Resultant loads and elastic modulus calibration of long bone cross sections

doi:10.1016/0021-9290(81)90030-0

Journal of Biomechanics

Volume 14, Issue 11, 1981, Pages 739-741, 743-745

https://doi.org/10.1016/0021-9290(81)90030-0 Get rights and content

Abstract

A method of calibrating a long bone cross-section for the resultant axial force and bending moments is presented. At least three single gages must be bonded at circumferential locations at the section of interest. In the laboratory, strains are recorded when known anterior-posterior and lateral-medial bending moments are applied. Strains are also recorded when a known axial force (of unknown eccentricity) is applied. From these measurements one can calculate the resultant loads acting at the section whenever the three simultaneously recorded strain values are known. In addition, the section axial stiffness and effective axial elastic modulus of the section can be determined. This calibration method is especially pertinent in the analysis of in vivo bone strains which have been previously recorded.

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Measurement and analysis of in vivo bone strains on the canine radius and ulna
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Stress fields in the unplated and plated canine femur calculated from in vivo strain measurements
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There are more references available in the full text version of this article.

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Semiautomated finite element mesh generation methods for a long bone
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Reconstructed bone end loads on the canine forelimb during gait
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The objective of this work was to determine bone loading conditions that, when applied to a finite element model, would best reproduce the in vivo strain field as measured by surface-mounted strain rosettes. The present study adopts the basic mathematical approach to load reconstruction introduced by Weinans and Blankevoort (J. Biomech. 28 (1995) 739) who determined the relationship between applied loads and bone strain distribution using ex vivo calibration testing. Our method eliminates the need for subsequent ex vivo calibration tests by instead substituting a computational calibration procedure. This first application of the method is with in vivo strains on the canine forelimb during gait (Coleman et al., J. Biomech. 35 (2002) 1677), but with further refinements the method could be used to reconstruct the in vivo loading conditions in living subjects.
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Reconstruction of bone loading conditions from in vivo strain measurements
1995, Journal of Biomechanics
A method is described whereby bone loading conditions can be reconstructed from in vivo strain measurements. The method uses ex vivo calibration measurements to find the relationship between the strain data and the loads applied to the bone. Using singular value decomposition, a transformation matrix is determined which provides the best linear relationship available between the measured strain data and the measured loading components in the calibration measurements. The transformation matrix can then be used to calculate the loads which correspond best with any given strain data set made with that specific bone and strain gages. In this manner, the applied loads of earlier performed in vivo strain measurements can be reconstructed. The method was tested for the reconstruction of the loads on a tibia of a goat. After determining the transformation matrix from a set of calibration measurements, the transformation matrix was used to reconstruct all loading components (three forces and three moments) of a set of test measurements whereby the applied loads were measured. It was found that the axial force and the torsional moment on the bone could be reproduced very accurately, showing a root mean square error (RMSE) of only 2% of the maximal load in the test. The reconstruction of the bending moments was slightly worse. showing a RMSE of 5–8% of the maximal moments. The reconstruction of the transverse force components proved less accurate and a RMSE up to 24% of the maximum was found. Accuracy can be improved by using weight factors for the loading conditions and a more accurate measurement of the location of the loads during the calibration measurements.
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A strain gage based experimental method is presented which provides an alternative to use of area sectional properties for obtaining the cross sectional centroids, flexural rigidities and axial stiffness of whole bone specimens. While area sectional property computations require detailed records on the geometry of cross sections, the experimental method presented here requires only gage locations plus the applied loads and recorded strains. Both techniques are used to analyze the midshaft sectional properties of canine radii. The results demonstrate the advantage of the experimental method for the analysis of heterogeneous cross sections with an unknown distribution of bone elastic modulus. By applying the experimental and area methods together, effective elastic modulus values for the sections were obtained.

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Abstract

References (10)

Measurement and analysis of in vivo bone strains on the canine radius and ulna

J. Biomechanics

Stress fields in the unplated and plated canine femur calculated from in vivo strain measurements

J. Biomechanics

The relationship of functional stress and strain to the processes of bone remodelling. An experimental study on the sheep radius

J. Biomechanics

An extended structural analysis of long bones-application to the human tibia

J. Biomechanics

In vivo and analytical studies of forces and moments in equine long bones

J. Biomechanics

Cited by (19)

Evidence of isometric function of the flexor hallucis longus muscle in normal gait

Semiautomated finite element mesh generation methods for a long bone

Reconstructed bone end loads on the canine forelimb during gait

The mechanical properties of catgut in holding and bonding fractured bones

Reconstruction of bone loading conditions from in vivo strain measurements

Experimental determination of whole long bone sectional properties