*2.2. Methods*

To quantitatively compare the consistency of the three reanalysis datasets with in-situ observations and evaluate their errors of daily average temperatures, the reanalysis data from 2017–2018 are divided into eight times per day (00, 03, 06, 09, 11, 14, 17, 20 UTC), which is the division used in GLDAS. The arithmetic mean is taken as daily mean temperature for individual reanalysis datasets. Based on the latitude and longitude information of the observation sites, daily mean temperatures from reanalysis are interpolated to the observation sites using the nearest neighbor interpolation method. Two sequences of daily temperatures from the reanalysis and from the in-situ observations, with 11,635 samples in each sequence, are then compared. Pearson correlation coefficient (CC), mean bias error (MBE), root-mean-square error (RMSE), Nash–Sutcliffe efficiency coefficient (NSE) [50,51], Kling–Gupta efficiency (KGE) [52,53], and Willmott's Index of Agreement (WIA) [54] are then calculated to evaluate the accuracy and applicability of CLDAS, ERA5L, and GLDAS

temperature data in the alpine region of the QTP. The calculations of the aforementioned indices are as follows:

$$\text{CC} = \frac{\sum\_{\mathbf{i}=1}^{\text{n}} (\mathbf{R}\_{\mathbf{i}} - \overline{\mathbf{R}})(\mathbf{S}\_{\mathbf{i}} - \overline{\mathbf{S}})}{\sqrt{\sum\_{\mathbf{i}=1}^{\text{n}} (\mathbf{R}\_{\mathbf{i}} - \overline{\mathbf{R}})^2} \sqrt{\sum\_{\mathbf{i}=1}^{\text{n}} (\mathbf{S}\_{\mathbf{i}} - \overline{\mathbf{S}})^2}} \tag{1}$$

$$\text{MBE} = \frac{1}{\mathbf{n}} \sum\_{\mathbf{i}=1}^{n} \mathbf{R}\_{\mathbf{i}} - \mathbf{S}\_{\mathbf{i}} \tag{2}$$

$$\text{RMSE} = \sqrt{\frac{1}{n} \sum\_{i=1}^{n} (\mathbf{R}\_i - \mathbf{S}\_i)^2} \tag{3}$$

$$\text{NSE} = 1 - \frac{\sum\_{i=1}^{n} (\mathbf{R\_i} - \mathbf{S\_i})^2}{\sum\_{i=1}^{n} (\mathbf{S\_i} - \mathbf{S})^2} \tag{4}$$

$$\text{KGE} = 1 - \sqrt{(\text{CC} - 1)^2 + (\alpha - 1)^2 + (\beta - 1)^2} \text{ with } \alpha = \frac{\overline{\text{R}}}{\text{S}}, \text{ and } \beta = \frac{\sigma\_{\text{R}}}{\sigma\_{\text{S}}} \tag{5}$$

n

$$\text{WIA} = 1 - \frac{\overset{\cdots}{\sum} \left( \mathbf{R\_i} - \mathbf{S\_i} \right)^2}{\sum\_{i=1}^n \left( \left| \mathbf{R\_i} - \mathbf{S} \right| + \left| \mathbf{S\_i} - \mathbf{S} \right| \right)^2} \tag{6}$$

where Ri is the reanalysis temperature interpolated to the observation site, Si is the in-situ observation at the site, n is the total number of records that participate in the evaluation, and R and S denote the averages of reanalysis data and observations during the study period, respectively. CC (Equation (1)) represents the correlation between reanalysis and observations with values that range within [−1, 1]. |CC| = 1 indicates that the two sequences are completely linearly correlated; CC = 0 means there is no correlation between the two sequences, and 0 < |CC| < 1 indicates that there is a certain degree of linear correlation between the two. The closer |CC| is to 1, the higher the linear relationship is; the closer |CC| is to 0, the weaker the linear correlation is between the two. CC>0 indicates that the reanalysis and the in-situ observations have the same trends of change, and CC<0 means that they have opposite trends. MBE (Equation (2)) reflects the deviations of reanalysis data from observations. Negative MBE values indicates that the reanalysis data are lower than the observation, and vice versa. RMSE (Equation (3)) shows the overall difference between the reanalysis and the observations, including systematic and non-systematic biases. A closer-to-0 RMSE corresponds to a more accurate reanalysis dataset. NSE (Equation (4)) is widely applied to quantify the prediction ability of hydrological models. It reflects the consistency of two datasets: NSE = 1 indicates that the reanalysis data are completely consistent with the observations; NSE ≤ 0 indicates that the two datasets are inconsistent with each other. The KGE (Equation (5)) is based on a decomposition of the NSE into its constitutive components (correlation, mean bias, and variability bias) and is increasingly used for model calibration and evaluation. *σ*R and *σ*S are the standard deviations in reanalysis and in-situ observations, respectively. KGE can vary from negative infinity to 1, and KGE = 1 indicates perfect agreement between simulations and observations. WIA (Equation (6)) is similar to NSE, but the denominator of the main term in the equation is the potential maximum difference [54]. The value of WIA ranges between 0 (not consistent) and 1 (perfectly consistent). On the scatterplot of reanalysis versus in-situ observations, both WIA and NSE indicate how close the data points are to the fitted 1:1 line. During the evaluation period, all samples used for evaluation are calculated based on the cumulative results of daily observations.

**Figure 1.** Elevation of the study area and distribution of in-situ observation sites.

Note: The properties of these sites are derived from the metadata provided in http://data.tpdc.ac.cn (accessed on 18 May 2022). The unit of latitude and longitude in degree, minute, and second is transferred to decimal unit in degree and keeps four decimal places. For a few sites where the metadata is missing, the properties are derived from other information. For example, the elevation at Shuanghu is derived from 90 m-resolution DEM, and the land cover type at Ali is derived from http://www.horn.ac.cn/index.jsp (accessed on 18 May 2022).

### **3. Results Analysis**

*3.1. Comparative Analysis of Spatial Distribution Characteristics*

Spatial distributions of average temperature for reanalysis datasets and in-situ observations during the study period of 2017–2018 are displayed in Figure 2, which clearly shows that the three reanalysis datasets and the in-situ observations roughly follow the variation of latitude and elevation. Despite the slight differences at local or regional scales, the magnitude and spatial distribution of temperature are basically the same for these datasets (Figure 2a). Temperature gradually increases from north to south, and high temperature

centers are located in southeastern Tibet, southwestern Sichuan, and northwestern Yunnan. The Qaidam Basin in the northwest of Qinghai is surrounded by mountains. The average elevation of the basin is about 2600 m, which is lower than the surrounding areas. The annual average temperatures in the three reanalysis datasets in the Qaidam Basin are all significantly higher than those of the surrounding areas. The average elevation of the Kunlun Mountains and Karakoram Mountains located in western Tibet is more than 5500 m, and the temperature is significantly lower than other areas in the same latitude. Compared to ERA5L and GLDAS, CLDAS describes more details of temperature changes with altitude. For example, CLDAS aptly describes the dramatic temperature changes caused by large altitude differences in the Hengduan Mountains region located at the junction of Tibet, Sichuan, and Yunnan, where mountains, valleys, and rivers are intertwined. In contrast, the other two reanalysis datasets can barely reflect this characteristic distribution of temperature in the Hengduan Mountains.

