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Medical and biological engineering

, Volume 14, Issue 3, pp 253–262 | Cite as

In vivo determination of mechnical properties of the human ulna by means of mechanical impedance tests: Experimental results and improved mathematical model

  • Gerald A. Thompson
  • David Orne
  • Donald R. Young
Article

Abstract

An experimental technique and associated apparatus for measuringin vivo the mechanical impedance of the human ulna are described in detail. An electromagnetic shaker is used to apply a steady-state harmonic excitation to the ulna near its mid-span and measurements of the complex driving-point impedance are made. Both stiffness and resonant frequency information, useful in assessing the mechanical integrity of bone, are inferred from the impedance measurements by means of a third-generation mathematical model of the system. Results for three male and two female test subjects are reported.

Keywords

Human ulna Mechanical impedance Resonant frequency Bone Mathematical modelling 

Nomenclature

L

span length of beam model of the ulna, cm

a

distance from olecranon process to point of load application, cm

r

external radius of tubular beam model of ulna, cm

ξ

ratio of internal radius to external radius of tubular beam model

α

shape factor for computing moments of inertia

E

Young's modulus, N/m2

ωn

undamped fundamental frequency of beam (or musculature) model, Hz

ζ

damping ratio of beam (or musculature) in its first (fundamental) mode of free vibration

ϱ

density of beam, g/cm3

I

απr 4(1−ξ4)/4=second moment of area of beam cross-section, cm4

A

πr 2(1−ξ2)= area of beam cross-section

μ

ϱA=mass per unit length of beam, g/cm

η

viscous modulus of musculature, N-s/m2

b

effective width of musculature rod model, cm

l

effective height of musculature rod model, cm

k

eleastic spring constant (depends on preload) for tissue under impedance head, N/m

c

viscous coefficient for tissue under impedance head, N-s/m

Sommaire

On décrit dans le détail une technique expérimentale et l'appareillage correspondant pour mesurer ‘in vivo’ l'impédance mécanique du cubitus humain. On se sert d'un trembleur électromagnétique pour appliquer une excitation harmonique en état statonnaire au cubitus, aux environs de la mi-envergure, et on prend des mesures de l'impédance complexe du point moteur. Des informations concernant la raideur et la résonance, utiles toutes les deux pour déterminer l'intégrité mécanique de l'os, sont déduites des mesures d'impédance à l'aide d'un modèle mathématique de troisième génération (pour circuits intégrés) du système. On donne les résultats obtenus sur trois sujets masculins et deux sujets féminins.

Zusammenfassung

Hierbei handelt es sich um die detaillierte Beschreibung eines Versuchsverfahrens und der hierfür eingesetzten Apparate zur Messung der mechanischen Impedanz der menschlichen Ellein vivo. Nahe der mittleren Ellenspanne wird zur Erzeugung einer statischen harmonischen Anregung eine elektromagnetische Schüttelvorrichtung angesetzt, und der komplexe Eingangsscheinwiderstand wird gemessen. Mit Hilfe eines mathematischen Systemmodells der dritten Generation können von den Impedanzmessungen Angaben über Steifigkeit und Resonanzfrequenz abgeleitet werden, die zur Beurteilung der mechanischen Knochenintegrität nürtzlich sind. Es wird über die mit drei männlichen und zwei weiblichen Versuchsobjekte erhaltenen Ergebnisse berichtet.

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References

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Copyright information

© International Federation for Medical & Bological Engineering 1976

Authors and Affiliations

  • Gerald A. Thompson
    • 1
  • David Orne
    • 2
  • Donald R. Young
    • 3
  1. 1.Control Data CorporationSunnyvaleUSA
  2. 2.Department of Mechanical EngineeringWayne State UniversityDetroitUSA
  3. 3.Environmental PhysiologyNASA Ames Research CentreMoffett FieldUSA

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