*5.1.2 Failure to realise the diversity of strategic thinking competencies*

The pitfall is that the frameworks of sustainable leadership emphasise the necessity of a long-term perspective as if this is the only strategic thinking competence. For instance, the framework by Avery and Bergsteiner [17] refers to only long- or short-term views and the capacity to endure over time. Hargreaves and Fink [29] discuss sustainability vision, values and holistic approach. Davies [20] hinge on the capacity to decipher strategic priorities and cohesive and longer-term development, while Lambert [21] focuses on commitment at all levels of leadership development. In each framework, there is a failure to recognise the broad scope and diversity of strategic thinking competencies critical for sustainability. Ledtka [43] asserts that there are five strategic thinking competencies: Systems perspective, intent-focused thinking, thinking in time, hypothesis-driven thinking and intelligent opportunism. With this in mind, it is clear that none of the frameworks in **Table 2** is inclusive enough to embrace all of these strategic thinking

### *The Nature of Sustainable Leadership: Pitfalls, Insights and New Model DOI: http://dx.doi.org/10.5772/intechopen.108833*

competencies. However, each competence highlighted by Ledtka [43] is crucial for sustainable leadership. For example, the competence of systems perspective is about seeing the inter-connectedness, interdependencies and patterns in the various components over time. Second, the competence of intent-focused or vision-driven thinking is driven by goals, strategic intent and a sense of destiny. Third, the competence of thinking in time is about connecting the past, present and future (e.g. understanding the gap between the present and the desired future and the clear focus on what needs to be done and what can be done). Fourth, the competence of hypothesis-driven thinking is the ability to see and formulate future possibilities and plans as hypotheses. Lastly, the competence of intelligent opportunism requires balancing strategic intent with the flexibility to adapt to emergent opportunities in the environment (e.g. willingness to re-examine strategic intent and adapt the strategy to changing situations). As an aspect of strategic thinking, creative thinking includes gaining new insights and different ideas through existing information to see new patterns of how to reinforce sustainability. Marketoriented thinking helps sustainable leadership to search for alternative ways to attain sustainable competitive advantage. A broad scope of strategic thinking competencies by sustainable leadership helps to create transformative capacity, build resilience and implement systemic interventions while considering unintended consequences and cascading effects.


*Article* **The Enhancement of Leak Detection Performance for Water Pipelines through the Renovation of Training Data**

#### **Tu T.N. Luong 1 and Jong-Myon Kim 2,\***

#### Received: 3 April 2020; Accepted: 28 April 2020; Published: 29 April 2020

**Abstract:** Leakage detection is a fundamental problem in water management. Its importance is expressed not only in avoiding resource wastage, but also in protecting the environment and the safety of water resources. Therefore, early leak detection is increasingly urged. This paper used an intelligent leak detection method based on a model using statistical parameters extracted from acoustic emission (AE) signals. Since leak signals depend on many operation conditions, the training data in real-life situations usually has a small size. To solve the problem of a small sample size, a data improving method based on enhancing the generalization ability of the data was proposed. To evaluate the effectiveness of the proposed method, this study used the datasets obtained from two artificial leak cases which were generated by pinholes with diameters of 0.3 mm and 0.2 mm. Experimental results show that the employment of the additional data improving block in the leak detection scheme enhances the quality of leak detection in both terms of accuracy and stability.

**Keywords:** intelligent leak detection; acoustic emission signals; statistical parameters; support vector machine; wavelet denoising; Shannon entropy

#### **1. Introduction**

Leakage detection is a primary problem in water management [1,2]. About 20–30% of the water has been lost in water supply system every year. Especially, the loss of water can be up to 50% in some systems [2]. The growing demand for water inspires reconsideration of the management and supply of pipeline systems. Complications in exploiting new water bodies can be beaten by decreasing water losses [3]. Furthermore, the present attention of environmental protection and issues related to water quality encourages a growing interest in leakage detection. The community concerned with water resources has been concentrated more on the natural environment. However, the guardianship of water against incursions in pipes and the protection of the environment from the arrival of a transported contaminant are as significant as the protection of aquifers and well-fields from contaminant discharge [4]. Subsequently, methodologies for early leak detection are strongly urged. Additionally, they should not induce the interruption of piping actions, and they should be simple enough to actualize in practice.

Many studies on leak detection for water supply systems have been conducted and published. The avenues may be passive or active [5], and hardware-based or software-based [6]. Passive methods require direct visual investigation or supervision of sites, while active methods include a signal analysis. Signals used in active methods can be acoustic, vibration, flow rate, or pressure. Besides, hardware-based methods are classified depending on the type of special sensing devices such as acoustic monitoring, vibration analysis, cable sensor, etc. On the other hand, software-based methods are categorized based on the type of software programs and techniques used for leak detection such as

support vector machine, harmonic wavelet analysis, genetic algorithm, etc. Among those avenues, acoustic emission (AE)-based methods, which are passive and hardware-based, are auspicious, since AE sensors can quickly recognize small leaks, offering high sensitivity in relation to fault buildup in a piping system. Accordingly, AE-based methods for pipeline diagnostics have been exploited [7–12].

In recent years, defect diagnosis methods based on modelling have been extensively used to improve the availability and reliability of mechanical systems subject to defects [13–15]. These avenues use high-dimensional signature vectors to prevent the hazards of dropping likely essential information. Nevertheless, some defect signatures are repetitious or inapplicable to the predicting models (namely unsupervised and supervised learning). As a result, these defect signatures can be a fundamental source of diagnostic efficiency deterioration. To address this issue, discriminative defect signature selection has turned into an indispensable part of trustworthy diagnosis. Basically, the subsequent two steps are carried out in the signature selection procedure, namely a configuration step of signature subsets and an assessment step of signature subset quality. Specifically, a number of signature subsets are first assembled and then assessed. Based on the assessment step, signature selection strategies are fundamentally assorted into wrappers or filters. Filter avenues use an assessment strategy that is separated from any classification strategy, while wrapper strategies employ accuracy estimates for particular classifiers during the evaluation of signature subset quality [16]. As a result, wrapper methodologies give better diagnostic efficiency for predetermined classifiers than filter strategies, theoretically. Nevertheless, filter avenues are computationally profitable because they bypass the accuracy estimation step for a specific classifier.

Practically, various conditions influence leakage signals, such as pipe diameter, surrounding environment, pipeline material, flow rate, and pressure [17,18]. Therefore, the data collected for training classifiers may not be large enough and extracted features from it may not be smooth enough to cover the whole probability space of features. As a result, the accuracy of feature evaluation and selection based on these data may be reduced. Furthermore, leak detection is a real application, and thus the techniques should be simple, effective, and easy to implement by hardware. Recently, Tu et al. offered an effective multivariable signature assessment coefficient (MSAC) to simultaneously evaluate the interclass separability and intraclass compactness depending on predicting the signature space from a restricted data point number [12]. Based on this coefficient, the diagnostic performance, in case the training data is not broad enough, is considerably improved. Nevertheless, the quality of leak detection is also affected by outsiders. These effects are regarded as noise data points with a low probability distribution, and they are far from the central data point in the same class. The accuracy and stability of a model greatly depends on the training dataset. If the training dataset is less generalized, the diagnostic model built on it will have reduced reliability and stability of performance. To deal with this problem, a data renovation method was introduced in this study. Particularly, the MSAC was first used to evaluate signatures as a filter method, and then the most discriminative signature subset was produced. Based on the selected signature subset, detecting and removing outsiders from the known dataset before training a diagnostic model is a key issue.