**Figure 2.** Spatial distributions of annual mean temperature over 2017–2018 ((**a**) CLDAS; (**b**) ERA5L; (**c**) GLDAS; (**d**) in-situ observations).

Spatial distributions of seasonal temperature are displayed in Figures 3–6. In the spring (Figure 3), CLDAS temperature is higher than ERA5L and GLDAS in the entire study area except the Qaidam Basin and the low-elevation region of southern Tibet, where CLDAS is lower than ERA5L and GLDAS. ERA5L and GLDAS show large differences in the spatial distribution of air temperature in the plateau area, though CLDAS has a small difference. ERA5L is also significantly lower than CLDAS and GLDAS in the central QTP. In the summer (Figure 4), the spatial distributions of CLDAS and GLDAS are similar to each other, while ERA5L is obviously lower than the other two reanalysis datasets. In the autumn (Figure 5), CLDAS and ERA5L are closer to each other, while GLDAS is lower than CLDAS and ERA5L in the high-elevation region of western QTP, but higher in the low-elevation region of the southeastern QTP. In the winter (Figure 6), spatial distributions of the three reanalysis datasets are basically consistent, although ERA5L is lower than CLDAS and GLDAS in southeastern Qinghai and northeastern Tibet. Overall, compared to GLDAS and ERA5L, CLDAS is closer to observations and demonstrates higher spatial consistency.

**Figure 3.** Spatial distributions of spring mean temperature over 2017–2018 ((**a**) CLDAS; (**b**) ERA5L; (**c**) GLDAS; (**d**) in-situ observations).

**Figure 4.** Spatial distributions of summer mean temperature over 2017–2018 ((**a**) CLDAS; (**b**) ERA5L; (**c**) GLDAS; (**d**) in-situ observations).

**Figure 5.** Spatial distributions of autumn mean temperature over 2017–2018 ((**a**) CLDAS; (**b**) ERA5L; (**c**) GLDAS; (**d**) in-situ observations).

**Figure 6.** Spatial distributions of winter mean temperature over 2017–2018 ((**a**) CLDAS; (**b**) ERA5L;(**c**) GLDAS; (**d**) in-situ observations).

### *3.2. Accuracy of the Reanalysis Datasets for the Evaluation Period*

Table 3 lists the evaluation results over the period 2017–2018. The mean temperatures of CLDAS, ERA5L, and GLDAS are 1.49 ◦C, −2.491 ◦C, and −0.44 ◦C, respectively. The mean value of CLDAS is the closest to the average of the in-situ observations (0.956 ◦C). The correlation coefficient (CC) between CLDAS and the observations is the highest (0.969), followed by the correlation between ERA5L and the observations (0.934); the correlation coefficient between GLDAS and the observations is the lowest (0.92). The MBEs of ERA5L and GLDAS are −3.45 ◦C and −1.40 ◦C, respectively, which suggests that temperature is underestimated in the two reanalysis datasets, to a certain degree. Conversely, the MBE of CLDAS is 0.53, which indicates that CLDAS overestimates temperature in those in-situ observation sites. The RMSEs of CLDAS, ERA5L, and GLDAS are 2.18 ◦C, 4. 83 ◦C, and 3.64 ◦C, respectively, which indicates that the errors of CLDAS are smaller than the other two reanalyses. The values of NSE and WAI are close to 1 (the premium value) for all the three reanalysis datasets, suggesting that they are highly consistent with the in-situ observations, especially CLDAS. From the value of KGE, CLDAS is closer to 1, which indicates that it is better than ERA5L and GLDAS. This result agrees with NSE and WIA. In general, CLDAS is noticeably better than GDAS and ERA5L during the evaluation period based on evaluation indices of correlation, bias, and consistency. GLDAS is better than ERA5L, although the differences between them are relatively small.

**Table 3.** Accuracy evaluation results of CLDAS, ERA5L and GLDAS for the period 2017–2018.

To better display the consistency of the three reanalysis datasets with the observations during the evaluation period, Figure 7 shows the scatter plots of reanalysis data versus in-situ observations and the results of univariate linear regression. The goodness of fit (R2) for CLDAS, ERA5L, and GLDAS are 0.939, 0.872, and 0.847, respectively, which indicates that CLDAS is more consistent with in-situ observations. This result agrees with the results shown in Table 3.

**Figure 7.** Scatter plots of reanalysis datasets versus in-situ observations ((**a**) CLDAS; (**b**) ERA5L; (**c**) GLDAS; n: total number of samples).

### *3.3. Evaluation of Temporal Variation*

### 3.3.1. Daily Variation

To analyze differences in daily temperature of the reanalysis datasets during the evaluation period, daily average temperatures of CLDAS, GLDAS, ERA5L, and in-situ observations over the evaluation period are displayed in Figure 8a, which shows that the daily variations and temporal changes of surface air temperature are basically consistent between the three reanalysis datasets and observations, and that CLDAS is closer to the observations than GLDAS and ERA5L are. Looking at the time series of daily CC (Figure 8b), we found that in 85. 6% of the days, the CCs of CLDAS with observations are above 0.8. However, the CCs of GLDAS and ERA5L with observations are below 0.8 in 60.7% and 90.5% of the days, respectively. Furthermore, the magnitude of daily variation of CLDAS is relatively small, which implies a more stable correlation with in-situ observations. The ranges of daily RMSE variation for CLDAS, ERA5L, and GLDAS (Figure 8c) are within 0.61–2.35 ◦C, 1.97–3.80 ◦C, and 2.43–3.76 ◦C, respectively. Note that the daily variation of RMSE for CLDAS is obviously lower than—the other two reanalysis datasets. In 76% of the total days, the RMSE values of GLDAS were lower than those of ERA5L, which indicates that the quality of GLDAS is higher than ERA5L in most days. The time series of daily MBE are displayed in Figure 8d, which shows that the MBEs of CLDAS are closer to the zero line than GLDAS and ERA5L are, which suggests that CLDAS is more consistent with observations than GLDAS and ERA5L. The MBE of CLDAS is positive in 78.5% of the days, whereas the MBE of GLDAS is negative in 90% of the days, and ERA5L is negative throughout the study period. This result indicates that daily temperature is overestimated by CLDAS and underestimated by GLDAS in most of the days, and it is always underestimated by ERA5L. The consistency indices of NSE (Figure 8e), KGE (Figure 8f), and WIA (Figure 8g) of CLDAS are closer to 1 with a smaller range of variation compared to that of ERA5L and GLDAS, which shows that CLDAS is more consistent with observations and demonstrates a higher stability.

