PT is the minimum stimulation amplitude that subjects can perceive at a certain stimulation frequency at a certain stimulation site and can be represented as PT(f, l). For any given frequency f and site l, the amplitude thresholds changes for each person, as shown in Clemente et al. (2017, 2016), and Mayer et al. (2019), thus it is necessary to be identified.

The JND is determined for amplitude as well as frequency describing the resolution of the interface and therefore specifying the possible information rate of the interface. It is the minimum difference a subject can discriminate with a pre-determined probability. The JND_f(f, a, l) varies with stimulation amplitude a for a given stimulation frequency f and site l. The JND_a(f, a, l) varies with stimulation frequency f for a given stimulation amplitude a and site l. For a non-invasive bone conduction interface applied to the elbow (a natural location for the case of a transradial prosthetic arm), three accessible bony landmarks exist, namely the epicondylus (medialis and lateralis) and the ulnar olecranon. Therefore, multiple vibrotactile transducers can be deployed and potentially be used simultaneously. The spatial domain is therefore characterized by the spatial parameter single-point location identification rate (SPLIR).

SPLIR is the success rate that the subject correctly identifies the correct stimulation site. SPLIR is different for each site l:

where N_corr(l) is the number of correct identified stimulations for the number of presented stimulations N(l) at site l.

Three B81 transducers T1-T3 from RadioEar Corporation (USA) were utilized to provide the vibrotactile stimulus to the bony landmarks. All three transducers were calibrated using an Artificial Mastoid Type 4930 from Brüel & Kjære (Denmark) adjusted to produce the same force output of 121.5 dB at f = 1 kHz. The transducers were affixed to the bony landmarks, see Figure 1, of the subjects using a 3D printed holder (PLA/TPU) and medical grade double sided sticker Type 1510 (3M™).

A National Instruments NI USB-6343 is used.

A 15W Public Address amplifier type A4017 from Redback Inc. (Australia) with 4 − 16Ω output to drive the 12.5Ω B81 transducers and achieve a harmonic distortion of < 3% at 1 kHz.

A Windows Surface Book 2 (Intel Core i7-8, 16GB RAM, Windows 10™) and a MATLAB^® GUI, guiding the user through the experiment and controlling the stimulation parameters.

A complete psychophysical evaluation of the perception threshold would imply determining the PT at a step size determined by the Just Noticeable Difference Frequency difference (JND_f). As the JND_f is not known a priori, the preliminary results obtained in Mayer et al. (2018, 2019, 2020c) are used to define the frequency range, where the three sites L1-3 are each individually perceivable as well as dominant tactile perception is shown in a frequency range of f ∈ [100, 400, 750] Hz. The perception threshold PT(f, l) is obtained via SIAM (Kaernbach, 1990) method. The threshold for each frequency f at the site l is obtained by presenting 26 repetitions and the amplitude adjusted according to the subjects feedback via SIAM method. The frequencies f are presented in a randomized manner at each site l. To allow for a technical implementation and selection of suitable transducers the Perception Threshold is given in Newton utilizing the previously obtained calibration (Figure 2).

Similar to PT, a complete psychophysical characterization of the JND would imply determining a full range in amplitude/frequency (AF). This would result in an impractically large number of measurements, resulting in an excessively long duration of experiments for subjects. Hence, the AF domain was divided into discrete steps, called AF reference points, where f_ref ∈ [100, 400, 750] Hz and a_ref ∈ [0.1, 0.3, 0.5] V resulting in a combination of 9 AF points where the reference amplitudes and frequencies where chosen according to the preliminary results obtained in Mayer et al. (2019). At each AF reference point, the JND_f and JND_a were obtained in increasing direction (toward the maximum value). The JND is given in Volt, which can be used to derive the smallest necessary step size for an implementation and selection of suitable driver circuitry.