Once the discriminatory feature subset is determined and the known dataset is renovated, they are further employed to train a Support Vector Machine (SVM) classifier, which is a supervised model with higher accuracy than unsupervised models such as *k*-NN classifier, and with faster processing speed and lower hardware requirements than deep learning. In this work, the offered method was used to detect artificial leaks created in a laboratory with hole diameters of 0.3 mm and 2.0 mm.

The organization of this paper is as follows. The offered method is presented in Section 2. The data collecting method for leak detection is illustrated in Section 3. The efficacy of the proposed method is validated in Section 4, and the final section shows the conclusions.

#### **2. The O**ff**ered Method**

The overall flow diagram of leak detection is illustrated in Figure 1. First, the acquired AE signals were denoised by a Wavelet algorithm based on normalized Shannon entropy, which was also adopted in some recent studies of leak detection [12,19,20]. After that, the denoised signals were divided into separate analysis and evaluation datasets. The isolation of the evaluation dataset from the analysis dataset was to ensure the reliability of the performance evaluation results. Based on the analysis dataset, a defect signature pool was configured and the most discriminative signature subset, which was also applied on the evaluation dataset, was determined. Subsequently, based on selected features, the analysis dataset was renovated by detecting and removing outsiders before it was used to train SVM classifiers. Finally, the efficacy verification of the proposed method was carried out on the evaluation dataset. Each specific part is described in detail as follows.

**Figure 1.** The overall flow diagram of the leak detection model.

#### *2.1. Noise Reduction Using a Wavelet Transform and Shannon Entropy*

Due to the nature of the AE mechanism, leakage noise is commonly nonstationary [21,22]. Time-frequency analysis methods, which are powerful tools to analyze the time-varying nonstationary signals, are recommended to study a signal in both the time and frequency domain simultaneously. Many studies have adopted the wavelet transform to detect the leak by reason of its multiresolution capability [23–25].

A form of wavelet transform which allows multiresolution investigation is known as a Wavelet packet transform (WPT) [26]. Signals can be decomposed into both wavelet coefficients and the scaling values through the WPT technique. Based on this technique, the complete decomposition hierarchy is provided. As a result, because of uniform frequency secondary groups, the decomposition becomes extremely adoptable [27].

A signal ψ(*t*) with a fixed energy, which is expressed as a mother wavelet, is a consecutive vacillating function of intensely short duration as indicated in Equation (1):

$$
\psi\_{s,\tau}(t) = \frac{1}{\sqrt{s}} \psi(\frac{t-\tau}{s}), s > 0; -\infty < \tau < \infty,\tag{1}
$$

where ψ*s*,τ(*t*) consists of the total standardized expressions (expansions) in time *t* designated by *s* > 0 (scale factor) and translation in time *t* is designated by −∞ <τ< ∞. Equation (2) expresses a cross correlation of *x(t)* with ψ*s*,τ(*t*) which depicts the Wavelet transformation of a signal *x(t)* [24,27–29]. Mathematically, the similarity between two signals can be identified by cross-correlation analysis. Given two sets of signals *xi* and *yi*, where *i* = 0, 1, 2, ... , *N* − 1, Equation (3) describes the function of normalized cross correlation with zero time-lag. The normalized cross correlation is a numerical quantity between 0 and 1, which predicts the closeness in characterization between two signals. Two signals which have identical characterizations generate a normalized cross correlation coefficient of 1.0 [30]:

$$\mathcal{W}T\_{\mathcal{X}}(\mathbf{s},\mathbf{r}) \triangleq \int \mathbf{x}(t)\psi\_{\mathbf{s},\mathbf{r}}(t)dt,\tag{2}$$

$$R = \frac{\sum x\_i y\_i}{(\sum x\_i^2)^{\frac{1}{2}} (\sum y\_i^2)^{\frac{1}{2}}} \,\, \tag{3}$$

The determination coefficient is made by executing the WPT with filter banks through recursive schemes. Low-frequency components (approximations) and high-frequency components (details) at each resolution level are obtained by transmitting the signal *x(t)* to a two-channel filter. Compared to the wavelet transform technique, which decomposes only the approximations, the WPT technique decomposes both details and approximations at every resolution level.

The most indispensable challenge in wavelet analysis is the selection of the mother wavelet function as well as the decomposition level of signal. Among orthogonal wavelets, Daubechies (DB) wavelets have been widely implemented, as they match the transient components in acoustic and vibration signals [31]. The order of the mother wavelet function and the level of decomposition were often determined by trial-and-error methods based on intrinsic characteristics of the data [31,32]. In this study, the selected mother function is DB15, and the number of levels was experimentally determined by Equation (3). Figure 2 illustrates the binary hierarchical tree of discrete wavelet packet transform (DWPT) coefficients. Each node of this tree was considered as a sub-band and numbered according to its level and its ordinal in level. Here, hierarchical levels and ordinals are numbered from 1.

**Figure 2.** The binary tree of the organization and numbering of sub-bands in discrete wavelet packet transform (DWPT).

An algorithm based on informative entropy was utilized to detect the unnecessary signatures in an AE signal acquired during a test, where the informative entropy was considered a cost function. In this method, only the sub-bands which focus the major information carried by the signal are intended to be picked. Generally, the following equations denote the Shannon entropy *H Xj* if *Xj* = *xj*, *k* is a cluster of coefficients of a specified sub-band of the WPT tree at stage of resolution *j*:

$$H(X\_{\bar{l}}) = -\sum\_{k} P\_k \ln(P\_k)\_{\prime} \tag{4}$$

$$P\_k = \frac{\left\|\mathbf{x}\_{j,k}\right\|^2}{\left\|\mathbf{X}\_j\right\|^2} \tag{5}$$

Here, *Xj* 2 = *k x*2 *j*,*k* signifies a norm of *Xj* [26]. A large value of *H Xj* means that the signal is in higher disorder and carries less information. As a result, the corresponding sub-band and its subordinates are discarded. This implies that the entropy computes a correlation of energy among the sub-bands. At this moment, the aim is to select the WPT branch which transports the minor disorders and has minimum conceivable energy. If the informative entropy of the current resolved sub-band is smaller than that of the subsequent resolved sub-band, then the total data is conserved. Otherwise, a lesser energy level of resolution is essential. In other words, the selected sub-band should have the lowest entropy value and the highest resolution level. After that, the preferred sub-bands are used to reconstruct the AE signal such that the most significant part of the signal is saved, and the complementary component which is known to be noise is removed.