**Figure 8.** Daily evaluation of during 2017–2018. (**a**) Time series of daily mean temperature; (**b**) CC; (**c**) RMSE; (**d**) MBE; (**e**) NSE; (**f**) KGE; (**g**) WIA.

### 3.3.2. Monthly Variation

Figure 9 presents characteristic changes in monthly mean errors of the reanalysis datasets. The time series of monthly mean temperature (Figure 9a) indicates that the variation trends of the three reanalysis datasets are similar to that of the observations, i.e., temperature is the lowest in January and gradually increases from then onwards, reaches the highest in July, and then gradually decreases. Monthly CCs for CLDAS are all higher than those for GLDAS and ERA5L (Figure 9b). CCs for GLDAS are higher than for ERA5L in all months except March 2017 and February 2018, when the CCs for GLDAS are slightly lower than those of ERA5L. The RMSEs of CLDAS, ERA5L, and GLDAS (Figure 9c) range between 1.637–3.046 ◦C, 2.535–8.353 ◦C, and 2.682–5.054 ◦C, respectively. Note that the RMSEs of CLDAS are smaller than those of the DLDAS and ERA5L in all months, while the RMSEs of GLDAS are lower than those of ERA5L in all months except August and September of 2017 and July and August of 2018, when the RMSEs of GLDAS are slightly higher than those of ERA5L. Monthly MBE variations (Figure 9d) indicate that CLDAS overestimates monthly mean temperature in all months except December 2018, when it slightly underestimates the monthly mean temperature by −0.025 ◦C. The largest overestimation of 1.172 ◦C occurs in March 2017. Monthly MBEs of ERA5L are negative in all months, with the largest negative bias of −7.395 ◦C occurring in November 2018. Monthly MBEs of GLDAS are negative in all months except December 2017, when the monthly mean temperature of GLDAS is higher than the observation by 0.445 ◦C. The largest negative bias of GLDAS occurs in March 2017 with the value of −2.993 ◦C. Monthly consistency indices of NSE (Figure 9e) for CLDAS, ERA5L, and GLDAS are within the ranges of 0.581–0.847, −2.253–0.363, and −0.191–0.541, respectively, and the ranges of KGE (Figure 9f) are 0.027–0.892, −26.714–0.736, and −8.948–0.709, respectively. The indices of WIA (Figure 9g) are within the ranges of 0.903–0.961, 0.545–0.855, and 0.685–0.865, respectively. The lowest value of NSE occurs in either July or August for all the three reanalysis datasets, whereas the lowest value of WIA occurs in either October or August. Compared to the other two reanalysis datasets, monthly values of NSE, KGE, and WIA for CLDAS are closer to one, suggesting that CLDAS is more consistent with observations. GLDAS overall is better than ERA5L, with the exception of a few months.

### 3.3.3. Seasonal Analysis

Figure 10 displays seasonal error characteristics during the evaluation period. The histograms of seasonal mean air temperature changes from reanalysis datasets and insitu observations are displayed in Figure 10a, which shows that seasonal temperatures of CLDAS, ERA5L, and GLDAS as well as in-situ observations all present a unimodal feature of being low in winter and high in summer. This result indicates that the three reanalysis datasets can well describe the seasonal variation of temperature in the QTP. Seasonal CCs (Figure 10b) of the three reanalysis datasets with observations are all the highest in autumn, while the CCs of CLDAS and ERA5L with observations are the lowest in winter and higher in spring than in summer. Although the CC of GLDAS with observations is the lowest in summer, the difference between CCs in winter and summer is quite small. Seasonal RMSEs (Figure 10c) of the CLDAS, ERA5L, and GLDAS all gradually increase from the minimum values in summer (1.819 ◦C, 2.863 ◦C and 2.828 ◦C) to the maximum values in winter (2.62 ◦C, 5.693 ◦C and 4.451 ◦C), and then decrease in the spring. Seasonal MBEs are displayed in Figure 10d, which indicates that CLDAS overestimates seasonal mean temperature in all seasons, though the overestimation is relatively small in autumn. Opposite to CLDAS, ERA5L and GLDAS both underestimate seasonal mean temperature, and the underestimation is more severe in ERA5L. The largest negative bias occurs in autumn and the smallest negative bias occurs in summer for both ERA5L and GLDAS. The histograms of seasonal NSE (Figure 10e) and WIA (Figure 10g) show that the consistency of the three reanalysis data with in-situ observations is relatively poor in winter, and is optimal in autumn. However, from the perspective of KGE (Figure 10f), the three reanalysis datasets are worst in spring and better in summer.

**Figure 9.** Monthly evaluation of during 2017–2018. (**a**): Series of monthly mean temperature; (**b**) CC; (**c**) RMSE; (**d**) MBE; (**e**) NSE; (**f**) NSE; (**g**) WIA.

### *3.4. Comparative Reanalysis at Individual Sites*

Figure 11 shows box plots of temperature errors of CLDAS, GLDAS, and ERA5L during 2017–2018. The numbers of stations with CC (Figure 11a) higher than 0.95 account for 82.4%, 52.9%, and 70.6% of the total number of stations for CLDAS, ERA5L, and GLDAS, respectively. The lowest CCs, with respective values of 0.902, 0.915, and 0.913 for CLDAS, ERA5L, and GLDAS, all occur at Ruoergai (Elinghu), while the highest CCs occur at Ali and Golmud (0.992 for CLDAS), Haibei (0.974 for ERA5L), and Mushitage (0.979 for GLDAS). RMSEs (Figure 11b) are within the ranges of 1.222–4.289 ◦C, 2.345–6.076 ◦C, and 2.366–5.736 ◦C for CLDAS, ERA5L, and GLDAS, respectively. The largest RMSEs of CLDAS and ERA5L occur at Ruoergai (Elinghu), where the correlation is the lowest. The largest RMSE of GLDAS is found at Lasa. The smallest RMSEs of the three datasets occur at different sites. The box plot of MBE (Figure 11c) shows that CLDAS is lower than observations at only 4 sites, i.e., Ruoerai (Elinghu), Sanjinagyuan, Golmud, and Shenzha, which account for 23.5% of the total observation sites. The largest negative bias (−1.995) is found at Ruoergai (Elinghu), and the largest positive bias (1.99 ◦C) occurs at Naqu (Hanhansuo). ERA5L data are lower than observations at all sites, and the largest bias is found at Mushitage (−4.968 ◦C). Positive biases of GLDAS only occur at Ruoergai (Maqu), Naqu (Qingzangsuo), Naqu (Hanhansuo), and Shuanghu, which account for 29.4% of the total stations. The largest positive bias occurs at Shuanghu (2.37 ◦C); the biases of GLDAS are negative at all other sites with the largest negative bias (−5.385 ◦C) at Lasa. The consistency indices of NSE for CLDAS, ERA5L, and GLDAS (Figure 11d) are within the ranges of 0.748–0.974, 0.102–0.919, and 0.219–0.934, respectively, and the ranges of KGE (Figure 11e) are −157.108–0.918, −389.193–0.537, and −138.881–0.882, respectively. The ranges of WIA (Figure 11f) are 0.936–0.994, 0.85–0.978, and 0.839–0.982, respectively. Based on NSE, KGE, and WIA, the consistency of CLDAS is the worst at Ruoergai (Elinghu) and the consistency of GLDAS is the worst at Lasa. The consistency of ERA5L is worst at Zhufeng, Zangdongnan, and Lasa. In summary, the various reanalysis datasets show different qualities and applicability.

