Multifractal analysis of chest CT images of patients with the 2019 novel coronavirus disease (COVID-19).

The present study was done to evaluate chest computed tomography (CT) images of patients with 2019 novel coronavirus disease (COVID-19) by multifractal technique as a new method to find a way for comparing lung infection quantitatively and identifying progression pattern of the disease. The multifractal spectra extracted from analysis of CT images showed that these spectra were correlated with lung infection amount and disease progression so that, multifractal parameters (αmin, αmax, ∆α, f(αmin), f(αmax), ∆f(α), α(q = 0), and f(α) max) were strongly dependent on amount of lung infection. The results demonstrated that multifractality of chest CT images was increased with the increase in lung infection in patients. The interesting and promising result was that capacity dimension (D0) as a new diagnostic parameter varied linearly with progression and reduction of lung infection. A critical value was found for D0, according to which patients with D0 lower than 1.4 can be healed by treatment. Therefore, herein, a way was found for quantitative assessment of lung infection of patients with COVID-19 by analyzing chest CT images using the multifractal method. This method can be very effective for physicians in diagnosis and treatment of pneumonia caused by COVID-19 and timely identification of therapeutic effects.

Introduction

Pneumonia caused by the 2019 novel coronavirus disease (COVID-19) is the most widespread disease today, which was first spread in Wuhan City in China, and now it has been almost spread in the whole world [1]. Many people in different countries, such as Italy, Korea, Iran, Singapore, France, Germany, Taiwan, Thailand, and Japan are infected with COVID-19 after a few months so that, the number of people affected with this virus is increasing every day. Fatigue, cough, fever, and shortness of breath are symptoms of patients infected with COVID-19 [2]. Based on the most recent experiences reported, computed tomography (CT) images of the lung can be useful in preclinical screening in order to diagnose an infected person before appearance of clinical symptoms [3]. Also, since diagnostic kits are limited for COVID-19 infection test in terms of number and availability to use for everyone susceptible to infection and they cannot be used for everyone, but CT scans are available in most hospitals therefore, the use of chest CT images is a good way for the initial diagnosis and clinical screening to control spread of the COVID-19. In this regard, many case reports and papers are published daily in various journals and sites on the effect of the COVID-19 on lungs of the infected individuals [4]. Hence, it is very important to investigate the chest CT scan images of patients with COVID-19 by effective methods for more accurate diagnosis and evaluation of disease severity. Fractal and multifractal analyses are useful methods to investigate various images in many fields that have recently received more attention by scientists due to their ability to describe complexity and irregularity of events in images [5]. When a single fractal analysis can not characterize the images, a better geometrical quantitative and qualitative description of complex images at local and global level can be provided by the multifractal technique. This technique is a free scaling method, making it very popular. Nowadays, fractal and multifractal methods are widely used in medical image analysis [6]. Therefore, given importance of spread of the COVID-19 in the world and the pandemic declared by the world health organization (WHO), here, multifractal analysis is applied on the chest CT images to evaluate diagnosis and progression of the disease.

Material and methods

In this study, 82 chest CT scan images of 38 patients with a positive test for COVID-19 were analyzed from China and Italy that had been reported as case report in Radiology Journal and Italian Society of Medical and Interventional Radiology. Among the cases, 63.16% of them were male patients, 28.95% of them were female patients, and 7.89% of them were unknown because, gender had not been mentioned in the reports.

The multifractal technique was applied to the CT images by MATLAB software. At least, 3 slice-CT scan was used for each patient in horizontal orientation. Resolution of the images was different but had no effect on our results. As we know, a digital image is numerically represented by a two-dimensional array with a configuration of M rows and N columns; with each index, known as pixel, containing a unique property. Depending on types of digital image, unique property of a pixel can be different. Multifractal technique describes fractal properties of an image using an intensity-based measure within neighborhood of each pixel. Each pixel in the image has an intensity value represented as a multi-level of gray value. These gray values are linearly interpolated from black to white, ranging from 0 to 1. A fractal is a new characterization to describe objects that are fragmented or rough, irregular and complex by two fundamental properties, self-similarity and Hausdorff-Besicovitch dimension. When complexities of objects are more and they are described with more than one fractal dimension, then multifractal technique can better explain the objects.

