1. Introduction

Terahertz (THz) spectroscopy and imaging have shown great potential for detecting the properties of various biological tissues because tissue water and molecular structure strongly interact with THz radiation [1,2]. Many types of tissues associated with cancers, burn wounds, articular cartilages, lymph nodes, and gastrointestinal tracts have been investigated in the THz region (0.1–10 THz) [3–9]. The common methods of distinguishing THz signals that interact with different biological tissues are comparing the maximum (Emax) or minimum (Emin) value of the temporal signal [E(t)], amplitude of the frequency spectrum [E(ω)], and refractive index or absorption coefficient as a function of frequency. For example, paraffin embedded liver-cancer tissues yielded 4% difference among the E(ω) signals acquired from healthy and cancerous tissues, and therefore, the presence of cancerous regions can be identified [10].

However, unlike many macromolecules, biological tissues usually have no significant absorption peaks in the THz region. For some tissues with a slight difference, the criteria based on Emax, Emin, and E(ω) are not satisfactory, especially when the E(t) and E(ω) signals are very noisy. Many methods have been proposed to improve the contrast among different tissues. Park et al. adopted the spectroscopic integration technique to enhance the signal gap between melanoma and healthy tissues, which achieved better discrimination than the use of a peak point or single spectral value [11]. Nakajima et al. applied the principal component analysis (PCA) and hierarchical clustering analysis for systematic and automatic analysis of THz spectroscopic image of cancer tissues [12]. Nonetheless, previous methods are still based on the THz frequency spectrum and refractive index or absorption coefficient of tissues. New parameters are highly desired to further improve the contrast among THz signals that interact with different tissues.

Quantifying the degree of complexity of a time series is an essential task in understanding the characteristics of a biological or mechanical system [13]. One of the most popular complexity measurements of a time series is sample entropy (SampEn), which is an unbiased estimator of the conditional probability that two similar sequences of m consecutive data points (m is an embedded dimension) will remain similar when one more consecutive point is included [14]. SampEn strictly characterizes the complexity at a time scale defined by the sampling procedure, which is applied to acquire the time series under assessment. However, the long-term structures in a time series cannot be characterized by SampEn [15]. With regard to this disadvantage, Wu et al. proposed the composite multiscale entropy (CMSE) algorithm, which uses SampEns of a time series at multiple scales [16]. The multiscale entropy method has been successfully applied to the analysis of many physiological signals [17–19] and vibrational signals [20]. It shows a great potential to provide a new index for THz signal identification of different biological samples.

In the present study, we attempt to introduce, for the first time ever, the CMSE method into the complexity analysis of reflective THz signal of biological samples. The information of a whole THz pulse was calculated by the CMSE algorithm, and SampEns at different scales were obtained. To verify the feasibility of this method, fresh porcine skin and muscle tissues were employed as two samples. The statistically significant difference and separation of the two tissues based on several parameters (multiscale entropy, Emax, Emin, E(ω), refractive index, and absorption coefficient at several specific frequencies) were analyzed for THz spectroscopic measurements. The results demonstrated the superiority of the multiscale entropy method for identifying different tissues.

2. CMSE method

The flowchart of the CMSE algorithm is shown in Fig. 1(a). At a scale factor of $\tau$, the SampEns of all coarse-grained time series at this scale factor are calculated, and the multiscale entropy value is defined as the mean of all the $\tau$entropy values [16],that is,

 

Fig. 1 (a) Flowchart of the CMSE algorithm. (b) Schematic illustration of the coarse-grained procedure (scale factor = 3).

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SampEn quantifies the likelihood that two sequences of m consecutive data points which are similar to each other will remain similar when one more consecutive point is included. Being “similar” means that the distance between two vectors is less than a tolerance threshold value r, and the distance is defined as the maximum of the absolute differences between their components in the two vectors [14,16]. In the present study, SampEn was calculated with m = 2 and $r=0.15\sigma$, where $\sigma$denotes the standard deviation of the time series (THz time-domain raw data). The cases of m = 2 and r value between $0.1\sigma$ and $0.25\sigma$ were widely adopted in previous SampEn calculation [14–20]. Because in the case of m = 2, the SampEn is significantly independent of the time series length [14,16]. The r value used in this study also falls within the reported range of SampEn applications and was adopted in the previous CMSE study [16].

