Participants

Twenty-three healthy older adults volunteered to take part in the experiment. Volunteers were included if they were 50–90 years old, self-reported to have no neurological conditions, and had no contraindications to TMS assessed using a safety checklist. Participants’ handedness was assessed with the short version of the Edinburgh Handedness Inventory (Veale 2014). Written informed consent was obtained before participation. The study was approved by the Auckland Health Research Ethics Committee in accordance with the declaration of Helsinki (REF AH24292).

Experimental arrangements

Two identical experimental sessions were used to investigate the test–retest reliability of the neurophysiological measures. The two sessions were completed at the same time of day, one week apart. For two participants, the sessions were three months apart due to equipment failure. Each session lasted approximately 2 h. The same experimenter responsible for data collection (MJS) completed all sessions which were conducted in the same laboratory at the University of Auckland.

Participants were seated comfortably in a chair with their arms resting on a pillow on their lap or hanging at their side. The position of the arms was chosen based on participant preference and optimal relaxation, which was determined by visual inspection of electromyography (EMG) recordings. The arm position for each participant was kept consistent across sessions.

Frameless stereotaxic neuronavigation (Brainsight®, Rogue Research Inc., Montreal, Canada; Polaris Vicra®, Northern Digital Inc., Ontario, Canada) was used to ensure consistent stimulation sites within and between experimental sessions. Briefly, the infrared camera tracked the participant via a reflective marker set attached near the centre of the forehead and secured with an elastic headband. A reflective marker set was also positioned on the handle of the TMS coil. The participant’s head position was co-registered to a template brain (MNI ICBM 152 average brain). The registration process was refined until the error was less than 3 mm.

Electromyography recordings

Surface EMG was recorded bilaterally from the first dorsal interosseous (FDI), abductor digiti minimi (ADM), extensor carpi radialis (ECR), and flexor carpi radialis (FCR) muscles. Muscle activity was recorded using 25-mm-diameter Ag–AgCl surface electrodes (Cleartrode™ RTL, ConMed, USA) arranged using a consistent belly-tendon montage appropriate for each muscle. A common ground electrode was placed on the dorsum of the left hand. The EMG signals were amplified (× 1000), band-pass filtered (10–1000 Hz), and sampled at 2000 Hz with a CED interface system (POWER1401mkll; Cambridge Electronic Design, Cambridge, UK). EMG data were recorded for 1 s, including a 0.5 s pre-stimulus window. Rectified and smoothed pre-stimulus EMG data were visually displayed to the participant, with a target line at 10 μV overlaid to assist maintenance of a resting state. Participants were instructed to keep the rectified, smoothed EMG trace for all muscles below the target line. Data were saved to a computer for offline analysis using Signal software (version 7.07, Cambridge Electronic Design).

Transcranial magnetic stimulation

TMS was applied using a figure-of-eight coil (MC-B70) connected to a MagPro X100 stimulator with Option, used in Power mode (MagVenture, Farum, Denmark). Due to technical complications, a MagStim 2002 stimulator with a D702 coil (The Magstim Company Ltd., Whitland) was used with four participants. For each participant, the same stimulator was always used for both sessions. The coil was held over the M1 area with the handle posterolateral at approximately 45° from the midline. Monophasic stimulation was used to induce a posterior-to-anterior current in the brain.

An optimal position for eliciting MEPs in all four contralateral muscles was determined and recorded using the Brainsight® software. This ‘global’ hotspot was used to elicit MEPs in all four upper limb muscles. The optimal coil position for eliciting MEPs in the contralateral FDI was also assessed and marked with Brainsight® as the ‘FDI’ hotspot. All recorded hotspots were stored and used in the second session to ensure the same stimulation site was used in both sessions. Sites were confirmed physiologically based on MEP presence.

A maximum-likelihood parameter estimation by sequential testing strategy without a priori information was used to determine FDI RMT (Awiszus and Borckardt 2011) as the lowest stimulator output required to elicit MEPs ≥ 50 μV in 50% of trials (Rossini et al. 2015). Separate FDI RMT values were obtained from stimulation at the global and FDI hotspots. For all participants, the right hemisphere global hotspot was investigated first, followed by the right hemisphere FDI hotspot, before completing the same process for the left hemisphere. A fixed testing order was proposed in a previous reliability study to ensure that any potential order effects consistently influence measurement variability (Schambra et al. 2015).