Spatial parameters were obtained according to Mayer et al. (2020c). The subjects were asked to report on the site L1-L3 of the stimulation. Therefore, the subjects were presented with the stimuli on the three different sites without a priori knowledge of the stimulation site. The order of stimulation sites were applied randomly from f ∈ [100, 200, 400, 750, 1,500, 3,000, and 6,000] Hz, a = 0.5 V and each repeated 10 times. Frequencies are choose according to the shown bandwidth in Clemente et al. (2017) and Mayer et al. (2019). Each stimulation was ON for 1 s. At the start of the experiment, the subjects were provided with the opportunity to familiarize themselves with the stimulation and therefore explore the association of the three stimulation sites by voluntary inducing stimuli on each site.

A non-parametric statistical analysis, specifically a Friedman Test (Daniel, 1990) was applied to compare the three physiological sites for each temporal and spatial parameter. In case of statistical significant differences, this was followed up by a post-hoc analysis via Wilcoxon signed rank test (Wilcoxon, 1945) to determine which of the three physiological sites was different. The p-value results are presented for the Friedman as well as the applied post-hoc Wilcoxon signed rank test.

The achieved results of perception threshold are visually presented by plotting the mean and the stand deviation as an error bar.

A summary plot shows the JND_a and JND_f at each AF reference point by its mean value, with the origin at the AF reference point. More details are shown in individual plots for each AF reference point for each site showing the obtained mean value and the stand deviation as an error bar.

The achieved results of perception threshold is visually presented similar as in Mayer et al. (2020c) by plotting the mean and the stand deviation as an error bar.

A qualitative comparison between able-bodied subjects and subjects with trans-radial amputation (ST) was carried out to compare the two subject groups for each temporal and spatial parameter. The obtained mean values for the parameters are use for such comparison.

The results for PT are shown in Figure 3 and Table 2. The results of the obtained perception threshold, for the three physiological sites of able-bodied subjects (SA) and trans-radial amputees (ST) are shown in Figure 3. The mean perception thresholds for SA is [0.015 0.45 0.2] N and for ST [0.015 0.21 0.25] N for [100 400 750] Hz.

The Friedman test results, comparing the three different sites, are shown in Table 2. The obtained results indicate a statistically significant difference in performance for [100 750] Hz for the perception threshold for the three different sites. No statistical difference is observed at 400 Hz. A post-hoc test (Wilcoxon signed rank test), is performed for [100 750] Hz and the corresponding p-values are shown in Table 2. In the following, the obtained results are summarized:

L1 vs. L2: A statistical significant difference for perception threshold at [100 750] Hz is shown in Table 2 with L1 having a lower PT.

L1 vs. L3: A statistical significant difference for perception threshold at [100 750] Hz is shown in Table 2 with L1 having a lower PT.

L2 vs. L3: No statistical significant difference was obtained for perception threshold at [100 750] Hz shown in Table 2.

Note that the p-values are at 0.059 for both cases, therefore they are only slightly above significance level of p < 0.05.

The results for the just noticable difference in amplitude JND_a are shown in Figure 5A and Table 3. The results for the just noticable difference in frequency JND_f are shown in Figure 5B and Table 4. A combined plot is shown in Figure 4, showing the mean at each site. The details of JND_a and JND_f are shown and discussed in the following.

The results of the obtained SPLIR are shown in Figure 6 for all three physiological sites. The Friedman results for the three different sites, as shown in Table 5, indicate no statistically significant difference in performance for the different sites for SPLIR, hence, no post-hoc test was performed.

The results obtained in this study suggest a usable bandwidth for bone conduction as a sensory feedback from 100 to 750 Hz when multiple transducers are used on multiple stimulation sites. The perception threshold is as low as 0.01 N at 100 Hz and increases to 0.2 N at 750 Hz. This range of force perception and frequency bandwidth suggest that commercially available transducers used in audiology could be used for bone conduction sensory feedback. Furthermore, the perception threshold for non-invasive bone conduction was found to be comparable to results obtained with invasive bone conduction techniques (Clemente et al., 2017). The study also revealed that frequency resolution was more distinguishable than amplitude. This finding could have implications for the design of future bone conduction feedback systems, as it suggests that greater attention may need to be paid to the frequency content of the feedback signals.

It should be mentioned that sensory feedback bone conduction is not applicable for subjects with diseases affecting the perception of such stimulation e.g., a potential subject in this study had to be excluded due to the inability to perceive stimulation likely caused by rheumatoid arthritis.