As we know, there are various methods to investigate multifractality of the surface, and one of the most common methods is box-counting method to study surface [7]. Therefore, here, the CT images of patients' lungs were analyzed using the box-counting method to study multifractality of the effect of COVID-19 on patients' lungs, which is briefly expressed below.

The CT images are partitioned into a number of boxes to cover the images. Then, Pij is defined as follows:

The Pij is deposition probability (height distribution probability) in the box (i,j) and hij is defined for the box (i,j) with ɛ size as average height. In terms of Lipschitz-Holder exponent (α), we have:

In multifractal spectrum, the number of boxes is provided as Nα(ɛ), where the boxes҆ size is ε with the same amount of α exponent:

Here, f(α) is singularity spectrum of α sub-datasets, denoted by fractal dimension and known as a multifractal spectrum. In random multifractal spectrum, singularity spectrum f(α) can be obtained using partition function χq(ε), which is given as follows:

Where, q (-∞

The exponent α and fractal dimension f(α) are obtained through Legendre transformation by the following equations:

In practice, the value of q (moment order) is finite. Width of the multifractal spectrum is given by ∆α=αmax-αmin, specifying value of the f(α) in these values to obtain ∆f(α). Some important parameters that can be obtained from the multifractal spectrum are ∆α, ∆f(α), D0(capacity dimension) and D1(information dimension), as shown in Fig. 1 schematically. In mathematics, capacity dimension or Hausdorff-Besicovitch dimension is a measure of roughness, which is also a criterion for measuring isotropic and non-isotropic nature of the system. Information dimension (D1) is an information-related measure for random vectors in Euclidean space, which is based on the normalized entropy of finely quantized versions of random vectors. Information dimension is considered a criterion to investigate entropy value of the system [8]. In this research, these equations were applied to the CT images using the MATLAB software.

Fig. 1

A schematic of the multifractal spectrum and its related parameters.

Results and discussion

For studying change pattern in pulmonary infection, chest CT images of the patients were analyzed using a multifractal technique. For this purpose, q parameter was optimized using Eqs. (4) and (5). Then, the τ(q) was plotted in terms of q and Lnχq with respect to Lnɛ. For applying the multifractal method, the τ(q) curve must be non-linear and Lnχq curve must be linear, so the diagrams were drawn for different q values, and the q values for which the τ(q) curve was non-linear (and Lnχq curve was linear) were selected to draw the multifractal spectrum. The obtained values varied from 10 to −10 for q.

Here, as an example, the multifractal spectra obtained from the CT images of 4 patients were randomly selected and presented,including Case 1: a man aged 32 years old [9], Case 2: a woman aged 46 years old [10], Case 3: a woman aged 47 years old [11], and Case 4: A man aged 71 years old [4]. Fig. 2 shows the CT scan of a patient's lung (32-year-old man) on the first, third, and eighth days after hospitalization, as reported previously [9]. As can be seen in Fig. 2, the CT images contain several structures like the heart, liver, aorta, vertebra, pleural cavity, vessels, and trachea in addition to the lungs. Thus, the multifractal algorithm was applied to the whole CT image without any initial editing. In fact, one of advantages of this technique is that the CT images are analyzed without any initial editing for colors, intensities, size, contrast, etc. The multifractal spectrum obtained from the multifractal analysis of these images using the MATLAB software is shown in Fig. 3 . The data obtained from the multifractal spectrum (Fig. 3(a), including αmin, αmax, ∆α, f(αmin), f(αmax), ∆f(α), α(q = 0), and fmax(α)=f(q = 0)=D0 (capacity dimension) are given in Table 1 . The variation in width, ∆f(α)=f(αmax)-f(αmin), and capacity dimension curves of the multifractal spectrum shown in Fig. 3(b) and (c) indicated that ∆α and D0 were increased 3 days after admission for this case, demonstrating progression of lung infection (disease). Eight days after hospitalization, analysis of CT image showed that two multifractal parameters (∆α and D0) were decreased and CT images showed reduction of lung infection in this period. The capacity dimension or box-counting dimension is related to the best box size that can cover the images. In Fig. 3(c), analysis of the capacity dimension(as function of days after admission and α) showed that 4 days after admission, with the increase in lung infection, the D0 was increased and also size of box for covering infection was increased indicating that the infection was spread and boundaries of the infection were increased. The variations in ∆f(α) as a function of admission days are not similar to the ∆α behavior. The Δf(α) is defined as ∆f(α)=f(αmax)-f(αmin), therefore, sign of the Δf(α) is attributed to how the infection is spread in the lung. For this case, sign of ∆f(α) is negative. When right tail of the multifractal spectrum is longer than the left tail, sign of ∆f(α) becomes negative, indicating multifractal structure of objects is independent of local fluctuations with large magnitudes. Accordingly, since sign of ∆f is negative for all 3 CT images, it can be concluded that, multifractality of pulmonary infection meaning timely spread of changes is insensitive to the lung infections҆ fluctuations with large magnitude and this is in agreement with quality of pulmonary lesions in the COVID-19 infection causing multiple ground-glass opacities as the most common lesion type [12], [13], [14] Table A.

