The mechanical resonances of a human tibia: part I--in vitro

Ultrasound Characterization of Bone Demineralization Using a Support Vector Machine

We propose an ultrasound-guided remote measurement technique, utilizing an acoustic radiation force beam as our excitation source and a receiving hydrophone, to assess non-invasively a bone's mechanical properties. Features, such as velocity, were extracted from the acoustic pressure received from the bone surface. The typical velocity of an intact bone (3540 m/s) was higher in comparison to that of a demineralized bone (2231 m/s). According to the receiver operating characteristic curve, the optimal velocity cutoff value of ≥3096 m/s yields 80% sensitivity and 82.61% specificity between intact and demineralized bone. Utilizing a support vector machine, the hours of bone demineralization were successfully classified with maximum accuracy >80% using 18% training data. The results indicate the potential application of our proposed technique and support vector machine for monitoring bone mechanical properties.

Vibration analysis of the human radius of elderly men

Vibration analysis seldom has been used in detecting structural and mechanical changes in physiologic and pathologic bone conditions. We sought to correlate natural frequency of the radius measured by vibration analyses with bone mineral density measured by dual-energy xray absorptiometry and quantitative computed tomography (including cortical thickness). Sixty sedentary men between 50 and 70 years old were deemed osteopenic or healthy. A higher natural frequency of the dominant and nondominant radius was seen in the healthy men compared with the osteopenic men. Natural frequency was consistent with bone mineral density in dominant and nondominant radius in both groups. Moreover, there was a correlation between bone mineral density measured by dual-energy xray absorptiometry and natural frequency in the dominant and nondominant radius. Cortical thickness of the dominant and nondominant radius also correlated with natural frequency. We concluded natural frequency measured by vibration analysis is a precise method for the assessment of structural properties of bone and correlates with the bone mineral density of the radius.

LEVEL OF EVIDENCE

Diagnostic study, Level II (Testing of previously developed diagnostic criteria on consecutive patients [with universally applied reference "gold" standard]). See the Guidelines for Authors for a complete description of the levels of evidence.

The use of low-frequency vibration measurement in orthopaedics

This paper reviews the literature regarding the use of applying conventional low-frequency vibration analysis as a possible diagnostic tool in the orthopaedic field. Although a considerable number of investigations have been carried out, including the effects of soft tissue, the technique has not been widely accepted clinically. The application of ultrasound appears to be a more realistic alternative.

Detection of internal fixation plate loosening by means of an analysis of vibratory responses

This paper reports an in vitro investigation of a non-invasive method for detecting the loosening of internal fixation plates. The technique involves the electromechanical vibration of the fixation plate and the electromagnetic detection of its vibratory response. Frequency domain analysis of both fixed and loosened plates are compared and spectral artefacts are suggested as a means of classifying the mode and extent of plate loosening. An algorithm for the diagnosis of loose plates using the new approach is included.

Development of a three-dimensional finite element model of a human tibia using experimental modal analysis

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.

Modelling human tibia structural vibrations

Mode shapes and natural frequencies of human long bones play an important role in the interpretation, prediction and control of their dynamic response to external mechanical loads. This paper describes an experimental and theoretical study of free vibrations in an excised human tibia. Experimentally, seven tibial natural frequencies in the range 0-3 kHz were identified through measured structural transfer functions. Theoretically, a beam type Finite Element model of a human tibia is suggested. Unknown parameters in this model are determined by a Bayesian parameter estimation approach, by which very fine model/observation-accordance was achieved with realistic parameter estimates. A sensitivity analysis of the model confirms that the human tibia in a vibrational sense is more uniform than its complicated geometry would immediately suggest. Accordingly, two simple tibia models are identified, based on uniform beam theory with inclusion of shear deformations.

Non-invasive method of measuring resonant frequency of a human tibia in vivo. Part 1

We describe a method for measuring resonant frequency of a human tibia in vivo. Although the main reason for this measurement is the assessment of a fractured tibia, we emphasize the special instrumentation required; in particular the novel techniques which are used to overcome the difficulty of obtaining results through skin and soft tissue.

Assessment of fracture healing by spectral analysis

The 'in vivo' impulse response of long bones was investigated with the object of assessing the reliability of data taken under various conditions. The ultimate goal of the research is to develop a non-invasive method of monitoring the healing of long bones. A spectrum analyser was developed specifically for this investigation and is presented here.

Vibratory properties and resonances of the isolated human ulna

The frequency response, at various points along the length and circumference, of two isolated human ulnas has been recorded during white noise excitation under 'free-free' conditions. Both bones showed a similar pattern of multiple frequencies of resonance; two fundamental mode resonances occurring in directions mutually at right angles. Further resonances appeared at higher frequencies, both in the same planes as the fundamental modes and in a second plane at 45 degrees; changing the plane of excitation through 90 degrees produced only small changes in the pattern of resonances. Both bones showed marked coupling between neighbouring resonances, with pulling of the frequencies of resonance so that the frequency of the resonant peak may appear to vary by up to 10%.