar 

  • Lammers AR (2007) Locomotor kinetics on sloped arboreal and terrestrial substrates in a small quadrupedal mammal. Zoology 110(2):93–103

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    Google Scholar 

  • Milne N (2016) Curved bones: an adaptation to habitual loading. J Theor Biol 407:18–24

    PubMed  Google Scholar 

  • Murray P (1936) Bones: a study of the development of structure in the vertebrate skeleton. Cambridge University Press, London

    Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    PubMed  PubMed Central  Google Scholar 

  • Rayfield EJ (2004) Cranial mechanics and feeding in Tyrannosaurus rex. Proc R Soc Lond B Biol Sci 271(1547):1451–1459

    Google Scholar 

  • 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

    CAS  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    Google Scholar 

  • Schneider CA, Rasband WS, Eliceiri KW (2012) NIH Image to ImageJ: 25 years of image analysis. Nat Methods 9(7):671

    CAS  PubMed  PubMed Central  Google Scholar 

  • Si H (2015) Tetgen, a delaunay-based quality tetrahedral mesh generator. ACM Trans Math Softw 41(2):11

    Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • Wauters L, Dhondt AA (1989) Body weight, longevity and reproductive success in red squirrels (Sciurus vulgaris). J Anim Ecol pp 637–651

    Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

  • 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

    Article  PubMed  PubMed Central  Google Scholar 

  • 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

    PubMed  Google Scholar 

  • 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

    Google Scholar 

  • 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

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

We are grateful to Fiete Meyer for his input and helpful advice during the early phase of this project and to Oliver Demuth for his kind assistance in handling sensitive meshes. We thank Jan Wölfer, Eli Amson, and Anneke H. van Heteren, who had acquired the CT-scan and provided it for this study. JAN was funded by the German Research Foundation (DFG EXC 1027). We want to thank Jordi Marcé-Nogué for his revision, which helped us to greatly improve this manuscript.

Author information

Authors and Affiliations

  1. AG Morphologie und Formengeschichte, Institut für Biologie, Humboldt Universität zu Berlin, Philippstraße 12/13, 10115, Berlin, Germany

    Maja Mielke & John A. Nyakatura

Authors
  1. Maja Mielke
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John A. Nyakatura
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Maja Mielke.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 9494 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mielke, M., Nyakatura, J.A. Bone microstructure in finite element modeling: the functional role of trabeculae in the femoral head of Sciurus vulgaris. Zoomorphology 138, 535–547 (2019). https://doi.org/10.1007/s00435-019-00456-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00435-019-00456-2

Keywords

Search

Navigation