Fig. 2

The CT images of a man with 32 years old and a positive COVID-19 test [9].

Fig. 3

The data obtained from CT images in Fig. 2 including (a) Multifractal spectrum, (b) Variation of ∆α and ∆f(α) as a functions of days after admission, and (c) The variation of capacity dimension, D0, as function of Lipschitz-Holder exponent (α) and days after admission.

Table 1

The multifractal parameters for 32-year-old man patient.

Days after admission	The 32-year-old male patient
	1	3	8
αmin	1.176	1.351	0.857
αmax	1.332	1.550	0.988
∆α	0.156	0.199	0.131
f(αmin)	1.174	1.347	0.855
f(αmax)	0.947	1.094	0.690
∆f	−0.227	−0.253	−0.165
f(α)max=f(q = 0)=D0	1.182	1.363	0.865
α(q = 0)	1.167	1.371	0.871

Table A

The multifractal parametiers from analyzing CT images of 38 patients.

		αmin	αmax	∆α	f(αmin)	f(αmax)	∆f	α(q = 0)	Fmax(q = 0)
Case 1	78-year-old female patient	2.156	2.409	0.253	2.151	1.738	−0.413	2.175	2.167
Case 2	87-year-old male patient	1.636	1.879	0.243	1.629	1.323	−0.306	1.663	1.653
Case 3	79-years-old	1.409	1.612	0.203	1.406	1.136	−0.270	1.431	1.421
Case 4	71-year-old male patient	1.489	1.692	0.203	1.486	1.202	−0.284	1.497	1.504
Case 5	47-year-old female patient	0.660	0.760	1.015	0.658	0.524	−0.134	0.666	0.669
Case 6	46-year-old woman patient	1.010	1.163	0.153	1.006	0.815	−0.191	1.020	1.029
Case 7	32-year-old male patient	1.176	1.332	0.156	1.174	0.947	−0.227	1.182	1.167
Case 8	42 years old man	1.149	1.325	0.176	1.145	0.927	−0.218	1.170	1.161
Case 9	71-year-old male patient	1.349	1.549	0.200	1.345	1.087	−0.258	1.367	1.361
Case 10	57-year-old male patient	1.734	1.968	0.234	1.730	1.399	−0.331	1.752	1.747
Case 11	45-year-old male patient	1.145	1.331	0.186	1.140	0.929	−0.211	1.170	1.163
Case 12	63-year-old male patient	1.243	1.440	0.197	1.240	1.009	−0.231	1.269	1.258
Case 13	43-year-old male patient	0.867	1.010	0.143	0.864	0.701	−0.163	0.886	0.879
Case 14	67-year-old	1.042	1.215	0.173	1.038	0.851	−0.187	1.065	1.057
Case 15	73-year-old female patient	1.619	1.870	0.251	1.611	1.320	−0.291	1.644	1.637
Case 16	55-year-old	1.045	1.202	0.157	1.042	0.835	−0.207	1.060	1.053
Case 17	50-year-old male patient	0.920	1.073	0.153	0.916	0.745	−0.171	0.933	0.940
Case 18	46-year-old female patient	0.855	0.994	0.139	0.852	0.691	−0.161	0.872	0.865
Case 19	80-year old male patient	1.338	1.527	0.189	1.333	1.075	−0.258	1.352	1.348
Case 20	69-year-old female patient	0.997	1.134	0.137	0.993	0.799	−0.194	1.006	1.002
Case 21	27-year-old male patient	1.301	1.511	0.210	1.296	1.065	−0.231	1.327	1.317
Case 22	71- year-old female patient	1.749	1.973	0.224	1.745	1.412	−0.333	1.763	1.758
Case 23	58-year-old female	1.545	1.763	0.218	1.540	1.247	−0.293	1.564	1.557
Case 24	48-year-old female	1.164	1.332	0.168	1.160	0.932	−0.228	1.177	1.172
Case 25	68-year-old male	0.875	1.016	0.141	0.872	0.700	−0.172	0.892	0.885
Case 26	64-year-old male	0.886	1.021	0.135	0.883	0.706	−0.177	0.899	0.893
Case 27	63-year-old male	1.159	1.338	0.179	1.153	0.934	−0.219	1.178	1.170
Case 28	55-year-old male patient	0.919	1.065	0.146	0.916	0.741	−0.175	0.936	0.930
Case 29	47-year-old male patient	0.779	0.912	0.133	0.775	0.629	−0.146	0.797	0.789
Case 30	72-years-old female patient	1.280	1.477	0.197	1.274	1.032	−0.242	1.300	1.292
Case 31	62-years-old female patient	1.200	1.390	0.190	1.193	0.974	−0.219	1.222	1.213
Case 32	84-years-old male patient	1.265	1.483	0.218	1.254	1.064	−0.190	1.306	1.291
Case 33	57-year-old male patient	1.373	1.583	0.210	1.366	1.114	−0.252	1.396	1.387
Case 34	40-year-old male patient	1.347	1.554	0.207	1.342	1.089	−0.253	1.372	1.360
Case 35	70 year-old male patient	0.825	0.964	0.139	0.821	0.666	−0.155	0.844	0.835
Case 36	56-year-old male patient	1.022	1.187	0.165	1.019	1.083	−0.064	1.041	1.033
Case 37	57-year-old male patient	1.303	1.508	0.205	1.299	1.060	−0.239	1.328	1.318
Case 38	74-year-old male patient	1.329	1.537	0.208	1.323	1.079	−0.244	1.353	1.343