#### *2.2. Fault Signature Pool Configuration*

*i*

According to the authors of [11,12], intelligent leak detection schemes are well corroborated with statistical parameters from the time and frequency domains. Thus, this study used them as fault signatures for the identification of leaks. Statistical parameters for the given one-second AE data, *x(n)*, are defined in Tables 1 and 2. These parameters were computed in the frequency and time domain, and involved the peak (*sp*1), the root-mean-square (*sp*2), kurtosis (*sp*3), crest-factor (*sp*4), impulse factor (*sp*5), shape factor 1 (*sp*6), skewness (*sp*7), the square-mean-root (*sp*8), margin factor (*sp*9), peak-to-peak (*sp*10), kurtosis factor (*sp*11), energy (*sp*12), clearance factor (*sp*13), shape factor 2 (*sp*14), the fifth normalized moment (*sp*15), the sixth normalized moment (*sp*16), entropy (*sp*17), spectral centroid (*sp*18), the root-mean-square of frequency (*sp*19), root variance of frequency (*sp*20), and the frequency spectrum energy (*sp*21).

**Table 1.** General statistical parameters in time-space of acoustic emission (AE) signals.

**x** = [*x*1, *x*2, ... , *xN*] denotes a signal in time-space, *mean*(**x**) = 1 *N N i*=1 *xi*, *s*td(**x**) = " 1 *N N i*=1(*xi* − *mean*(**x**))2 , *pi* = *x*2 *i N i*=1 *x*2 , *rms* = *sp*2, *smr* = *sp*8.

**Table 2.** General statistical parameters in frequency-space of AE signals.

$$sp\_{20} = \frac{sp\_{18} = \frac{\chi\_{\mathbb{C}}\mathfrak{s}^{\mathbb{F}}}{\sum\_{l=1}^{N} (X\_l - mean(\mathbb{X}))^2}}{\sqrt{\frac{1}{N}\sum\_{l=1}^{N} (X\_l - mean(\mathbb{X}))^2}} \qquad \begin{array}{c} sp\_{19} = \sqrt{\frac{1}{N}\sum\_{l=1}^{N} X\_l^2} \\ sp\_{21} = \sum\_{l=1}^{N} X\_l^2 \end{array}$$

**X** = [*X*1, *X*2, ... , *XN*] expresses a signal in frequency-space corresponding to the frequency vector **f**= [ *f*1, *f*2, ... , *fN*].

In summary, the dimensionality of the fault-signature pool used in the feature selection process is *Ndp* × *Nsp* × *Ncl*, where *Ndp*, *Nsp*, *Ncl* are the number of data points per leak condition class in the analysis dataset, the number of statistical parameters, and the number of classes to be discriminated in this study, respectively. Figure 3 illustrates an example of a data point configuration used to yield the most discriminatory feature subset. The set of elements in the fault-signature pool is denoted by *X* = *x*(*dp*,*sp*, *cl*) ! , with *dp* = 1, ... , *Ndp*, *sp* = 1, ... , *Nsp*, and *cl* = 1, ... , *Ncl*. Variables *dp*, *sp*, *cl* represent coordinates of data point *x* in the dataset *X*.

**Figure 3.** The illustration of data point configuration.

#### *2.3. The Generation of the Discriminative Signature Subset*

In order to achieve fairness, statistical parameters need to be standardized before evaluating and grading. This study used a simple scaling method with the following formula:

$$\overline{\mathbf{x}\_{i}} = \frac{\mathbf{x}\_{i} - \min(\mathbf{X}\_{k})}{\max(\mathbf{X}\_{k}) - \min(\mathbf{X}\_{k})},\tag{6}$$

Here, *Xk* = *xi*|*sp* = *k* ! , *Xk* = *xi sp* = *k* denote original and standardized sets of values of the *kth* signature (i.e., *kth* statistical parameter) respectively. After standardization, values of different signatures were all in the range [0,1].

To solve the small dataset problem, Tu et al. recently introduced an MSAC to evaluate the discrimination of fault signatures between two different classes [12]. The MSAC method estimates the potential value range of *kth* dimension of the signature sub-space of class *i* by interval *mean Xi k* − 3*std Xi k* , *mean Xi k* + 3*std Xi k* , where *Xi k* denotes the set of values of *kth* signature of data points in class *i*. Therefore, the crossing level between two signature sub-spaces of classes *i*, *j* at dimension *k* which is denoted by *MSACi*,*j k* is determined by Equation (7):

$$\text{MSAC}\_{\mathbf{k}}^{i,j} = 1 - \frac{\text{3}\{std\left(\mathbf{X}\_{k}^{i}\right) + std\left(\mathbf{X}\_{k}^{j}\right)\}}{\left|\max\left(\mathbf{X}\_{k}^{i}\right) - \text{mean}\left(\mathbf{X}\_{k}^{j}\right)\right|}, \text{ \textdegree \text{\textdegree} \{\text{spt\\_}} = \text{k}, \text{cl} = \text{i}\right\text{\textdegree}, \text{X}\_{k}^{j} = \text{\textdegree \text{\textdegree}}\{\text{spt\\_}} = \text{k}, \text{cl} = \text{j}\right\text{\textdegree} \qquad \text{(7)}$$

Values of*std Xi k* ,*std Xj k* represent the intraclass compactness of classes, and *mean Xi k* − *mean Xj k* represents the interclass separability. According to the authors of [12], the bigger the MSAC, the better discrimination. Thus, MSAC expresses the distinguishable ability of signatures for each pair of classes. Although it is simple and has low computing cost, it is still effective and suitable for real applications such as leak detection. In this paper, the MSAC was used to rank signatures from top to bottom and the discriminatory signature subset was created by picking the signatures on top.

#### *2.4. Data Renovation*

To build a classification model, the correctness and generalization of the training dataset are extremely important. If the dataset is inaccurate or not generalized, then the accuracy, reliability, and stability of the trained model may be reduced. Related studies have most focused on big data [33–35]. Meanwhile, the problem with leak detection using a smart fault diagnostic model is related to the small data problem, because leakage signals are affected by many external factors. Therefore, it is necessary to revamp the dataset. In machine learning, the quality of samples is more important than their quantity, especially when the quantity is not large. The higher quality the samples, the greater the generalization ability and the better the accuracy. In a class, points that are far from the center and have a low probability distribution are known as outsiders. They are less significant than the rest and may be noise points. Consequently, they should be detected and removed.