**Figure 10.** Seasonal evaluation during 2017–2018. (**a**): Seasonal changes of the average temperature; (**b**): CC; (**c**): RMSE; (**d**): MBE; (**e**): NSE; (**f**): KGE; (**g**): WIA.

To intuitively and easily understand the relationship between the consistency and errors of CLDAS, ERA5L, and GLDAS at the 17 observation stations, Taylor diagrams between the three reanalysis datasets and in-situ observations at each individual observation site are displayed in Figure 12. Figure 12a–q show that the standard deviations of CLDAS and GLDAS are relatively large at 11 and 7 sites, respectively, while ERA5L shows greater variability at 15 sites. The correlation coefficient between CLDAS and in-situ observations is larger than those between the other two reanalysis datasets and observations at all observation sites except Ruoergai (Elinghu), where the CC of CLDAS is slightly lower than the CC of GLDAS and ERA5L. The Taylor diagram between the three reanalysis datasets and all the in-situ observations (Figure 12r) indicates that CLDAS is closer to, and more consistent with, observations with smaller deviation.

**Figure 11.** Box plots of temperature errors in CLDAS, ERA5Land GLDAS: (**a**) CC, (**b**) RMSE, (**c**) MBE, (**d**) NSE, (**e**) KGE, (**f**) WIA.

### *3.5. Comparative Reanalysis at Different Terrain Elevations*

To explore the temperature variation characteristics of the three reanalysis datasets in different elevations, the observation sites are divided into four categories of elevation: <3500 m, ≥3500–4000 m, ≥4000–4500 m, and ≥4500 m. Figure 13 show the bias characteristics of the three gridded datasets at different elevations. In terms of evaluation indices (CC, NSE, KGE, and WIA), the consistency between CLDAS and the in-station observations is higher than the other analysis products at any altitude. The MBEs of CLDAS show a positive deviation relative to the observation station, while ERA5L and GLDAS are opposite. The RMSEs of CLDAS are lower than those of the other two reanalysis datasets, and GLDAS is better than ERA5L. Although the CCs of ERA5L is slightly higher than GLDAS, other indices (NSE, KGE and WIA) are relatively lower than GLDAS. Compared to ERA5L and GLDAS, the CLDAS temperature data is less affected by elevation.

### *3.6. Comparative Reanalysis at Different Land Covers*

According to the land cover type, the observation sites are divided into seven categories: alpine meadow (AE), desert (DT), grassland in forests (GF), gravel (GL), peatland (PD), sand and gravel (SG), and artificial grassland (AG). Figure 14 show the bias characteristics of CLDAS, ERA5L, and GLDAS at different land covers. The MBEs of ERA5L and GLDAS showed negative deviation in in-station observations at different land covers, while CLDAS is opposite. The deviation of CLDAS at land cover of artificial grassland is the smallest, as are ERA5L and GLDAS with alpine meadow and peatland, respectively. In essence, the consistency indices (CC, NSE, KGE, and WIA) and deviation (MBE and RMSE) between CLDAS and in-station observations have a small range of variation, and are better than ERA5L and GLDAS in each land cover.

**Figure 12.** Taylor diagrams of (**a**–**q**) CLDAS, ERA5L, GLDAS against in-situ observations at 17 stations and (**r**) all observation stations.

**Figure 13.** The errors at different altitudes: (**a**) CC; (**b**) RMSE; (**c**) MBE; (**d**) NSE; (**e**) KGE; (**f**) WIA.

**Figure 14.** The errors at different land covers: (**a**) CC; (**b**) RMSE; (**c**) MBE; (**d**) NSE; (**e**) KGE; (**f**) WIA.


**1. Introduction**

Ultrasonic guided waves are widely used in engineering structures' non-destructive testing (NDT). They are mostly applied to detect and localise damage [1–3] or determine elastic [4,5] and thermal properties [6–8]. For a comprehensive interpretation of results, experimental investigations can be enhanced with wave propagation simulations in numerical models. The calculations are typically performed in software implementing the finite element method (FEM). Modelling elastic wave propagation in the FEM is widely described in structural elements like rods and beams, plates and other more complex structures [3,9–11]. The FEM is mostly used for modelling structures made of homogeneous materials (e.g., isotropic steel or orthotropic composites). However, it can also be successfully applied in the case of highly heterogeneous materials (e.g., concrete). Several works consider the mesoscale structure of materials in terms of wave propagation [12,13]. For modelling and characterising the fracture properties of concrete, the discrete element method (DEM) is increasingly used, which allows for the study of its mechanical behaviour at the aggregate level. However, for discrete element-based techniques, the problem of wave propagation is not widely considered.

The discrete element method is a numerical modelling approach with many applications in various industries, e.g., hydromechanics, grinding, or even medicine [14–16]. The modelled structure is built from particles (mostly discs and spheres) that may interact with each other. For this reason, it is very popular in the fracture analysis of granular media such as sand [14–17] or concrete elements [18–26]. The geometry of the model, such as the

**Citation:** Knak, M.; Nitka, M.; Wojtczak, E.; Rucka, M. Modelling of Longitudinal Elastic Wave Propagation in a Steel Rod Using the Discrete Element Method. *Materials* **2022**, *15*, 2738. https://doi.org/ 10.3390/ma15082738

Academic Editor: Michele Brun

Received: 3 March 2022 Accepted: 6 April 2022 Published: 8 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

interactions between particles, are crucial issues. The DEM allows computing the motion of a large number of elements. Its main advantage is the high level of detail of the behaviour of each particle (at the macro- or even micro-level). The particles are considered perfectly rigid bodies but with smooth (soft) contacts (so-called overlaps). The DEM is based on the use of an explicit numerical integration scheme where the interaction of particles is monitored contact by contact. The motion of the particles is modelled one by one. It is based on Newton's second law, which is discretised by a finite difference shape, solved explicitly. In general, the DEM can be considered more complex than FEM, thus enabling an accurate reconstruction of the actual concrete mesostructure and a realistic prediction of fracture. An emerging research area is the investigation of the scattering of elastic waves within heterogeneous materials. However, the literature dealing with wave propagation problems in the DEM is still limited. An example of this kind of research was presented by Rojek et al. [27]. The authors described a micro-macro relationship in wave propagation simulation using the DEM. Their work involved calculations performed on 2D models using DEMPack software. The presented results confirmed the possibility of application of DEM for the simulation of guided wave propagation in solid materials.