Comparison of changes in CT images with their multifractal spectrum variations and the curves derived from them (including ∆α, ∆f(α), and D0 curves) showed that the changes in multifractal spectrum were just commensurate with pulmonary infection and stage of the disease. As can be seen in Figs. 4 –9 , for the other 3 cases, this process of interpretation of multifractal spectrum was perfectly proportional to changes in the CT images.

Fig. 4

The CT images of 46-years-old woman that her COVID-19 test was positive [10].

Fig. 9

The multifractal data obtained from CT images analysis of woman with pneumonia in Fig. 8 including: (a) Multifractal spectrum, (b) The variation of ∆α and ∆f(α) against days after admission, and (c) Capacity dimension, D0, against days after admission and α.

Fig. 6

The chest CT images of 47-years-old woman with a positive COVID-19 test [11].

Fig. 8

The CT images of a woman (71-years-old) with pneumonia caused by COVID-19 [4].

In Fig. 4, the chest CT images are shown for a woman aged 46 years old. The CT images were obtained at 1, 7, and 13 days after the patient's admission [10]. The multifractal spectra related to these CT images are presented in Fig. 5(a) and the obtained data from these multifractal spectra are listed in Table 2 , where corresponding curves are plotted in Fig. 5(b) and (c). In Fig. 5(c), it can be seen that how the capacity dimension obtained from multifractal spectrum (Fig. 5(a)) changes with α and days after admission simultaneously. The ∆α and D0 curves obtained from the multifractal spectrum are a descending function in terms of admission time for this case. As previously reported, this patients' COVID-19 test has become negative after 7 days of treatment, indicating recovery of the patient [10]. Therefore, the process of changing these multifractal parameters is entirely in line with the patient's recovery process and it can be concluded that a decrease in these parameters (∆α and D0) reflects a decline in lung infection with COVID-19 and thus recovery of the patient. The ∆f(α) is increased as a function of admission time for patients in the first period but in the second period, it remains unchanged. The sign of ∆f(α) is negative and is similar to the first case.

Fig. 5

The data obtained from CT images in Fig. 4 including: (a) Multifractal spectrum, (b) ∆α and ∆f(α) versus days after admission, and (c) Capacity dimension, D0, as function of days after admission and α.

Table 2

The multifractal parameters for 46-year-old woman patient.