This study focuses on improving the quality of data before training the classification model with a simple and effective technique. This technique includes three processes of detecting, eliminating outsiders, and updating dataset alternately until there no longer exist outsiders in the renovated dataset. In this study, we assumed that the statistical parameter values were Gaussian random variables. In term of statistics, the probability that each statistical parameter value in a specific class lies in the interval [*mean* − 3*std*, *mean* + 3*std*] is equal to 99.73% [36], where *mean* is the mean and *std* is the standard deviation of their values in that class. This study used such range as the limit for outsider detection to ensure that outsiders were both far from central points and had a low probability distribution. Outsiders were defined as data points that were outside the confident interval (CI), which was determined through the central coordinate (CC) (i.e., the central point) and the standard deviation of each dimension (i.e., each statistical parameter or signature) of the signature space. Figure 4 illustrates an example about how to identify the central point, inner points, and outsider points in a signature space having two dimensions.

**Figure 4.** The illustration of how to classify data points.

Denote *Xi k* = *x sp* = *k*, *cl* = *i* ! as the set of values of *kth* statistical parameter of all data points in class *i*. The CC of class *i*, *CCi*, is defined in Equation (8). The CI of value of *kth* statistical parameter (i.e., *kth* dimension) of data points in the signature space of class *i* is given in Equation (9). A data point is considered as an outsider if any dimension of that data point is outside the CI of such dimension. The process of improving the dataset was implemented separately for each class and illustrated in Figure 5. Whenever outsiders are detected and eliminated, the dataset needs to be updated. After that, values of CC and CIs also needs to be updated, and as a result, new outsiders can be detected and eliminated. This process ends when no outsider is detected in the updated dataset:

$$\text{CC}\_{i} = \left( \text{mean} \left( \mathbf{X}\_{1}^{i} \right), \text{ mean} \left( \mathbf{X}\_{2}^{i} \right), \dots, \text{ mean} \left( \mathbf{X}\_{N\_{\text{sp}}}^{i} \right) \right) \tag{8}$$

*CIi k*=

*mean Xi k* − 3*std Xi k* , *mean Xi k* + 3*std Xi k*

, (9)

**Figure 5.** The process of improving the training dataset.

#### *2.5. Classification*

This study used a two-class SVM classifier whose theory is based on the idea of structural hazard minimization [37]. In the SVM method, the generalization error is minimized and the geometric margin between two classes is maximized. This method is also known as the maximum margin classifier. In this study, the kernel function was used to map the input data into a high-dimensional signature space and detect the best hyper plane to discriminate between the two classes of input data. The margin between two classes in the feature space was maximized by the best hyper plane. This quadratic optimization problem was worked out using Lagrange multipliers. The term "support vectors" is used to refer to the points which are nearest to the optimal hyper plane for each class [38]. Support vectors are selected along the surface of a kernel function which can be chosen among different functions such as polynomial, linear, radial-based, and sigmoid for the SVM during the training phase [39]. Based on a set of predetermined support vectors that are members of the set of training inputs, SVM distributes data with two class labels.

Kernel function parameter selection is one of the significant details of SVM modeling. In this paper, we used the radial based function (RBF), which is a common kernel function that can be employed to any sample distribution through parameter selection. The RBF has been used more and more in the nonlinear mapping of SVMs. The RBF kernel function expression is:

$$K(\mathbf{x}\_i, \mathbf{x}\_j) = \exp\left(-\gamma \left\|\mathbf{x}\_i - \mathbf{x}\_j\right\|^2\right),\tag{10}$$

The corresponding minimization problem of an SVM is expressed below:

$$\min\_{a\_i} \frac{1}{2} \sum\_{i=1}^{n} \sum\_{j=1}^{n} y\_i y\_j \alpha\_i \alpha\_j \exp\left(-\gamma \left\|\mathbf{x}\_i - \mathbf{x}\_j\right\|^2\right) - \sum\_{i=1}^{n} \alpha\_{i\prime} \sum\_{i=1}^{n} y\_i \alpha\_i = 0, \; 0 \le a\_i \le \mathbb{C},\tag{11}$$

The minimum value of Equation (11) depends on the choice of parameters (*C*, γ). In this study, the grid search method was used to get the final optimal parameters (*C*, γ) [40]. This method respectively takes *m* values in *C* and takes *n* values in γ, for the *m* × *n* combinations of (*C*, γ), trains different SVM respectively, then estimates the learning precision. We can obtain the highest study accuracy of the best combination as the optimal parameters in the *m* × *n* combinations of (*C*, γ).

#### **3. Experiment Setup**

Figure 6 shows the setup of the AE signal acquisition from a water pipeline system. The pipe, which was made of stainless steel 304, had an outside diameter of 34 mm and a wall thickness of 3.38 mm. A pump was employed to keep the water flow constant at a pressure of 3 bar. The experiments were executed under a balanced temperature of approximately 29 ◦C. AE sensors were mounted on both sides of the testing pipe fragment. The distance from sensors to the leak position was 1000 mm. In this study, wideband differential-auto sensor test (WDI-AST) sensors were used to provide high sensitivity and a wide frequency band. The characteristics of the sensors are recapped in Table 3.

**Figure 6.** AE signal acquisition from a water pipeline system: (**a**) The test pipeline and component arrangement; (**b**) the pinhole size of 0.3 mm; (**c**) the pinhole size of 2.0 mm.

**Table 3.** Specifications of the wideband differential-auto sensor test (WDI-AST) sensors.

The experiments were based on two leak cases with different pinhole diameters, i.e., 0.3 mm and 2.0 mm, which were considered dataset 1 and 2, respectively. The AE signals were collected in one-second time lengths and sampled at a frequency of 1 MHz. Details of the datasets which were used to assess the offered method are described in Table 4. In this table, "normal" means the no leakage case. Since different datasets were acquired in different dates, and operating conditions such as temperature,

pressure, flow rate, etc. have impacts on AE signals, each "normal" data is taken accordingly with the leak data to have coherence with background condition.

**Table 4.** Details of the datasets employed to assess the offered method.

#### **4. Results and Discussion**

Figures 7 and 8 illustrate one obtained AE signal sample of each case for each dataset over the time and its fast Fourier transform in frequency domains. It is clear that these original signals contained noise, and that there was not much difference between signals at healthy and unhealthy states.

**Figure 7.** The illustration of the obtained AE signals in dataset 1 over the time and frequency domains.

**Figure 8.** The illustration of the obtained AE signals in dataset 2 over the time and frequency domains.

To extract the most informative part of the signals, sub-bands were first produced by implementing the DWPT on each raw AE signal. Then, the optimal sub-band was selected depending on the minimum wavelet entropy before being employed to restore the AE signal. Figure 9 shows the difference between signals before and after denoising in both the time and frequency domains.

**Figure 9.** Differences between the signals before and after filtering noise in both the time and frequency domains.

In the next step, the fault signature pool was created from reconstructed AE signals in the analysis dataset. Then, the MSAC was used to evaluate the signatures. Table 5 lists signatures in order of best to worst in terms of leak detection, together with their MSACs corresponding to each case.

**Table 5.** Lists of signatures in order of best to worst together with their multivariable signature assessment coefficients (MSACs).