The discrete element method is mainly used for modelling heterogeneous media. However, since concrete structures usually are reinforced by bars, reinforcement cannot be ignored in modelling, even though it is mostly made of steel. Thus, the current work is focused on the steel rod problem as the first step for further analysis directed to wave propagation-based diagnostics of reinforced concrete structures. The paper presents the guided wave propagation problem formulation in a circular rod using the DEM. A novel model preparation and calibration algorithm based on experimental and FEM analysis is developed. The main attention is paid to the process of the determination of discretisation and mechanical parameters.

The paper is structured as follows. The theoretical background of the DEM is given in Section 2, including basic formulae and computational methods. The proposed methodology for elastic wave modelling using the DEM is shown in Section 3. The description of the tested object with the details of experimental investigations and numerical calculations using the FEM and DEM methods is presented in Section 4. Moving on, Section 5 shows the results of the analyses performed. The guided waveforms obtained with the DEM were correlated with the experimental and FEM results. The theoretical dispersion curves were also incorporated to verify the proposed modelling algorithm. The paper completes in Section 6, which presents the main findings of the current study.

#### **2. The Theoretical Background**

### *2.1. Guided Waves in a Circular Rod*

Longitudinal guided wave modes propagating in a circular rod with a radius *r* can be described by the Pochhammer-Chree frequency equation [28]:

$$\frac{2\alpha}{r}\left(\beta^2 + k^2\right)I\_1(ar)I\_1(\beta r) - \left(\beta^2 - k^2\right)^2I\_0(ar)I\_1(\beta r) - 4k^2a\beta I\_1(ar)I\_0(\beta r) = 0,\tag{1}$$

where *J*0 and *J*1 stand for Bessel's functions of the first kind, parameters *α* and *β* are related to the wavenumber *k*, the angular frequency *ω* by:

$$
\alpha^2 = \frac{\omega^2}{c\_P^2} - k^2, \; \beta^2 = \frac{\omega^2}{c\_S^2} - k^2 \tag{2}
$$

In Equation (2), *c*2 *P* and *c*2 *S* denote the velocities of longitudinal and shear waves, respectively, and they are given by:

$$c\_P = \sqrt{\frac{E(1-\nu)}{\rho(1+\nu)(1-2\nu)}}, \ c\_S = \sqrt{\frac{E}{2\rho(1+\nu)}}\tag{3}$$

where *E* is the young's modulus, *ρ* is the mass density and *ν* is the Poisson ratio. The solution of Equation (1) provides dispersion curves, which relate the group velocity to the angular frequency by the relation:

$$
\varepsilon\_{\S} = \frac{d\omega}{dk} \tag{4}
$$

#### *2.2. Outline of Discrete Element Method*

The numerical analysis was performed with the open-source code Yade [29,30]. The algorithm for DEM calculations using spherical elements can be as follows. First, the position of every particle is established. Then, the contact between each particle and its neighbours (adjacent particles or other objects like walls or boxes) is found. If the contact exists, the overlap *u* is calculated from the equation:

$$
\mu = d - (R\_A + R\_B)\_\prime \tag{5}
$$

where *d* is the distance between the centres of the elements and *RA* and *RB* are the radius of the elements in contact. Compression forces exist if the overlap is negative (if it is positive, tension appears).

The forces in contact points are calculated from the constitutive laws (Figure 1). This paper used the simple linear elastic (in compression) law. The equations are as follows:

$$\mathbf{F}\_n = \mathbf{K}\_n \boldsymbol{\mu} \mathbf{N}\_\prime \tag{6}$$

$$\mathbf{F}\_{\sf s} = \mathbf{F}\_{\sf s,prev} + K\_{\sf s} \Delta \mathbf{X}\_{\sf s,} \tag{7}$$

where, **F***n* and **F***s* are the normal and tangential contact forces, respectively (Figure 2), **N** is a unit normal vector on contact points connecting centres of the elements, **X***s* denotes the relative tangential displacement increment and **F***s,prev* is the tangential force calculated from the previous time step. Contact stiffnesses (i.e., normal stiffnesses *Kn* and tangential stiffnesses *Ks*) can be calculated from the following relations:

$$K\_{\rm n} = E\_{\rm c} \frac{2R\_A R\_B}{R\_A + R\_B}, \quad K\_{\rm s} = v\_{\rm c} E\_{\rm c} \frac{2R\_A R\_B}{R\_A + R\_B}, \tag{8}$$

where *Ec* is Young's modulus of particle contact and *νc* is the ratio between normal and tangential contact stiffness. For the normal (in tension) and tangential force, the limit is imposed:

$$F\_s^{\text{max}} = \text{CR}^2, \quad F\_n^{\text{min}} = TR^2,\tag{9}$$

where *C* corresponds to the cohesive contact stress (maximum shear stress at a pressure equal to zero) [29,31] and *T* to the normal tensile contact stress [29] (*R* is a minimum value of *RA* and *RB*). The current study's force values are relatively low (significantly lower than the limit); thus, contact break was not considered.

**Figure 1.** Mechanical response of DEM: (**a**) tangential contact model, (**b**) normal contact model, and (**c**) modified Mohr-Coulomb model [29].

**Figure 2.** Two spheres in contact with the forces and momentum acting on them (**F***n*—normal contact force, **F***s*—tangential contact force, and **N**—normal contact vector) [29].

Moreover, the Coulomb friction is introduced. The model is described differently, depending on whether the contact is broken or not. The equations for the situation before and after the contact break can be expressed as follows, respectively:

$$\|\|\mathbf{F}\_{\rm s}\|\| - F\_{\rm s}^{\rm max} - \|\|\mathbf{F}\_{\rm n}\|\| \tan \mu\_{\rm c} \le 0,\tag{10}$$

$$||\mathbf{F}\_s|| - ||\mathbf{F}\_n|| \tan \mu\_c \le 0,\tag{11}$$

where *μc* is the Coulomb inter-particle friction angle.