Days after admission	The 46-year-old woman patient
	1	7	13
αmin	1.010	0.869	0.831
αmax	1.163	1.006	0.955
∆α	0.153	0.137	0.124
f(αmin)	1.006	0.866	0.828
f(αmax)	0.815	0.703	0.665
∆f	−0.191	−0.163	−0.163
f(α)max=f(q = 0)=D0	1.020	0.880	0.838
α(q = 0)	1.029	0.889	0.842

The next case was a 47-year-old woman [11] whose chest CT images obtained at 3, 7, 11, and 20 days after her admission (Fig. 6) were analyzed by multifractal technique. Multifractal spectra extracted from the CT images of this case are illustrated in Fig 7(a). According to the results presented in Table 3 , the curves of ∆α, ∆f(α), and D0 are plotted in Fig. 7(b) and (c). As can be seen, the trend of changes in ∆α and D0 was increasing until the 11th day after admission of the patient, and then they were decreased till the 20th day. This indicates the increase in the patient's lung infection followed by reduction of the infection, which is in good agreement with the CT images. Changes in ∆f(α) were initially decreased and then, they were increased by increasing and decreasing lung infection, respectively. The variation in ∆f(α) shows that the fractal dimension of minimum singularity strength is different from the maximum and this discrepancy is increasing until the 11th day after admission. Then, with the decrease in lung infection, this difference is diminished.

Fig. 7

The data obtained from analyzing CT images in Fig. 6 including: (a) Multifractal spectrum, (b) The variation of ∆α and ∆f(α) versus days after admission, and (c) Variation of capacity dimension, D0, versus α and days after admission.

Table 3

The multifractal parametiers for a 47-year-old woman patient.

Days after admission	The 47-year-old woman patient
	3	7	11	20
αmin	0.660	1.070	1.120	0.720
αmax	0.760	1.226	1.289	0.844
∆α	1.015	1.555	1.681	1.237
f(αmin)	0.658	1.068	1.116	0.717
f(αmax)	0.524	0.860	0.904	0.583
∆f	−0.134	−0.208	−0.212	−0.134
f(α)max=f(q = 0)=D0	0.666	1.079	1.131	0.730
α(q = 0)	0.669	1.084	1.140	0.737

The last case was a 71-year-old man [4] whose chest CT images (obtained at 1, 3, and 4 days after his admission (Fig. 8)) were analyzed by multifractal technique. The multifractal spectra based on the CT images of this patient are plotted in Fig. 9(a). The ∆α, ∆f(α), and D0 curves extracted from the multifractal spectrum in Fig. 9(a), according to the data presented in Table 4 are presented in Fig. 9(b) and (c). The ∆α and D0 parameters showed an increasing trend, indicating an increase in lung infection, but the ∆f(α) is different and unlike the other two parameters. In this case, the ∆f(α) was increased in all three periods, showing the increase in fractal dimension difference between the minimum singularity strength and the maximum.

Table 4

The multifractal parametiers for the male patient with 71-year-old.

Days after admission	The 71-year-old male patient
	1	3	4
αmin	1.489	1.495	1.713
αmax	1.692	1.707	1.966
∆α	0.203	0.212	0.252
f(αmin)	1.486	1.492	1.708
f(αmax)	1.202	1.202	1.385
∆f	−0.284	−0.290	−0.323
f(α)max=f(q = 0)=D0	1.497	1.505	1.728
α(q = 0)	1.504	1.515	1.741

It was observed that, as the patient's lung infection is increased like cases 1, 3, and 4, their multifractal spectrum width (∆α) is also increased; meaning that multifractality of lung infection with COVID-19 is increased. This refers to the increase in complexity of spread of lung infection. For all the studied cases, multifractal spectrum width (∆α) was decreased with the decrease in the patient's lung infection. Therefore, ∆α can be considered as a diagnostic factor for progression of pulmonary infection. The increase in ∆α indicates an increase in lung infection originating from the increased complexity of COVID-19 in chest CT images confirming that nature of spread of lung infection with COVID-19 is multifractal.Therefore, less width of the multifractal spectrum indicates less lung infection with COVID-19.