For the construction the threshold matrix, ten stimuli at ten intensities were delivered to the global hotspot. Stimulation intensities were fixed and ranged from 10 to 100% maximum stimulator output (MSO) in 10% increments. For the construction of S–R curves, ten stimuli at 11 intensities were used with 65% MSO as the additional intensity. The 65% MSO intensity was included to increase sensitivity around the midpoint of the linear portion of the S–R curve. Stimulation intensities were randomised and delivered at an inter-stimulus interval of 6 s with 15% variability.

Data analysis and statistics

Data were processed using custom scripts in MATLAB (R2020b, v9.9; The MathWorks). All statistical analyses were performed in JASP (JASP Team (2022). JASP (Version 0.16.4)).

Threshold matrix construction

A time–frequency analysis of the EMG data was applied to identify the presence or absence of MEPs, similar to a previous report (Tecuapetla-Trejo et al. 2021). This method of automatic MEP detection has a similar performance to manual inspection of EMG traces whilst providing time saving benefits and decreasing manual inspection subjectivity (Tecuapetla-Trejo et al. 2021). Trials with a root mean square (RMS) greater than 15 μV in a 50 ms pre-stimulus window were excluded from analysis for each muscle.

A Short-Time Fourier Transform (STFT) was applied to each EMG signal from each trial using a window size of 10 ms with a 5 ms overlap. The STFT outputs are a frequency vector, a time vector, and a matrix with complex STFT coefficients across both time and frequency. The frequencies ranged from 0 to 1000 Hz. The power spectral density (PSD) was calculated by squaring the absolute value of the STFT coefficients. The PSD represents the distribution of the signal’s energy into frequency components (Dempster 2001). The maximum PSD value was determined for each time window by identifying the highest power observed across all frequency ranges. Across all trials for each muscle, the largest maximum PSD value in a 50 ms pre-stimulus time window was identified and set as the criterion for MEP detection. If the maximum PSD value in a 15–30 ms post-stimulus window was greater than the criterion set from the pre-stimulus PSD values, the trial was deemed to have a MEP response. For trials with a MEP, the peak-to-peak MEP amplitude and pre-stimulus RMS were calculated from the same time windows used for the PSD analysis.

The threshold matrix has forty elements comprised of ten stimulation intensities and four muscles. Stimulation intensities ranged between 10 and 100% MSO in 10% increments. Ten stimuli were delivered at each intensity. If trials were rejected due to noise or background EMG, at least five trials had to be retained for any given intensity and muscle. If less than five trials were available for analysis for any muscle and intensity, the participant’s data were excluded from the analysis.

Each cell of the threshold matrix was colour-coded based on RMT criteria. Stimulation intensity and muscle combinations that resulted in MEPs ≥ 50 μV in at least 50% of trials were coloured green. Stimulation intensity and muscle combinations that produced MEPs which did not meet RMT criteria were coloured orange. Stimulation intensity and muscle combinations that did not produce any MEPs were coloured red.

A schematic of threshold matrix construction using a participant’s data is shown in Fig. 1. Threshold matrix composition was calculated across the four muscles and ten stimulation intensities by dividing the number of cells of the colour of interest by the total number of squares in the matrix (i.e. 40) and multiplying by 100. The green, orange, and red compositional elements are termed suprathreshold, subthreshold, and subliminal, respectively.

Fig. 1

Threshold matrix construction. A A 40-cell threshold matrix comprised of four upper limb muscles (columns) and TMS intensity in %MSO (rows). Other variations are possible. Cells that produce a set of MEPs that meet the criteria for RMT are coloured green. Cells that produce a set of MEPs that fail to meet RMT criteria are coloured orange. Cells that do not elicit MEPs are coloured red. B Threshold matrix composition is calculated by determining the proportion of each coloured element. The red, orange, and green elements are termed the subliminal, subthreshold, and suprathreshold elements, respectively and sum to 100%. FDI first dorsal interosseous, ADM abductor digiti minimi, ECR extensor carpi radialis, FCR flexor carpi radialis

Compositional data analysis

The three compositional elements in the matrix are constrained to sum to 100% and any change in one matrix element will necessarily change one or both remaining elements. This means the relationship between the elements is of interest, rather than the absolute sum (Greenacre 2021). Elements cannot have negative values as they are proportions. Together with the constant-sum constraint, this means that the data do not fit the assumptions of normality and must be transformed before applying parametric statistical techniques. Logarithms of ratio transformations (log ratios) were applied to the data, preserving the elements’ composition but removing the dependency between elements (Greenacre 2021). Amalgamation log ratios (ALRs) are used as they are more readily interpreted than balance measures obtained from isometric log ratios (Greenacre et al. 2021). Each ALR was computed as one element relative to the sum of the remaining elements. For example, the ALR for the suprathreshold element was calculated as ln(suprathreshold/(subthreshold + subliminal)). Calculating the exponent of the ALR (eALR) returns the percentage difference of the numerator compared to the denominator (Greenacre et al. 2021). Zero values can become problematic in compositional data analysis due to their incompatibility with log ratios. As such, a conventional replacement method has been used in this dataset, whereby the zeros were replaced with 65% of the smallest unit, which is one cell of the threshold matrix (i.e. 0.65*(1/40*100)) (Martín-Fernández et al. 2003). Once the ALRs were calculated, parametric statistics were conducted.