After force calculations, external forces (e.g., gravity or boundary conditions) may be added. In the next step, the motion of the elements is upgraded using Newton's second law. The acceleration, velocity, and finally, new particle position are calculated. Then, the first step is repeated. Note that in this paper, no damping is introduced (however, usually, for quasi-static calculations, it is necessary to use it). In the first step, the initial overlapping was calculated (*u*int). Next, in every future step, Equation (6) was changed into:

$$\mathbf{F}\_n = \mathbf{K}\_n (\boldsymbol{\mu} - \boldsymbol{\mu}\_{\rm int}) \mathbf{N}. \tag{12}$$

So, the overlap can exist in the geometry; however, no initial forces are generated.

#### **3. A Methodology of Building a DEM Model for Wave Propagation Problems**

The simulation of the guided wave propagation phenomenon using the DEM is much more complex than in the FEM, even in the case of symmetric wave mode propagating in a rod with a circular cross-section. The current research proposes to build an appropriate model based on the calibration with experimental results. The methodology scheme developed using Yade software is presented in Figure 3. At first, it is assumed that the geometry of the rod (length *l*, diameter of the cross-section *D*), the density of the material *ρ*, and Young's modulus *E* are known (measured on the physical model). Some representative wave propagation signals need to be measured (using the particular excitation signal, e.g., wave packet). The first step of the scheme is the preparation of geometry, reflecting the physical model, including the length and cross-section of the rod. The discretisation with the use of spherical particles with the radius corresponding to the cross-section of the rod is required. The particles are arranged in a single line. An important parameter that must be assumed initially is the distance between the centres of the adjacent particles *d*. Furthermore, the number of adjacent particles with which a specific particle can interact can be set. It is determined by the parameter *Lint* specifying the area in which the centres of adjacent particles should be included to create an interaction. It is assumed that the specific particle should interact only with the closest neighbours (in general, two, one at each side); thus, the following condition needs to be satisfied:

$$d \le L\_{int} < 2d.\tag{13}$$

**Figure 3.** A scheme of building a DEM model of a rod with a circular cross-section for wave propagation using Yade DEM.

Having determined the model's geometry, the calculation of two crucial material parameters, i.e., the density of particles *ρp* and normal contact stiffness *Kn* needs to be performed using procedure 1 (as presented in Figure 3). First, the initial value of *ρp* is assumed. Based on this value, the total mass of the model is calculated and compared with the actual mass of the physical model. The ratio between these two values is the correction coefficient that is further applied to the initial value of *ρp* to obtain the final particle density. When the value of *ρp* is established, a series of models with different values of *Kn* is prepared. A simple tensile test simulation is performed for each model to determine the stress-strain relation, also used to calculate Young's modulus *EDEM*. The comparison between the series of *EDEM* values and the experimental Young's modulus *E* allows for choosing the model with the appropriate contact stiffness. The resulting values of *ρp* and *Kn*, such as the geometry and discretisation previously established, are then incorporated into the second procedure concerning the wave propagation problem. The guided waves are excited and acquired. The signals obtained are compared with the experimental ones to validate the prepared model. The shape of waveforms, such as the wave velocity, can be verified, e.g., by determining the correlation between the two approaches. If the compatibility is satisfactory, the model is considered correct. If not, the model needs modifications, and the algorithm returns to the discretisation. The distance between particles must be changed, and the further steps in procedures 1 and 2 must be repeated. In the present case, if the wave velocity in the numerical signals is too low, the distance between particles needs to be decreased. Inversely, the distance should be increased if the velocity is too high. In general, multiple repetitions of the steps presented can be required.

#### **4. Materials and Methods**

*4.1. Object of Research*

The object of the investigation (Figure 4a) was a rod with a circular cross-section (diameter *D* = 10.2 mm) and a length of *l* = 1000 mm. The rod was made of steel, with the following material parameters: mass density *ρ* = 7850.66 kg/m3, Young's modulus *E* = 208.72 GPa (determined in a static tensile test) and Poisson's ratio *ν* = 0.3.

**Figure 4.** An object of research: (**a**) specimen geometry, (**b**) numerical FEM model, (**c**) numerical DEM model.

#### *4.2. Experimental Procedure*

The experimental measurements of guided waves were carried out using piezoelectric plate transducers Noliac NAC2011 with dimensions of 2 × 2 × 2 mm3. One of the transducers acted as an actuator (A), while the second (S) acted as a sensor. The actuator was attached to one end of the rod, while sensor S was attached to the other end, as shown in Figure 5a, so the waves were excited and sensed in the longitudinal direction. The wave packet induced by the actuator was a five-cycle sine function modulated with a Hann window (Figure 5b). The central frequency of the wave packet was set in the frequency range of 50–150 kHz with a step of 10 kHz. Signals were further processed with the Hilbert transform to obtain signal envelopes [32].

**Figure 5.** (**a**) Experimental setup. (**b**) Five-cycle sine wave packet with the carrier frequency of 100 kHz (time-domain signal and frequency spectrum).

#### *4.3. Numerical Modelling*

#### 4.3.1. Finite Element Method

Numerical analysis was performed in the Abaqus software based on the finite element method. The created 3D model of a bar (Figure 4b) reflected the experimental object (including geometry and mechanical parameters). A linear-elastic, homogeneous, isotropic material model was used. Rayleigh proportional damping was assumed with a mass proportionality coefficient equal to *α* = 2000 1/N, neglecting the influence of stiffness (*β* = 0 m/N). The use of damping allows one to reflect the real wave propagation in the tested object. Boundary conditions were assumed as free edges. The numerical model was made of solid 8-node finite elements with reduced integration (C3D8R). The mesh grid had a size of 1 × 1 × 1 mm3. The explicit module was used to calculate the guided waves propagation problem. An algorithm of the central difference method has been applied to integrate the equation of motion. The total calculation time was assumed to be 1.5 ms with the time step equal to 1·10−7 s. The wave was excited by applying a concentrated force of a certain amplitude at one end of the rod. The input signal was the same as in the experimental investigations. The results of the analysis were recorded at the point at the opposite end.

#### 4.3.2. Discrete Element Method

Numerical calculations based on the discrete element method were performed in the Yade environment. There are a few significant parameters in wave propagation calculations: the particle density *ρp*, normal contact stiffness *Kn*, the geometry (initial distance between the spheres *d*) and the coordination number (the number of contacts for every element, determined by the interaction zone *Lint*). In the first step, samples with a predetermined geometry were prepared. The steel bar was created as a 3D model as one row of spherical elements with a length of *l =* 1000 mm (Figure 4c). The radius of each particle was constant and equal to half the diameter of the real bar (*R =* 5.1 mm). The parameter of the initial distance of the particle *d* has been changed. The interaction zone *Lint* was chosen so that the specific particle interacted only with its nearest neighbours. For such prepared

geometry, the quasi-static tension test was performed (only elastic part, with no breakage). The density parameter was unique for a specified distance to keep the overall mass of the bar in agreement with the real value. The modification of the stiffness coefficient directly affects the global Young's modulus *EDEM*. The prepared model was used for the 1D problem of longitudinal wave propagation. An explicit procedure was used, and the time step equal to *dt =* 5 × 10−8 s was adopted (critical time step *dtcr =* 1.3 × 10−5 s). The total computation time was 1.5 ms. No additional damping was applied to the model; nevertheless, attenuation was observed in the signals (resulting from the geometrical damping). The disturbance was induced by force applied to the first particle. The signal was recorded at the last particle (at the end of the bar, sensor S).