$y_{\text{k}}^{(\tau )}\text{=}\left\{y_{k,1}^{(\tau )},y_{k,2}^{(\tau )},\cdots ,y_{k,p}^{(\tau )}\right\}$ is the k_th coarse-grained time series at a scale factor of $\tau$ and is defined as follows [16]:

For example, in the case of scale factor of three, the coarse-grained time series derived from the original time series is shown in Fig. 1(b).

3. Experimental details and results

The THz time-domain waveforms were measured using a commercial reflection THz system, which is shown in Fig. 2(a). The setup consists of a fiber femtosecond laser (Vitesse, Coherent Inc., USA), a pair of fiber-based photoconductive antennas (Menlo Systems TERA8−1, Martinsried, Germany) as generator and detector, and a rapid-scan delay line (ScanDelay 50, APE Berlin, Germany). The imaging sample was placed on a thick quartz window.

 

Fig. 2 (a) Schematic diagram of the reflective THz spectroscopic and imaging system. (b) Average reference THz pulsed signal (10 measurement times). For clarity, the standard deviation of the reference THz signal is not marked in the figure. (c) Corresponding multiscale entropy results with the standard deviations (10 measurement times).

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The fresh porcine skin and muscle tissues were used to test the effectiveness of the method owing to their various texture and hydration content. All samples were cut from the collar region. To accurately determine the sample properties, step scan was used to measure the central area of each sample. THz signals reflected by six skin and six muscle samples were acquired. A THz signal reflected from the top interface between the quartz window and air was measured as a reference. The adopted temporal resolution is 0.052 ps. The method to calculate frequency-dependent refractive index and absorption coefficient can be found in References [21–23]. The data point of each THz signal for CMSE calculation was 580.

All statistical analyses were performed using Matlab (MathWorks Inc., Natick, MA, USA). Each index of the different tissues (muscle and skin) was separately calculated as mean ± standard deviation. A two-sample t-test was applied to assess the statistical differences between the two tissues. Three statistically significant difference levels were considered to be indicated by a P value of less than 0.05 (*significant difference), 0.01 (**very significant difference) and 0.001 (***extremely significant difference) [24]. In the present study, Euclidean distance was further adopted to measure the separation of two groups of samples [25]. Assuming that the two groups are $s_1\text{=}\left\{{\text{s}}_{1\text{1}},{\text{s}}_{12},\cdots ,{\text{s}}_{1n}\right\}$and $s_2\text{=}\left\{{\text{s}}_{2\text{1}},{\text{s}}_{22},\cdots ,{\text{s}}_{2n}\right\}$, the Euclidean distance (d) is calculated according to the following Eq.:

Furthermore, we used the relative Euclidean distance to compare the performance of the different parameters to distinguish the different groups. The definition of the relative Euclidean distance (Rd) is expressed as follows:

The average reference THz pulsed signal (air) and the corresponding multiscale entropy results from 10 measurement times are shown in Fig. 2(b). The entropy value increased with increasing scale from 1 to 14. Then, it gradually dropped when the scale increased from 15 to 20. The coefficient of variance (standard deviation/mean) was adopted to demonstrate the stability of the CMSE method. The mean E_max, E_min, E_max − E_min value of reference THz pulsed signal were 0.989 ± 0.045, −1.595 ± 0.025 and 2.603 + 0.021. The corresponding coefficients of variance were 4.55%, 1.57% and 0.81%. The mean entropies of reference THz signal at scales of one, five, ten, fifteen and twenty were 0.090 ± 0.0003, 0.380 ± 0.002, 0.601 ± 0.002, 0.616 ± 0.003 and 0.487 ± 0.003. The corresponding coefficients of variance were 0.33%, 0.53%, 0.33%, 0.49%, and 0.62%. The standard deviations of the multiscale entropies from 10 measurement times were very small, which demonstrates the stability of the CMSE method for THz signal analysis.

The average time-domain THz signal, frequency-domain spectrum, refractive index, and absorption coefficient of the fresh muscle and skin tissues are shown in Fig. 3. The corresponding statistical, t-test, and Euclidean distance results of E_max, E_min, E_max − E_min, frequency amplitude, refractive index, and absorption coefficient at 0.3, 0.6, and 0.9 THz are listed in Tables 1 and 2. Because the texture and water content in the muscle and skin tissues were similar, the differences in the profile and amplitude of the time- and frequency-domain THz signals between the two tissues were small. Among all the assessment indexes, significant differences (P < 0.05) existed between the two tissues relative to refractive index at 0.3, 0.6 and 0.9 THz and frequency amplitude at 0.6 and 0.9 THz. The refractive index at 0.6 and 0.9 THz and amplitude at 0.9 THz of the skin tissue were extremely significantly different to those of the muscle tissue (***P < 0.001). The corresponding relative Euclidean distances were 16.52%, 19.13% and 95.81%.

