## 2 Materials and Methods
### Data Analysis  
For exercise phase, an 11 th-order high-pass Butterworth filter was firstly performed to remove long-period shift in the TOI (Figure 1A) and \(\Delta\)Hb (Figure 1B) signal. The cutoff frequency was set to be 0.015 Hz. The gray areas in Figure 1A,B show the heel lift period. Secondly, the wavelet transform was applied to acquire the 3-dimensional (3D) wavelet amplitude (WA) in the time-frequency domain (Figure 1C,D), with the red boxes highlighting the oscillations related to muscle contractions. Thirdly, the 3D WA was averaged over the time domain to show the spectral distribution and to extract the hemodynamic components related to muscle contraction (Figure 1E,F). Lastly, iTOI and itHb, the exercise-induced fluctuations in the TOI and \(\Delta\)Hb signal, were reconstructed through the inverse wavelet transform (Figure 1G,H). The frequency band assigned in the inverse wavelet transform was determined by a 2-step iteration method. Step 1, an approximate frequency was calculated by \(F=40/Tc\), where 40 means the total number of heel lifts and \(Tc\) means the duration of the exercise. Then, around the frequency \(F\), the adjacent WA peak and the whole peak area were identified as the main frequency components related to the heel lift exercise, as shown by the gray areas in Figure 1E,F. In this study, the inverse wavelet transform was conducted by the icwt function provided by MATLAB Release R2019a version 9.6 (The MathWorks Inc., Natick, MA, USA).  
For both rest phases, the TOI signals were averaged over the 30-min measurement to acquire the mean tissue blood oxygenation level before and after the exercise. The \(\Delta\)Hb signals were preprocessed by an adjusted moving-average method to remove abrupt spikes induced by sudden movement and/or background light. Then a sixth-order Butterworth band-pass filter (0.005-2 Hz) was used to remove irrelevant frequency components and long-term shift (Figure 2A) [27]. Wavelet transform was applied to decompose the \(\Delta\)Hb time series from the time domain into the time-frequency domain in distinct scales with the frequency band ranging from 0.005 to 2 Hz (Figure 2B). To quantify the oscillation magnitude of different frequency components (Figure 2C), we calculate the mean wavelet amplitude (WA) of each frequency interval defined above by the following equation:\[\text{WA}(i)=\frac{1}{t(s_{i2}-s_{i1})}\int_{0}^{t}\int_{s_{i1}}^{s_{i2}}\left|W(s,t )\right|ds\;dt \tag{4}\]  
The wavelet amplitude can represent the magnitude of hemodynamic oscillations caused by different physiological activities. To further evaluate the contribution of each physiological origin, the average energy within a given frequency interval was introduced as  
\[\varepsilon(i)=\frac{1}{t}\int_{0}^{t}\int_{s_{i1}}^{s_{i2}}\frac{1}{s^{2}} \left|W(s,t)\right|^{2}ds\;dt \tag{5}\]  
and normalized by the total average energy \(\varepsilon_{total}\) of the whole frequency band of interest (0.005-2 Hz)  
\[E(i)=\frac{\varepsilon(i)}{\varepsilon_{total}} \tag{6}\]  
The normalized wavelet energy reflects the relative energy contribution of each frequency interval to the total signal. This normalization could also reduce the variance induced by spatial and temporal inhomogeneities of the blood flow [21; 25; 33].  
Figure 1: Hemodynamic oscillations induced by muscle contraction in tissue oxygenation index (TOI) (**A**) and total hemoglobin signal (\(\Delta\)tHb) (**B**) signal with the gray box showing the exercise phase. Scalograms of TOI (**C**) and \(\Delta\)tHb (**D**) signal after wavelet transform, with the red box showing the contraction-induced component in the corresponding signal. Time-averaged wavelet amplitudes of TOI (**E**) and \(\Delta\)tHb (**F**) signal, with the gray box showing the frequency component related to contraction. Inverse wavelet transform of contraction-related frequency component in TOI (**G**) and \(\Delta\)tHb (**H**) signal, with the gray box showing the exercise phase.