After that, the two best signatures on top were selected as a discriminatory feature subset. In such a manner, the feature sub-set that was most discriminative for both cases included one parameter on the time domain, namely the square-mean-root, and one parameter on the frequency domain, namely the spectral centroid. Figure 10 illustrates the distribution of data points according to the selected features corresponding to each leak case. It can be seen that data points in the same class, in the case of a lower-level leak (pinhole size of 0.3 mm), had a higher concentration than in the case of a higher-level

leak (pinhole size of 2.0 mm), while the separation between classes in the first case was lower than the other. The reason for this may be that instability of the AE signal increased belong with the leakage level. It follows that the leak detection method of using statistical parameters of AE signals was limited by leak level in both directions. Specifically, the greater the leakage level, the lower the concentration level in the same class and the greater the interclass separability.

**Figure 10.** The distribution of data points according to the selected features corresponding to each leak case: (**a**) Leak size of 0.3 mm; (**b**) leak size of 2.0 mm.

To enhance the stability and quality of the SVM classifiers, the training dataset needs to be improved by detecting and removing outsiders, which may be noise data points because of their low probability distribution and weak generalization. Based on the renovated analysis dataset, the SVM classifiers were trained before being used to detect leaks in the evaluation dataset. To evaluate the proposed method, this study used a 10-fold cross validation to compare classification accuracies (CAs). The CA given in Equation (12) is the ratio between the number of correctly classified data points (i.e., true points), *NTP*, and the total of data points, *Ntotal*. The results of CAs of three methods are shown in Table 6. Here, "All" represents the conventional method, which uses all of 21 fault signatures without signature selection and data renovation, whereas the conventional method [12] uses a signature selection with MSAC without data renovation. In general, the proposed method, which added the data enhancement block, outperformed the method in [12], which had the same signature subset. Specifically, the former had no worse results than the latter in 10 total assessments of both cases. In addition, the former surpassed the latter by four times in dataset 1 and three times in dataset 2. It follows that the former enhanced the average CA of 4.61% and 1.58% compared to the latter when datasets 1 and 2 were used, respectively. Therefore, it is proven that the proposed method is both more accurate and more stable than the previous method.

$$
\mathbb{C}A = \frac{N\_{TP}}{N\_{total}} \times 100\% \tag{12}
$$

**Table 6.** The classification accuracy results (%) for 10-fold cross validation.

Compared to the method of using all the signatures in terms of CA, the proposed method was better in dataset 1, but worse in dataset 2. However, the proposed method, which used only two features, significantly reduced the number of dimensions of the fault signature vector compared to the non-signature-selection method, which used 21 features. This means that it is possible to mitigate the computational responsibility in the configuration of signature vectors in real applications. Moreover, low-dimensional signature vectors can assist in reduction of consumed time to train classifiers. Table 7 shows computational time comparison between the proposed and conventional method which employed all 21 signatures. Compared to the conventional method, the processing speed of the proposed method was improved by 31.17% in training, 76.77% in test, and 40.14% in total for the dataset 1. Similarly, those improvements for the dataset 2 were 41.63%, 76.80%, and 48.63% respectively. All experiments were implemented with MATLAB R2018b on an Intel Core i7-7700 CPU operating at 3.60 GHz.

**Table 7.** Computational time comparison between the proposed and the conventional methods.

#### **5. Conclusions**

In this paper, an intelligent leak detection method based on a model using statistical parameters extracted from AE signals was used for early leak detection. Since leak signals depend on many operation conditions, the training data in real-life situations usually has a small size. To solve the problem of a small dataset, a data improving method based on enhancing the generalization ability of the data was proposed. To evaluate the effectiveness of the proposed method, this study used the datasets obtained from two artificial leak cases which were generated by pinholes with diameters of 0.3 mm and 0.2 mm. Experimental results showed that the employment of the additional data improving block in the leak detection scheme enhances the quality of leak detection in both terms of accuracy and stability.

**Author Contributions:** Conceptualization, T.T.N.L. and J.-M.K.; Data curation, T.T.N.L.; Formal analysis, T.T.N.L.; Funding acquisition, J.-M.K.; Methodology, T.T.N.L. and J.-M.K.; Software, T.T.N.L.; Supervision, J.-M.K.; Validation J.-M.K.; Visualization, T.T.N.L.; Writing—original draft, T.T.N.L.; Writing—review & editing, J.-M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No.<PHONE_NUMBER>2510).

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

#### **References**

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).


**Author details**

Alicia Puyana Mutis1 \* and Cinthia Márquez Moranchel2

1 FLACSO, Mexico

2 UNAM, Mexico

\*Address all correspondence to<EMAIL_ADDRESS><EMAIL_ADDRESS>
© 2021 The Author(s). Licensee IntechOpen. 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.


**2.2.1 Principle of the stretch reflex**

When muscle is stretched, it reflexively contracts in response. This kind of muscle response is called the stretch reflex. The stretch reflex is the target of the pendulum test. Fig. 3 shows the conceptual pathway of the stretch reflex. When muscle is stretched by some factor, receptor (called muscle spindle) detects it as a stimulus and transmit it as an afferent signal up to the spinal cord i.e., the α-motoneuron. The spinal cord receives the signal and sends a command (efferent signal) to effector (muscle) to restore this stretched state to the original state. These processes are executed unconsciously. Afferent fiber and efferent fiber function respectively as the transmission pathways for the afferent signal and efferent signal, which are both transmitted as impulses.

Fig. 3. Path of stretch reflex.

The reflex pathway described above (receptor → spinal cord → effector) is called a reflex arc. The stretch reflex is generated not only by passive muscle stretching, but also in response to conscious stretching of a muscle. The pendulum test is a test to estimate the sensitivity with which the reflex arc responds to the stimulus of knee flexion (extension of the quadriceps femoris muscle). The knee joint motion in this case is induced unconsciously by adding external force with the subject in a resting state for ease of estimation.

### **2.2.2 Structure of the spindle and its functions**

Muscle is made up of many extrafusal muscle fibers arranged in parallel. Both ends of each muscle spindle are attached to one of these extrafusal muscle fibers. The muscle spindle is covered with a capsule, as shown in Fig. 4. In the capsule, there exist two types of intrafusal muscle fibers, called nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber. Stretching of the extrafusal muscle fiber affects the nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber, and stretch velocity and displacement, respectively, are detected. The detection sensitivities of the stretch velocity and displacement are regulated by efferent commands that are sent from phasic γ-motoneuron and tonic γ-motoneuron present in the spinal cord, respectively. The two kinds of detected information are consolidated into the afferent signal within the muscle spindle and transmitted to the spinal cord through Group Ia afferent fiber. Group II afferent fiber that send only nuclear chain intrafusal muscle fiber information to the spinal cord is also present, but they have a little influence on the stretch reflex in the pendulum test, and so it is not shown in the figure.