 

Fig. 3 (a) Average time-domain THz signal of the fresh muscle and skin tissues (n = 6). For clarity, the standard deviation is not marked in the figure. (b) Corresponding average frequency-domain spectrum, (c) refractive index, and (d) absorption coefficient of the fresh muscle and skin tissues with the standard deviations (n = 6).

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Table 1. Characteristics of the time- and frequency-domain amplitudes of the different tissues (n = 6)

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Table 2. Characteristics of the refractive index and absorption coefficient of the different tissues (n = 6)

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The average value and corresponding standard deviation of the entropies at different scales of the fresh muscle and skin tissues is shown in Fig. 4. The entropies of the skin tissue increased continuously with increasing scale from 1 to 20, while the entropies of the muscle tissue increased gradually with increasing scale from 1 to 15 and tended to saturation with the scales above 15. In particular, a clear boundary of the entropies existed at different scales between the two samples, which shows the effectiveness of the CMSE method for distinguishing different biological samples.

 

Fig. 4 Average value and corresponding standard deviation of the entropies at different scales of the fresh muscle and skin tissues (n = 6).

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The corresponding statistical, t-test, and Euclidean distance results of the entropies at 1, 5, 10, 15, and 20 are listed in Table 3. As expected, very significant differences (P < 0.01) existed between all sample entropies at different scales. Furthermore, at scales of ten, fifteen and twenty, the sample entropies of the skin tissue were extremely significantly higher than those of the muscle tissue (***P < 0.001). The corresponding relative Euclidean distances were 58.64%, 71.68%, and 125.80% at scales of ten, fifteen and twenty, respectively, which were much higher than those in the above time- and frequency-domain analyses. The results demonstrate that the CMSE-based multiscale entropy analysis performed better in distinguishing the different biological samples than the previous time- and frequency-domain indexes.

Table 3. Characteristics of the entropies at different scales in the different tissues (n = 6)

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To further demonstrate the potential of the CMSE method for imaging applications, we adopted the step-scan imaging strategy (0.5-mm step in the transverse direction and 1.25-mm step in the vertical direction) using a programmed stepper. THz images of the fresh muscle and skin tissues based on the multiscale entropy were acquired. Furthermore, by adopting the maximal value of the muscle images as the threshold value, dichotomized difference images were obtained. When the value of the skin image was higher than the threshold value, the value in the difference image was set to one; otherwise, the value in the difference image was set to zero.

The THz imaging results obtained from the fresh skin and muscle tissues according to multiscale entropy are shown in Fig. 5. The dichotomized difference images between the two different tissues were calculated to demonstrate the superiority of the CMSE method. Only one point existed in the multiscale entropy images (at scales of 5 or 10) of the skin tissue whose entropy was lower than the maximal value of the muscle tissue, whereas all those of the other points were higher. This image was very homogenous, which means that the multiscale entropy method can be used as a new index for complementary and better analysis and differentiation of different biological samples.

 

Fig. 5 THz imaging results of the fresh muscle and skin tissues and the corresponding dichotomized difference images based on multiscale entropy at the scales of 5 and 10.

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4. Discussion and conclusion

The CMSE-based complexity analysis of a THz signal could provide a new index for THz spectroscopy and imaging application. In particular, it is very appropriate for distinguishing the THz signal interaction with different biological tissues, which usually have no significant absorption peaks. Because all time-domain data are adopted in the CMSE method, the multiscale entropy has higher discriminability of the different tissues than the traditional indexes at a specific time or frequency point. Furthermore, by combining CMSE with other indexes and classification methods such as the PCA, clustering analysis, and support vector machine [12,26,27], this method could be useful in systematic and automatic identification of cancer tissues.

In conclusion, the feasibility and effectiveness of the multiscale entropy analysis of reflective THz signals based on the CMSE method for discrimination of different biological tissues have been proven. SampEns at different scales exhibited better performance in terms of the statistically significant difference and relative Euclidean distance of two biological samples (porcine skin and muscle tissues) than the existing indexes (Emax, Emin, E(ω), refractive index, and absorption coefficient at some frequencies). The difference image of the two different tissues based on multiscale entropy further demonstrated the superiority of the CMSE method. This multiscale entropy index of a THz signal could be valuable for analyzing different biological samples. It can also facilitate cancer diagnosis in combination with other existing time- and frequency-domain parameters.