It was observed that the sign of ∆f(α) is negative for all CT images of all the analyzed patients. As mentioned earlier, the sign of ∆f(α) is negative when the left tail of multifractal spectrum is shorter than right one, so in these circumstances, the properties obtained from analysis of images by the multifractal technique are sensitive to local fluctuations at small scale and independent of large-scale fluctuations. For the positive value of ∆f(α), this dependence of multifractal properties is the opposite. Therefore, due to negative sign of the ∆f(α) for all the studied cases, it can be concluded that the multifractal method is a method that can be applied to analyze CT images of patient's lung without sensitivity to image size. Using this method, there is no need to remove any extra portions of the chest CT image, because this method is free scaling. Taking a close look at the multifractal spectra, one can find that variations in the maximum value of multifractal spectra known as capacity dimension (D0=f(α)max=f(q = 0)) are linear for different periods of hospitalization for each patient, which is an interesting and promising result because, linearity of changes in capacity dimension was almost the same for all patients. Slope of the linear D0 function was equal to 1.00, 0.98, 0.99, and 0.98 for the studied cases (1, 2, 3, and 4), respectively. The data obtained from performing linear fitting of capacity dimension are presented in Table 5 . The results of linear fitting presented in Table 5 confirmed that changes in capacity dimension are quite linear in all cases and R2 is almost equal to 1. The D0 as a function of α(q = 0) for all the studied cases is plotted in Fig. 10 . As can be clearly seen, the D0 changes are quite linear with R2=0.9997. Finally, a linear equation was obtained for D0 changes as follows:Where, slope of this linear equation, B, is equal to 0.9967 and value of A is equal to −26.2 × 10−4.

Table 5

data for perform linear fitting of the capacity dimension.

	Intercept		Slope		Statistics
	Value	Standard Error	Value	Standard Error	Adj. R-Square
32 years old man	−3.84278E-4	0.06905	1.00181	0.05987	0.99288
46 years old woman	0.01162	0.01972	0.97939	0.02135	0.99905
47 years old wonam	−3.48041E-4	0.00581	0.99377	0.00625	0.99988
71 yeears old man	0.02552	0.02235	0.97782	0.01405	0.99959

Fig. 10

the linear variations of Capacity dimension, D0, vs. α(q = 0) for all studied cases.

Therefore, it can be concluded that the fractal dimension, D0, changes linearly with the change in lung infection and disease progression in patients with COVID-19. Thus, this parameter is suitable for quantitative diagnosis of progression of the disease. As we know, finding a parameter changing linearly with progression of the disease is the best way to diagnose and study progression of the disease and compare it with the others. Therefore, in this research, it was tried to look for such a parameter and our results showed that the obtained fractal dimension has these characteristics. As a result, this parameter is suitable for quantitative detection of progression of the COVID-19. Since, it is difficult to distinguish amount of change in lung infection from chest CT images using the bare eye in many cases, a multifractal technique using the capacity dimension provides physicians with a useful tool to quantify and compare changes in lung infection caused by the COVID-19 for implementing timely treatment. Also, assessing the results of this study, it was found that the critical point of D0 is about 1.4 and the patients whose value of D0 obtained from their chest CT images is less than 1.4 have a high chance of being cured. The results of multifractal analysis showed that from studied patients, 7 cases (18.42%) had a D0 above than 1.4 and the value of D0 was less than 1.4 for 81.58% of patients.

Conclusion

In summary, in the present study, chest CT images of 4 patients with pneumonia caused by COVID-19 were analyzed by the multifractal method. It was found that the variations in lung infection of patients were reflected in the multifractal spectrum. So that, multifractal properties (αmin, αmax, ∆α, f(αmin), f(αmax), ∆f(α), α(q = 0), and fmax(α)=f(q = 0)=D0 (capacity dimension)) changed with progression and decline of disease. Therefore, the capacity dimension was considered as the best parameter because of its linear variations with progression and decline of disease, which is a promising result for early diagnosis of the COVID-19, through which the prognosis is predicted in each patient based on multifractal properties of his chest CT images or at different stages of the disease, which can be used to evaluate efficacy of drugs and can be helpful to timely investigate therapeutic effects in contagious pandemic of this newly found disease. The resulting linear equation for variation of D0 can be used by physicians as a fast and simple method in diagnosis and treatment of pneumonia caused by the COVID-19 and quantitative comparison of progression of lung infection in different patients that is accompanied with saving the time.

CRediT authorship contribution statement

Bandar Astinchap: Conceptualization, Methodology, Validation, Formal analysis, Writing – original draft. Hamta Ghanbaripour: Software, Formal analysis. Raziye Amuzgar: Data curation, Validation, Writing – review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financialinterestsor personal relationships that could have appeared to influence the work reported in this paper.