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. 2019 Oct 14:6:2408-2419.
doi: 10.1016/j.mex.2019.10.004. eCollection 2019.

Improvements to mechanical response tissue analysis

Lyn Bowman  1   2 , Anne B Loucks  1   2
Affiliations

Improvements to mechanical response tissue analysis

Lyn Bowman et al. MethodsX. .

Abstract

Cortical Bone Mechanics Technology™ (CBMT) comprises certain improvements over a previous method known as Mechanical Response Tissue Analysis (MRTA). Both methods are dynamic 3-point bending tests intended for measuring the mechanical properties of cortical bone in living people. MRTA presented a theoretical potential for direct measurement of skeletal fragility, but it had acquired a reputation for error and fallen into disuse. We found sources of error in both MRTA data collection and data analysis. We describe here the fundamentals of MRTA, the major sources of error we found in MRTA, and our innovations for avoiding them. •Data collection at many sites across the mid-shaft of the ulna bone in the forearm.•Parameter estimation by fitting analytical complex compliance and stiffness transfer functions to empirical complex compliance and stiffness frequency response functions.•Optimization by selecting results from frequency response functions with the smallest deviations between fits to compliance and stiffness frequency response functions.

Keywords: Bending stiffness; Bending strength; Cortical Bone Mechanics Technology; Cortical bone; Noninvasive; Validation.

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Figures

None
Graphical abstract
Fig. 1
Fig. 1
Mechanical models for QMT (left) and MRTA (right) tests. (F = force; x = displacement; M = mass, D = damping, K = stiffness; S = skin, B = bone, P = peripheral soft tissue. In QMT, skin and peripheral soft tissue are absent, and F changes so slowly that effects of MB and DB are negligible.
Fig. 2
Fig. 2
Typical QMT data (left) and MRTA data (right). Note the presence of two resonances in the MRTA data indicated by two peaks in the imaginary part and two sigmoidal curves in the real part of accelerance.
Fig. 3
Fig. 3
The real and imaginary parts of an oscillatory response at a single frequency f = 1/T.
Fig. 4
Fig. 4
Fits of complex compliance (left) and stiffness (right) transfer functions to typical complex compliance and stiffness frequency response functions measured in MRTA tests of a forearm. Note: the X-axis begins at 40 Hz.
Fig. 5
Fig. 5
MRTA data collection from a tibia of a living human subject [15].
Fig. 6
Fig. 6
Real parts of tibia stiffness FRFs collected in the manner illustrated in Fig. 5 [6].
Fig. 7
Fig. 7
Cross-sectional microtomographic images at the mid-shaft of selected ulna bones [1].
Fig. 8
Fig. 8
Complex compliance FRFs with (left) and without (right) an extraneous mode of vibration at 121 Hz. Blue = real part of FRF; black = imaginary part of FRF; red = real part of TF; pink = imaginary part of TF; dashed = TF fitted to complex compliance FRF; solid = inverted TF fitted to complex stiffness FRF. Note: the X-axis begins at 40 Hz.
Fig. 9
Fig. 9
Variation of estimates of ulna bending stiffness from fits of the complex stiffness TF to the complex stiffness FRF (kbS, left), and from fits of the complex compliance TF to the complex compliance FRF (kbC, right), with the frequency range over which fits were performed. Note: fmin = minimum frequency of the fitting frequency range; fmax = maximum frequency in the fitting frequency range.
Fig. 10
Fig. 10
Variation in RMS7 and KB in a transit across a forearm.
Fig. 11
Fig. 11
Variation in RMS7 across subranges of frequency in a single FRF.
See this image and copyright information in PMC

References

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