#### **5. Results**

A series of calculations were carried out to calibrate the DEM numerical model with the experiment. In the following steps, due to the size of the calculation, only the results for selected particle distances *d* = {0.95*R*, 1.03*R*, 1.05*R*, 1.15*R*} are presented. This set was chosen to show all aspects of the considered issue and the arising difficulties as clearly as possible. The experimental signal was taken as a reference one, to which the numerical signals were matched. The adjustment accuracy was determined qualitatively by visual evaluation of the signals and quantitatively using the Pearson correlation coefficient (PCC), such as the sum of squared errors of the longitudinal wave velocities.

The first step of the calculation for each different distance was to determine the static parameter (Young's modulus). The static tensile test simulation was performed for different values of contact stiffness *Kn* (assumed heuristically). Young's modulus *EDEM* was determined for each calculation by linear approximation of the stress-strain relation obtained from the measurements. The final value of the contact stiffness *Kn* corresponded to the model with an *EDEM* value close to the real value of *E*. Figure 6 presents an example of the stress-strain relationship and its approximation for the model with *d* = 1.03*R*.

**Figure 6.** Stress-strain relation for the 1.03*R* model for the determination of *Kn*.

Having determined all the appropriate parameters, the guided wave propagation calculations were carried out. Figure 7 shows the signals of the longitudinal wave collected at the sensor. The signals for four selected distances of particles (*d =* {0.95*R,* 1.03*R,* 1.05*R*, 1.15*R*}) are presented. Excitation frequencies equal to 50 kHz, 100 kHz, and 150 kHz were analysed. Firstly, there is a decrease in velocity with increasing frequency. When considering the models' signals with different particle distances, it is evident that the *d =* 0.95*R* strongly deviates from the others. The densification of the rod particles implies an increase in the propagation speed of the wave. Moreover, a numerical dispersion is much more pronounced (in comparison to the three other models) at higher frequencies. When comparing the waveforms presented, it can be concluded that the 0.95*R* model is the most unstable.

**Figure 7.** Comparison of signal for selected DEM models (various overlap) and frequencies.

Correlation calculations were performed using the PCC to determine which model is the most unambiguously compatible with the experiment. Table 1 shows the estimated static parameters for selected models with different particle distances with correlation coefficients. The comparison is intended to show the influence of the agreement distance parameter on the obtained agreement with reference (experimental) measurements and FEM calculations. A strong effect of the distance applied in the DEM model on the obtained correlation can be observed. This confirms previous observations, that the signals received for *d =* {1.03*R*, 1.05*R*, 1.15*R*} are comparable. Their average correlation coefficients (for all particular frequencies) indicate high similarity. However, this requires verification over a wider frequency range.

Figure 8 presents the PCC variation in relation to the wave frequency. The correlation between numerical (FEM and DEM with different overlaps) and experimental waveforms are shown in Figure 8a. First, it can be observed that there is a rapid decrease in the PCC at higher frequencies. The decrease is related to the presence of an increasing numerical dispersion. A good agreement between the experimental and FEM results can be observed (PCC above 0.85). In the case of DEM results, the PCC is above 0.7 only for the 1.03*R* model; it could be considered a strong correlation [33]. When the experimental vs. DEM correlation curves are considered, a characteristic decrease in the PCC value is observed with an increase in the distance between the particles. Furthermore, it can be seen that in the frequency range of 50–90 kHz, the PCC values of DEM vs. experimental signals are noticeably higher than the PCC values of FEM vs. experimental signals, but above a frequency of 100 kHz FEM model gives a stronger correlation. Figure 8b illustrates a plot of the PCC calculated between the FEM and DEM signal envelopes. A strong agreement between the methods is shown within the analysed frequencies. The PCC for all models

ranges between 0.8 and 1.0. This confirms that these two different numerical approaches can give comparable results.

**Figure 8.** Pearson correlation coefficient in relation to excitation frequency: (**a**) FEM and DEM vs. experimental results, (**b**) DEM vs. FEM results.

For wave propagation analysis, it is crucial to recognise the relationship between velocity and frequency. Thus, the characteristic dispersion curves were determined for the steel bar analysed. Theoretical curves were obtained using PCDISP software based on the Pochhammer-Chree theory [34,35]. The numerical FEM/DEM curves were obtained by calculating wave propagation velocity based on two adjacent wave packets using the 'peak to peak' method. Figure 9 shows the dispersion curves obtained by different approaches. The DEM curves for four different distances were compared with the theoretical ones. This comparison is intended to highlight the accuracy of the adopted discrete model. First of all, it is worth noting that the obtained curves indicate the dispersive nature of the waves in DEM. Second, it can be pointed out that the group velocity is closely related to the applied particle distance. The shorter the distances between the particle's centres, the faster the wave propagates. As the distance increases, the group velocity decreases. Additionally, as the frequency increases, the velocity decreases. In the case of *d =* 1.05*R* and *d =* 1.15*R*, the curves that fit the theoretical curve at lower frequencies start to deviate increasingly from the theory as the frequency increases. The dispersion curve obtained for the DEM model at *d =* 1.03*R* was selected to present the greatest agreement with the theory and the numerical FEM result (the group velocity of the numerical FEM is in accordance with the theoretical one at all frequencies). To determine the degree of similarity and confirm the proposed solution's validity, the residual sum of squares (RSS) was calculated [5]. The results obtained are summarised in Table 2. The RSS values clearly show the agreement of the applied models. Analysing the values for the numerical DEM models, it can be observed that the best agreement (the lowest value of RSS) is shown for the *d =* 1.03*R* model.

**Figure 9.** Comparison between dispersion curves for numerical models and Pochhamer-Chree theory.

**Table 2.** Residual sum of squares between numerical models and Pochhammer-Chree theory.

The wave propagation results for the final DEM model (*d =* 1.03*R*) are shown in Figure 10. The experimental results are compared with the numerical results obtained from FEM and DEM calculations. By analysing the graphs, it is possible to observe the compatibility of the speed of wave propagation and the compatibility of the shape of the wave packets. The first wave packets that appear are compatible with each other. The satisfactory compatibility of guided wave calculations was achieved using the discrete element and finite element methods. As mentioned earlier, the superiority of DEM over FEM can be seen at lower frequencies (50–90 kHz). The packet shapes obtained in the DEM calculations reflect the experimental ones clearly enhanced. A characteristic effect of dispersion is seen in both numerical models at higher frequencies. There is an elongation of the numerical packets, while their beginnings are consistent with the experimental ones.