The afferent signal of Group Ia fiber is given as follows as the impulse frequency *f*s (primary approximation) (Harvey & Matthews, 1961).

$$f\_{\rm s} = k\_{\rm 1s}x + k\_{\rm 2s}f\_{\rm 3s} + k\_{\rm 1d}\dot{x} + k\_{\rm 2d}f\_{\rm 3d} \tag{1}$$

Here, *x* is extrafusal muscle fiber (muscle) displacement, *f*γd and *f*γs are the respective impulse frequencies from the brain to phasic and tonic γ-motoneurons, and *k*1s, *k*1d, *k*2s, and *k*2d are constants. As shown in the above equation, there are two types of components in stimuli detected by the muscle spindle in the stretch reflex: a stretch velocity component expressed by the first and second terms, and a muscle displacement component expressed by the third and fourth terms.

Fig. 4. Structure of muscle spindle.

22 Advanced Topics in Measurements

When muscle is stretched, it reflexively contracts in response. This kind of muscle response is called the stretch reflex. The stretch reflex is the target of the pendulum test. Fig. 3 shows the conceptual pathway of the stretch reflex. When muscle is stretched by some factor, receptor (called muscle spindle) detects it as a stimulus and transmit it as an afferent signal up to the spinal cord i.e., the α-motoneuron. The spinal cord receives the signal and sends a command (efferent signal) to effector (muscle) to restore this stretched state to the original state. These processes are executed unconsciously. Afferent fiber and efferent fiber function respectively as the transmission pathways for the afferent signal and efferent signal, which

> spinal cord (α-motoneuron)

The reflex pathway described above (receptor → spinal cord → effector) is called a reflex arc. The stretch reflex is generated not only by passive muscle stretching, but also in response to conscious stretching of a muscle. The pendulum test is a test to estimate the sensitivity with which the reflex arc responds to the stimulus of knee flexion (extension of the quadriceps femoris muscle). The knee joint motion in this case is induced unconsciously

Muscle is made up of many extrafusal muscle fibers arranged in parallel. Both ends of each muscle spindle are attached to one of these extrafusal muscle fibers. The muscle spindle is covered with a capsule, as shown in Fig. 4. In the capsule, there exist two types of intrafusal muscle fibers, called nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber. Stretching of the extrafusal muscle fiber affects the nuclear bag intrafusal muscle fiber and nuclear chain intrafusal muscle fiber, and stretch velocity and displacement, respectively, are detected. The detection sensitivities of the stretch velocity and displacement are regulated by efferent commands that are sent from phasic γ-motoneuron and tonic γ-motoneuron present in the spinal cord, respectively. The two kinds of detected information are consolidated into the afferent signal within the muscle spindle and transmitted to the spinal cord through Group Ia afferent fiber. Group II afferent fiber that send only nuclear chain intrafusal muscle fiber information to the spinal cord is also present,

by adding external force with the subject in a resting state for ease of estimation.

afferent nerve efferent nerve

effector (muscle)

contractile force (muscle contraction)

receptor (muscle spindle)

stimulation (muscle stretch)

**2.2.2 Structure of the spindle and its functions**

**2.2 Physiology of the stretch reflex 2.2.1 Principle of the stretch reflex**

are both transmitted as impulses.

Fig. 3. Path of stretch reflex.


**1.3 Needs for cryopreservation**

260 Current Frontiers in Cryobiology

quail *Coturnix japonica*, opossum *Monodelphis domestica* and marmoset *Callithrix jacchus*, etc. For example, sea lampreys are cyclostomes in a basal group of vertebrates. Comparative studies on lamprey and jawed fish, e.g., zebrafish, reveal key elements guiding jaw evolution. Characteristics shared between lamprey and other vertebrates but absent in nonvertebrate chordates include the presence of neural crest cells and a jaw. Comparative studies can direct us to the origins of these features. Therefore, study of these emerging model organisms does offer a unique approach to understand the relatedness of species in the living world. Another example illustrating the importance of new model systems in

studying the evolution of body plan is shown in Figure 1 (Kosik, 2009).

Fig. 1. The identification of miRNAs in different metazoan lineages revealed that the number of microRNAs (in brackets) is generally correlated with the complexity of body plan. Comparative studies involving "non-classical" model organisms further suggested a possible role of new microRNAs in evolutionary innovation. The figure is reproduced from

Kosik (2009) with permission from the publisher.

## **1.3.1 Archives of genetic resources**

Modern evolutionary developmental biology and molecular genetic studies on model organisms largely rely on manipulation of tissues and genomes. The advancement of technologies for genomic modification of these model organisms, in turn, affects the popularity of usage of particular model organisms. Eventually, this leads to a rapid increase in the number of transgenic/mutant strains in each popular species.

For the *Caenorhabditis* Genetic Center, mutants had been deposited by individual research groups and various genome wide mutagenesis projects such as the National BioResource Project for The Nematode and *Caenorhabditis elegans* Gene Knockout Consortium. In the National BioResource Project, random mutagenesis was performed for nematodes with UV in the presence of trimethylpsoralen. Affected genes are identified by screening with a genespecific primer set (Gengyo-Ando & Mitani, 2000). As of April 2010, about 4,400 mutants were available and mutants of some 2800 genes were being screened. Without convenient procedures for cryopreserving these species, maintenance of these strains is a heavy burden to these centers, and in other laboratories using these mutants extensively for their studies. On the other hand, passaging parasitic nematode models in plants and in donor animals, e.g., *Cooperia oncophora* in the cattle host (Borgsteede & Hendriks, 1979), is particularly labor intensive and costly and poses risk of cross contamination.

At Bloomington *Drosophila* Stock Center, more than 30,000 strains of *Drosophila* are currently present. Preparations are in progress to expand the facility to hold up to 70,000 stocks in order to meet the needs of stocking transgenic strains to be generated for a wide range of studies, including those made by tissue specific knocking-out of genes for the modeling of human diseases. In Flybase, 112,278 fly stocks were recorded for 2011 (Flybase FB2011\_07 Release Notes).

In The Jackson Laboratory, over 4,000 mouse strains have been deposited and are available to the public. At the Medical Research Council Harwell and at The European Mouse Mutant Archive, over 1300 and 2200 mouse strains are stocked respectively (Eppig & Strivens, 1999). In various mouse stock centers in Japan, including BioResources Center (Riken) and Trans Genic Inc., about 8,000 mouse strains are stocked. More than 16,000 of the 24,954 protein coding genes in the mouse genome have been modified by the International Knockout Mouse Consortium (IKMC), as conditional knockout alleles in embryonic stem cells. So far, more than 1,000 mutant mice, each containing one of these conditional knockout alleles, are made available to the community. The ultimate goal is to generate different targeted alleles in embryonic stem cells (for targeted mice generation) or in targeted mice, to be available to the research community worldwide (Skarnes et al., 2011). On the other hand, about 1,200 zebrafish lines and about 100 *Xenopus* lines have been archived in the Zebrafish International Resource Center and European *Xenopus* Resource Centers, respectively.

Since keeping live animals is costly in terms of requirements of space, consumables and manpower, strains not being used need to be cryopreserved to reduce the running cost. It is, therefore, a very important technology that keeps various genome-wide knockout consortia affordable to average research laboratories.