The average threshold matrix composition was calculated across the two sessions for each participant from the dominant and non-dominant sides. The average compositions from the dominant and non-dominant sides were visualised in a ternary plot along with the centre of the composition, calculated using geometric means. Ternary plots are the standard graphical tool for visualising three-part compositional data sets with each vertex representing one element as a percentage. The sum of the three percentages for any data point always equal 100%. The closer a data point is to any vertex, the more of that element is present in the composition.

Stimulus–response curve construction

The pre-stimulus window was set for 50 ms prior to stimulation onset. Trials were removed if pre-stimulus EMG RMS was greater than 15 μV. The MEP amplitude window width was 50 ms, starting 10 ms post stimulation onset. Averages of pre-stimulus RMS and MEP amplitude for each stimulation intensity for each muscle were calculated. The average MEP amplitude for each muscle was plotted as a function of TMS intensity, and a sigmoid function was fitted in MATLAB, similar to previous studies (Capaday 1997; Devanne et al. 1997). The slope of the function at S50 was determined as a measure of the gain of the corticomotor pathway (Devanne et al. 1997). The S–R curve slopes are expressed in mV/10% MSO.

Reliability measures

Intraclass correlation coefficients (ICC) were used to examine test–retest reliability (De Vet et al. 2011). The ICC indicates the extent to which people in the sample could be distinguished from one another in the presence of measurement error (Polit 2014). ICC scores range from 0 to 1, with higher scores representing less measurement error and higher reliability. The following criteria are commonly used for ICC interpretation: < 0.5 poor reliability; 0.5 ≥ 0.75 moderate reliability; 0.75 ≥ 0.9 good reliability; > 0.9 excellent reliability (Koo and Li 2016).

Before performing the ICC calculations, the normality of the S–R curve slope and RMT data were checked using Shapiro–Wilk tests and visual inspection of Q–Q plots. Logarithmic transformations were used to correct non-normal data.

The ICC was calculated for the three elements of the threshold matrix, RMT from both the global and FDI hotspot, and the slope of the S–R curve obtained for each muscle. All ICC calculations were determined from data obtained for both the dominant and the non-dominant sides. An ICC3,1 model was used to fit the data obtained from the two-way mixed effects and single rater design. Bland–Altman plots were used to visually inspect the test–retest measures (see supplementary material).

Dominant versus non-dominant sides

Bayesian paired t-tests were used to assess differences in the threshold matrix elements between the dominant and non-dominant sides. The ALRs were calculated from the geometric mean composition across the two sessions for each participant. The Bayes Factor in favour of the null hypothesis (BF01) was calculated with Bayesian paired t tests. A BF01 greater than one supports the null hypothesis and values less than one support the alternative hypothesis. The strength of evidence for the null hypothesis was determined by interpreting the effect size as small (BF01: 1–3), medium (BF01: 3–10), or large (BF01: > 10) (van Doorn et al. 2021).

Subthreshold responses versus resting motor threshold correlations

A Bayesian correlational analysis was performed for both the dominant and non-dominant sides to assess whether the subthreshold element of the threshold matrix was associated with RMT. Support for the null hypothesis was determined by the BF01 value using the same criterion as above.

Threshold matrix composition of distal versus proximal muscles

Bayesian paired t tests were used to compare the threshold matrix composition of the two hand and two forearm muscles. The dominant and non-dominant threshold matrices for each participant were split into an FDI and ADM, and an ECR and FCR matrix. The same compositional data analysis process was used with the two muscle matrices as the four muscle matrices. The average hand and forearm composition was calculated for each participant across the two sessions. Support for the null hypothesis was determined by the BF01 value using the same criterion as above.

Resting motor threshold comparisons

Bayesian paired t-tests were used to assess differences in the RMT values obtained from the global and FDI hotspot for the dominant and non-dominant sides. The average RMT value was calculated for each participant across the two sessions. Support for the null hypothesis was determined by the BF01 value using the same criterion as above.