## 2 Materials and Methods
### Biospeckle Activity Measurement  
To analyse biospeckle data, we applied both quantitative and qualitative methods using the Biospeckle Laser Tool Library--BSLTL ver. 1.3.1. [26; 27] working on MATLAB 2021a with the Image Processing Toolbox (MathWorks Inc., Natick, MA, USA). In the qualitative approach, we obtained activity maps using the average difference method, known also as [PERSON]'s method (AD) [16; 28; 29], and the generalized difference method (GD) [16; 29; 30]. [PERSON]'s method consists of creating a map of biospeckle activity by summing the weighted differences between intensities of corresponding pixels in two consecutive images of the sequence, thus preserving information on temporal changes. The Fujii index for each pixel was calculated from Equation (1) [16]:  
\[F(x,y)\ =\ \sum_{k\ =\ 1}^{N}\frac{|I_{k}(x,y)\ -\ I_{k\ +\ 1}(x,y)|}{I_{k}(x,y)\ +\ I_{k\ +\ 1}(x,y)} \tag{1}\]  
The generalized difference method is an alternative to AD but does not include normalization. Each value of the GD map corresponds to the cumulative sum of differences  
Figure 3: Scheme of biospeckle imaging setup. in single pixel intensity calculated between each image and all other images in the sequence, which is represented by Equation (2) [16]. \[GD(x,y)\ =\ \sum_{k\ =\ 1}^{N\ -\ 1}\sum_{l\ =\ k\ +\ 1}^{N}\ |I_{k}(x,y)\ -\ I_{l}(x,y)| \tag{2}\]  
In Equations (1) and (2) \(k\) = 1,2,... \(N\) stands for image index in the image sequence and \(I_{k}\) is the intensity of pixel with \(x\),\(y\) coordinates. Activity maps generated by AD and GD were obtained using functions fuiji() and gendiff() respectively. The quantitative approach to evaluate biospeckle activity was realised by creating time history speckle patterns (THSPs). A THSP was formed by chronologically arranging the same column taken from each image in the sequence. Consequently, changes in pixel intensity over time were shown in the horizontal direction, while spatial changes were shown in the vertical direction [1]. On this basis, a second order histogram, i.e., co-occurrence matrix (COM) was calculated to represent the frequency of changes in pixel intensities over time. Each COM value corresponded to the number of pairs of pixels with intensity \(i\) and \(j\) that appeared in the THSP image, one after another, in the direction of 0\({}^{\circ}\) (time lapse) [7; 31; 32]. Normalisation of COM leads to reduction of image heterogeneity by making the sum of all values equal to one, according to Equation (3) [32]. \[NCOM_{ij}\ =\ \frac{COM_{ij}}{\sum_{ij}COM_{ij}} \tag{3}\]  
where \(COM_{ij}\) stands for the value in a row \(i\) and a column \(j\) of the co-occurrence matrix. NCOM was the basis to calculate other biospeckle activity indices, such as inertia moment (IM), absolute values of differences (AVD), regular value of differences (RVD) and average differences (obtained by numerical analysis) (NAD) [1; 2; 33; 34]. The inertia moment corresponds to dispersion of NCOM values around the principal diagonal and was calculated by Equation (4) [1]:  
\[IM\ =\ \sum_{i,j}NCOM_{ij}|j\ -\ i|^{2} \tag{4}\]  
The higher the IM values, the stronger the biospeckle activity. Nonetheless, a square operation may result in distortion of variations that occur in THSP; therefore, absolute value of differences were calculated by Equation (5) [33]:  
\[AVD\ =\ \sum_{i,j}NCOM_{ij}|j\ -\ i| \tag{5}\]  
The regular value of differences is similar to AVD but substitutes absolute value of differences with the ordinary difference that occurs between two consecutive pixels, as follows (6) [26]:  
\[RVD\ =\ \sum_{i,j}NCOM_{ij}(j\ -\ i) \tag{6}\]  
The numerical version of AD proposed by [PERSON] et al. [34] measures mean relative contrast between intensities of consecutive images, and was calculated by Equation (7):  
\[NUMAD\ =\ \sum_{i,j}NCOM_{ij}\frac{|i\ -\ j|}{(i\ +\ j)} \tag{7}\]  
In addition, correlation of THSP (TCORR) was obtained from Formula (8) given by [PERSON] et al.