A repeated-measures study design was used to assess the reliability of FDA measured on two occasions at three different ROI and with varied levels of lower limb loading.

A convenience sample of children, adolescents, and adults (n = 20) were recruited from the greater Brisbane metropolitan area. As recommended for method-comparison studies [29], a broad age range was evaluated to ensure that FDA measurements encompassed the full physiological range of values reported within the literature [5, 30]. Participants ranged in age from 8 to 71 years, with a median age of 42.0 years. Four of the 20 participants were aged less than 18 years, while four were greater than 60 years. The mean (± SD) height and weight of participants were 1.70 ± 0.16 m and 70.2 ± 23.0 kg, respectively. Of the twenty participants recruited for this study, thirteen were male and seven were female. No participant reported a medical history of autoimmune disease, bone disease, cancer, calcaneal fracture, or foot surgery. Sample size for the study was estimated based on previously published data for healthy children and adults [31]. A sample size of 20 participants was found to be sufficient to achieve a point estimation of 0.30 in the width of the 95% confidence interval, assuming a correlation of 0.80 among repeated measures [32]. Moreover, participant numbers also provided sufficient statistical power (β = 0.20) to detect a 15 dB MHz difference in measures of FDA, at an α-level of 0.05. Hence, the study was statistically powered to not only determine stable absolute estimates of reliability but to also identify differences equivalent to the minimum important difference reported within the literature for FDA in children and adult populations [23,24,25,26,27,28]. Consent was obtained from participants following a verbal and written explanation of the methods. Assent was obtained from participants under the age of 18 years, along with consent from the legal guardian. Ethical approval for all aspects of the project was received following review by the University Human Research Ethics Committee (1500001041).

FDA (dB/MHz) at the calcaneus was determined using a gel coupled ‘dry’ contact transmission-mode ultrasound system. The system included a portable signal generator and receiver (Omniscan MX, Olympus Australia Pty Ltd, Notting Hill VIC) and two coaxially aligned 1 MHz transducers (0.5 MHz bandwidth), each 1.27 cm in diameter (Olympus NDT, MA, USA). The transducers incorporated nominally 10 mm silicone coupling pads and were mounted in an adjustable calliper. Transducer separation, from pad to pad, was measured using a digital Vernier gauge with a resolution of 10 µm. The Omniscan MX system generated a high-voltage pulse (90 V), and received signals were digitised at 100 MHz (10 bits). Radio-frequency signals were subsequently sampled at 20 MHz providing 640 data points over a measurement range of 50 mm at a system velocity of 1480 m/s. FDA was calculated, relative to degassed water (at room temperature), over a 0.3–0.8 MHz frequency range using established methods [33] and custom software (Matlab software; MathWorks Inc., Natick, Massachusetts, USA).

Three different ROI were evaluated (Fig. 1). Two anatomical ROI (BW and JA) have been previously detailed elsewhere [5, 15] and require knowledge and palpation of relevant anatomy. A third, novel ROI (FG) was also tested. A custom-built foot gauge was used to identify a ROI that was one third of the distance between the dorsal–anterior ankle and the most infero-posterior aspect of the heel. The foot gauge was designed to allow for identification of a standardised anatomical location while considering differences in foot shape and size.

Illustration of the three ROI used for FDA assessment: a Brooke-Wavell (BW) [15], b Jaworski (JA) [5], and c foot gauge (FG)

Participants reported to the laboratory wearing lightweight, comfortable clothing. For each ROI, ultrasound data were collected under four different loading conditions: (1) non-weightbearing (NWB), (2) semi-weightbearing (SWB), in which the participant was seated with their knee and ankle positioned perpendicular to the supporting surface, (3) weight-bearing during dual limb stance (DLS), and (4) weight-bearing during single limb stance (SLS). Prior to ultrasound measurement, the skin was prepared with conventional ultrasound gel. Calcaneal ultrasound signals were subsequently recorded at each ROI under each loading condition. For each participant, replicate measures at each ROI were made with incremental loading, from NWB through to SLS, with each measurement taking no longer than 30 s to complete.

To evaluate the location of each ROI relative to the underlying osseous anatomy, spherical radiopaque markers (Ø, 1.5 mm) were fixed to the skin at the centroid of each ROI. Standard anteroposterior and lateral foot radiographs were then acquired (MULTIX Impact C1, Siemens, Brisbane, Australia) using a radiation exposure equivalent to 2.5 mA s−1, an intensity of 52 kVp, and a focal distance of 1 m. To minimise the exposure of participants to ionising radiation, radiographic images were acquired only under the most extreme weightbearing conditions; namely, NWB and SLS. Anteroposterior and lateral images were acquired with the central ray focused at 50% of foot length. Spatial distortion within the imaging system was minimised using a rectilinear calibration grid (32 × 32 cm) positioned within the object plane and perpendicular to the central ray [34], in combination with a distortion correction procedure [35]. The root-mean-square error for repeated linear measures of nine known calibration structures positioned within the field of view was less than 0.2 mm using this method. Radiographic images were evaluated using custom software (Matlab software; MathWorks Inc., Natick, Massachusetts, USA). The anterior, posterior, inferior, and superior aspects of the calcaneus were manually digitised and fit with a rectangular bounding box. The coordinates of the centroid of each ROI were expressed relative to the posterior and inferior origin of the bounding box and normalised to calcaneal length and height.

The SPSS™ statistical package (SPSS, Chicago, IL) was used for all statistical procedures. Shapiro-Wilke tests were used to evaluate underlying assumptions of normality. Outcome variables were determined to be normally distributed, and hence, means and standard deviations have been used as summary statistics. Absolute reliability was estimated using the Standard Error of Measurement (SEM), and 95% Limits of Agreement (LA) as outlined by Bland and Altman [36]. Plots were visually and statistically evaluated for evidence of heteroscedasticity using the approach outlined by Darlington [37]. Fixed bias between methods was assessed using one-sample t-tests, while proportional bias was evaluated using ordinary least squares regression. In the absence of proportional bias and heteroscedasticity, 95% limits of agreement were calculated using the method outlined by Ludbrook [38], which includes adjustments for small sample sizes (n < 60). In addition, 95% tolerance limits (95%TL), which represent the range within which a single, new, observation taken from the same population would be expected to lie, were calculated using exact parametric confidence intervals as outlined by Carkeet [39]. The 95%TL are conceptually the same as the Minimum Detectable Change (MDC95%), representing the minimum change that is likely to reflect the true change, at and individual level (with 95% confidence), instead of measurement error alone [40].

Potential differences in FDA between each ROI and loading condition were assessed using a two-way repeated measures analysis of variance (ANOVA) within a generalised linear modelling framework. In each case, ROI (BW, JA, FG) and loading (NWB, SWB, DLS and SLS) were treated as within-subject factors. The effect of weightbearing on the location of the centroid of each ROI was investigated using a one-way repeated measures ANOVA. Mauchly’s test of sphericity was used to assess assumptions of sphericity of the variance–covariance matrix. Where significant departures from sphericity occurred, the most conservative adjustment with Greenhouse–Geisser Epsilon was used [41]. Statistically significant main effects were evaluated using simple contrasts. An alpha level of 0.05 was used for all tests of significance.