Cryopreservation of Embryos from Model Animals and Human 263

Fig. 2. Role of cryopreservation in assisted reproduction technology. Conflict between the time allowed for genetic diagnostic tests and the amount of genetic materials available (represented by the numbers of haploid genomes, N) from biopsies at different embryonic stages exists in a continuous pre-implantation genetic diagnosis program (dashed arrow). The release of the time constraint by a cryopreservation cycle after blastocyst biopsy is

The mammalian zygote (Figure 3D) is formed by fertilization of the oocyte by spermatozoa, normally in the oviduct. With advancement of the embryo culture technology, fertilization can be initiated outside the body (i.e. *in vitro* fertilization). The embryonic development continues up to hatched blastocysts, i.e. maximum of 4 days in mouse and 6 days in human, without compromising the development of the embryos after they are transferred into the recipient's uterus/oviduct. The preimplantation stag eembryo is composed of a single cell or multiple blastomeres surrounded by an outer membrane called the zona pellucida, glycoprotein layer of a thickness of about 6m in mouse and 8m in human. The embryos have an outer diameter of about 0.10 mm in mouse and 0.12 mm in human. The volume enclosed by the mouse zona pellucida is limited to about 200 ρl and the diameter of the

**2. Cryopreservation of mammalian preimplantation embryos**

**2.1 Mammalian pre-implantation embryos at different stages**

denoted by the solid arrow.


**6. References**

268 Some Critical Issues for Injection Molding

Fig. 16. Morphology of 5vol%HDPE/WaxGNP-15 (20:80wt%) sample in the center.

mechanical properties in the resulting nanocomposites.

**5. Acknowledgment**

Various properties of HDPE/GNP nanocomposites made by melt-extrusion and injection molding were explored and analyzed in this book chapter, including mechanical properties, crystallization behaviors, thermal stability, thermal conductivity, and electrical conductivity. Results show some unique features of these injection molded nanocomposites. First of all, HDPE/GNP nanocomposites exhibit anisotropic thermal and electrical conductivity, that is, in-plane thermal and electrical conductivity were found to be much higher than the through-plane conductivity. Higher in-plane thermal and electrical properties of these nanocomposites are on the account of the alignment of GNP platelets along the material flow direction during injection molding, which were verified by their morphology. Secondly, it was found that the morphology of injection molded nanocomposites varies from the edge to the center. GNP platelets exhibit strong preferential alignment at the edge where the shear forces under injection molding are maximum while they are randomly orientated in the center where the shear forces are minimum. Additionally, sever GNP aggregation was detected in the melt-extrusion and injection molded samples, which is due to the insufficient shear force attainable during the processing conditions to shear GNP platelets apart and to achieve a uniform GNP dispersion. Regardless of this disadvantage, the technique of melt-extrusion and injection molding still remains as the major processing method used for manufacturing thermoplastics in industry because of its design flexibility, low cost and labor, short cycle time and minimum scrap loss. In order to improve the dispersion of GNP in HDPE, a wax coating technique was reported in this book chapter. It is concluded that the dispersion of GNP in HDPE was dramatically enhanced due to the steric repulsive forces between wax coated GNP platelets, which leads to the better electrical and

The authors gratefully acknowledgment the support of the Michigan Economic Development Commission, 21st Century Jobs Fund for partial support of this research. And the generous

**4. Conclusions**

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**Author details**

Devarakonda Ramadevi1 \*, Radha Rayi2 , Subhash Chandra Mandal3 , Ganga Rao Battu4 , Babu Gajji5 and Pachaiyappan Jayaram6

1 AU College of Pharmaceutical Sciences, Pharmacognosy and Phytochemistry Division, Andhra University, Visakhapatnam, India

2 Institute of Pharmaceutical Technology, Sri Padmavathi Mahila Visvavidyalayam, Tirupathi, Andhra Pradesh, India

3 Division of Pharmacognosy, Faculty of Engineering and Technology, Department of Pharmaceutical Technology, Kolkata, India

4 Adikavi Nannaya University, Rajamandry, Andhra Pradesh, India

5 CCRAS (Central Council Research in Ayurvedic Sciences), Ministry of Ayush, Uttar Pradesh, India

6 Plant Anatomy Research Centre (PARC), Chennai, Tamil Nadu, India

\*Address all correspondence to<EMAIL_ADDRESS>
© 2022 The Author(s). Licensee IntechOpen. 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.

*Detailed Pharmacognostical Standardization Studies on* Calotrophis Procera *(Aiton) Dryand… DOI: http://dx.doi.org/10.5772/intechopen.104549*


**7. Conclusions**

In this work we used the method of the Lewis-Riesenfeld invariant in order to analyze in which sense the dynamical properties of the Mukhanov-Sasaki equation select possible candidates for initial states in the context of inflation. We started in the classical theory and rederived a time-dependent canonical transformation that relates the system of a time-dependent harmonic oscillator to the one of a time-independent harmonic oscillator, where in our case the explicit time-dependence is determined by the frequency involved in the Mukhanov-Sasaki equation. Using this map, the entire time dependence of the oscillator can be removed leading to a simplification as far as finding solutions for the time-dependent system is concerned. As a first step, this was done for systems with finitely many degrees of freedom using an extended phase space in which time and its corresponding momentum are part of the phase space, following the work in Reference [11]. This has the advantage that the time rescaling involved in this transformation can be naturally embedded in the framework of the extended phase space, whereas in early work such as Reference [13], the corresponding phase factor needs to be introduced with a less clear physical motivation. The ansatz we used employed techniques introduced in Reference [11] and was based on an idea from Reference [12], which was generalized to arbitrary even and finite phase space dimensions. This transformation revealed the relationship between the Lewis-Riesenfeld invariant, the time-dependent and time-independent harmonic oscillator Hamiltonian already implicitly used in Reference [13].

Since at the level of the extended phase space the system of the time-dependent harmonic oscillator is a constrained system, we could choose between Dirac and reduced quantization in order to later extract the physical sector of the quantum theory. Because the time rescaling included in the canonical transformation involves an integral over a time interval, a Dirac quantization might be problematic if an analytic expression for the anti-derivative does not exist. In order to circumvent this problem, we chose reduced phase space quantization for which it was necessary to construct Dirac observables and consider the physical phase space according to the methods introduced in References [18,19]. Fortunately, the Dirac observables satisfy the standard canonical algebra so that representations thereof can be easily found. Their dynamics is generated by the Dirac observable associated with the time-dependent Hamiltonian that consequently becomes the physical Hamiltonian of the system. As a preparation for the quantum theory, we constructed the associated generator of the canonical transformation on the physical phase space, giving rise to a corresponding flow that represents the canonical transformation on the physical degrees of freedom. A crucial ingredient for the construction of the Lewis-Riesenfeld invariant as well as the corresponding canonical transformation that removes the time dependence from the Hamiltonian is a time-dependent auxiliary function *ξ*(*t*) that has to satisfy the Ermakov differential equation. This requirement ensures that the Lewis-Riesenfeld

invariant is a quadratic polynomial in the elementary configuration and momentum variables, that can be interpreted as a Dirac observable in the extended phase space because it commutes with the first class constraint. Given a solution of the Ermakov equation, we can use it to construct the canonical transformation on the finite dimensional physical phase space, whose generator is shown in (23).