**Figure 10.** Comparison of wave propagation for experimental and numerical FEM/DEM results.

#### **6. Conclusions**

The paper describes the modelling of longitudinal wave propagation in a circular steel rod using the discrete element method. An experimental approach was applied to verify the appropriateness of DEM modelling in the Yade open-source code. The finite element calculations performed in Abaqus software supported the performed analyses. Based on the results, the following conclusions could be formulated.

• The Yade platform can be successfully used for experimentally assisted guided wave modelling. The geometric and material parameters need to be determined on a physical model. Moreover, measurements of a certain number of wave propagation signals are required.

In summary, it can be concluded that the discrete element environment can be successfully used for wave propagation analysis. The present work is a beginning consideration for more complex problems, especially to explain the mechanism of propagation and scattering of elastic waves in concrete members at the aggregate level. In the next steps, the calibration of waveforms in concrete and reinforced concrete elements using DEM will be performed.

**Author Contributions:** Conceptualization, M.K., M.N., E.W. and M.R.; methodology, M.K., M.N., E.W. and M.R.; numerical investigation, M.K. and M.N., experimental investigation, M.K., E.W. and M.R.; software, M.K. and M.N.; formal analysis, M.K., M.N. and E.W.; writing—original draft preparation, M.K., M.N. and E.W.; writing—review and editing, M.R.; visualization, M.K. and E.W.; supervision, M.R. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data underlying this article will be shared on reasonable request by the corresponding author.

**Conflicts of Interest:** The authors declare no conflict of interest.


**2. Pathophysiology**

One of the typical complications of acute myocardial ischemia respectively myocardial infarction is ventricular fibrillation. Ischemic cells loose their membrane stability and a compound of such ischemic cells may cause electrical instability. Revascularization, if in time, restores cellular function and leads to electrical restabilization. One has to be aware however, that the so called reperfusion injury in the early phase after revascularization may also cause ventricular arrhythmias.

Chronic ischemia with a significant reduction of left ventricular function, the so called ischemic cardiomyopathy, is also prone to ventricular fibrillation and also in these patients revascula‐ rization may lead to a risk reduction by an improvement of the myocardial function and left ventricular ejection fraction.

If a myocardial infarction has happened, tissue is irreversibly damaged and replaced by scar. The center of this postinfarct scar is homogenious, but the border zone to vital myocardium is not linear but shows irregular interdentations between the two tissues.Within this inhomogenious

© 2013 Moosdorf; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

borderzone, reentry circuits may induce ventricular tachycardia, which is not influenced by re‐ perfusion (1).

for an ICD depends on the standardized criteria like reduced ejection fraction, incomplete revascularization or recurrent Vfib. In case of doubt, an electrophysiological investigation

Ventricular Arrhythmias and Myocardial Revascularization

http://dx.doi.org/10.5772/54694

39

Patients with coronary artery disease and a status post infarct, who have experienced already a VT, are scheduled for a combined procedure of bypass grafting and VT-surgery. If the VT is documented in the charts, no further testing is necessary. If a reliable record is missing, an electrophysiological testing should be performed. The lack of major scar or an aneurysm is no exclusion criterion, in these cases a sole epicardial procedure is scheduled and the patient has

testing should be performed. The lack of major scar or an aneurysm is no exclusion criterion, in these cases a sole epicardial procedure is scheduled and the patient has to be informed about the lower cure rate because of the limited

Anyway, a sole revascularization with or without aneurysm resection, is an incomplete therapeutic approach. Patients, who need a surgical revascularization and/or an aneur‐ ysm resection and ventricular restoration, should also be offered a curative therapy of their ventricular arrhythmia. Without a directed ablation, a disappearance of the VT can not be expected and the implantation of an ICD is only palliative! Surgery should be cu‐

Anyway, a sole revascularization with or without aneurysm resection, is an incomplete therapeutic approach. Patients, who need a surgical revascularization and/or an aneurysm resection and ventricular restoration, should also be offered a curative therapy of their ventricular arrhythmia.  Treatment algorithm (CAD:coronary artery disease, MI:myocardial infarction, EPS:electrophysiological study, CABG:coronary artery bypass grafting, LAS:laser arrhythmia surgery, ICD implantable cardioverter defibrillator)

**CABG + LAS EPS - ICD**

**PostMI + VT MI + Vfib**

**EPS CABG**

The procedure is performed via a median sternotomy and after establishing extracorporeal circulation and placing pacing wires on the surface of the right ventricle, the left ventricle is opened through the aneurysm and blood is evacuated bya vent, which is inserted via the right upper pulmonary vein as usual. It is important however to maintain a sufficiently high flow of the extracorporeal circulation to keep the aortic valve closed and to avoid an air embolism. After inspection of the ventricular cave and definition of the resection

The procedure is performed via a median sternotomy and after establishing extracorporeal circulation and placing pacing wires on the surface of the right ventricle, the left ventricle is opened through the aneurysm and blood is evacuated by a vent, which is inserted via the right upper pulmonary vein as usual. It is important however to maintain a sufficiently high flow of the extracorporeal circulation to keep the aortic valve closed and to avoid an air embolism. After inspection of the ventricular cave and definition of the resection lines, the VT is induced with the epicardial electrodes and mapping is performed with a small finger electrode.

lines, the VT is induced with the epicardial electrodes and mapping is

performed with a small finger electrode. Whenever a typical early potential is detected by the electrophysiologist, lasing is performed with the gas cooled fiber kept at a distance of approximately 5mm away from the tissue. So a sufficiently deep lesion can be created without removal of tissue and distruction of the

to be informed about the lower cure rate because of the limited access.

only palliative! Surgery should be curative if ever possible.

**CAD**

should be considered.

rative if ever possible.

defibrillator)

**The surgical procedure**

**6. The surgical procedure**

access.


**3. Classification of Schiff bases and their metal complexes**

By coordinating the d-block metal ion with the electron-donating ligand atom, a complex is created that modifies the metal's steric and electrical properties. By doing so, the metal ion's reactivity is stabilized and regulated, which is especially helpful for ions at higher oxidation states where they are less stable. Auxiliary ligands, or Schiff bases, are compounds that modify the structure and reactivity of a transition metal ion inside a complex. On the other hand, they do not incur any irreversible modifications, unlike reactive ligands. Atoms like nitrogen, sulfur, or oxygen can act as donors in the coordination process.