For the quantum theory we first restricted our analysis to the case of finitely many degrees of freedom and as a special case considered the one-particle Hilbert space. All results obtained in this context can be easily generalized to more but finite degrees of freedom. On the one-particle Hilbert space, the time-dependent canonical transformation can be implemented as a unitary operator Γˆ *ξ* whose explicit form is given in (27). With the help of Γˆ *ξ* we can remove the explicit time dependence of the Schrödinger equation, analogous to the treatment in Reference [17] and map it to a Schrödinger equation involving a time-independent harmonic oscillator Hamiltonian. In this way we further obtain a time evolution operator *U*ˆ (*t*0, *t*) which can be shown to correspond to the Dyson series of the time-dependent theory, consisting of three individual unitary operators. When having a closer look at the occurring exponentials, there is an obvious explanation of the required additional phase factor in the solutions of the Schrödinger equation in Reference [13], amounting to some function multiplying either the exponentiated time-independent Hamiltonian or the Lewis-Riesenfeld invariant, depending on the relative ordering we chose in *U*ˆ (*t*0, *t*). The immediate effect of the time-rescaling *ξ*(*t*) becomes evident in this exponential, as the relative phase is sensitive to the background spacetime. Each of the operators in *U*ˆ (*t*0, *t*) corresponds to an exponentiated unitary representation of the sl(2, R) Lie algebra, as can be shown by explicitly evaluating the Lie brackets of the generators. For practical computations and later applications, we used a generalized Baker-Campbell-Hausdorff decomposition of unitary representations of non-compact groups shown in Reference [30] to decompose Γˆ *ξ* into normal- or anti-normal ordered contributions, respectively. This gave us the possibility to rewrite the unitary transformation Γˆ *ξ* on the one-particle Hilbert space as an explicitly time-dependent Bogoliubov transformation, where the time dependence enters through the solution *ξ*(*t*) of the Ermakov equation.

This was an important preparation for the generalization to the field theory context we were mainly interested in in this work. The crucial criterion for the existence of a unitary implementation of a Bogoliubov transformation on the Fock space is the Shale-Stinespring condition [31], which essentially denotes that the product of off-diagonal entries of the Bogoliubov map needs to be Hilbert-Schmidt. As our results show a straightforward generalization to Fock space where the time-dependent oscillator is described by the Mukhanov-Sasaki equation and the target system is for each mode a harmonic oscillator with constant frequency does not work because either infrared or infrared and ultraviolet divergences occur, leading to a violation of the Shale-Stinespring condition. Here we considered two common choices used in the existing literature, where the constant frequency is either *ω*(0) **k** = *k* or *ω*(0) **k** = 1 respectively, which corresponds to two slightly different Ermakov equations in our case. Both choices yield an infrared divergence caused by the infrared modes, whereas for the second choice in addition an ultraviolet divergence occurs. If we compare our results obtained with the existing results in the literature, the work in Reference [15] takes as the starting point a charged massive scalar field in a de Sitter space time and hence the Ermakov equation in this case includes an additional friction term and cannot directly be compared to our result. The author of Reference [15] also uses the map to a harmonic oscillator with frequency *ω*(0) **k** = *k* and also obtains no ultraviolet divergences for his slightly different map. However, as far as we can see, a careful analysis of the Shale-Stinespring condition is not presented in Reference [15] and thus we expect that, similar to our case, infrared singularities are present. In Reference [14] the map with constant frequency *ω*(0) **k** = 1 was considered and in agreement with our results, they also obtain an ultraviolet divergence for the operator Γˆ *ξ* . In their work the theory is defined on a torus allowing them to isolate the zero mode and exclude it from their analysis, hence no infrared divergences occur. Thus, we can conclude that the second choice, where the target frequency is chosen to be *ω*(0) **k** = 1, cannot be implemented unitarily on Fock space, whereas for the first choice there might be a chance to find a unitary implementation for the first case

with target frequency *ω*(0) **k** = *k* if we are able to consistently modify the map for the infrared modes such that the infrared divergence are no longer present. One possibility can be to also formulate a model where the spatial slices have the topology of a torus chosen in such a way that experimentally one cannot distinguish between a model whose spatial slices have the topology of a torus and one with non compact spatial slices. In this case we could also exlucde the zero mode and modify the map for this specific mode in a way that the Shale-Stinespring condition is satisfied. The corresponding Bolgoliubov transformation can then be defined for all but the zero mode. Note that this case further allows to identify the background with the zero mode, as it is for example usually done in hybrid loop quantum cosmology, see for instance Reference [39]. However, if we stick to non-compact spatial slices we have to consider a slightly different strategy.

As possible solutions in this direction we discussed the quantum Arnold transformation introduced in Reference [16]. The goal was to apply it to the modes below a certain infrared cutoff, that is for the sphere with "**k**" ≤ "**k**" in Fourier space. We found that the Arnold transformation cannot be understood as a Bogoliubov map, since it renders the creation and annihilation operators in the transformed picture equal up to a global sign. A closer look at the involved terms shows that the reason for this pathological behavior is the absence of a the *q*2 contribution in the Lewis-Riesenfeld invariant. It is precisely this aspect that disrupts the commutator algebra and hence does not qualify as an infrared extension of Γˆ *ξ* . Our proposal for an infrared extension is to use the identity map within the cutoff region, the reasons are twofold. Firstly, the identity map can be trivially regarded as a Bogoliubov transformation that exists on this sector of the Fock space. Secondly, by not altering the form of the Hamiltonian in the infrared regime, the off-diagonal terms remain as in the standard case, which means that they are subdominant for very early times where *kη* 1. Hence, by adopting this strategy we are able to define a unitarily implementable Bogoliubov transformation on the entire Fock space as depicted in Equation (61), that performs a Hamiltonian diagonalization on all modes with norm greater than the infrared cutoff "**k**".

In Section 5 we showed how the solution of the Ermakov equation can be used to construct a solution of the Mukhanov-Sasaki equation and as expected, the time-rescaling plays a pivotal role here. If we rewrite the solution to the Mukhanov-Sasaki equation in a polar representation as shown in (62), the Mukhanov-Sasaki equation requires that the real part in the polar representation needs to be a solution of the Ermakov equation, opening a clear connection between the two formalisms. Following this route further, we can also recover the defining differential equation for adiabatic vacua from the Ermakov equation, meaning that if we have a solution of the Ermakov equation given, from this we can easily construct a non-linear solution of the adiabatic vacua differential equation, where non-linear refers to the fact that it is a full solution without truncating the solution at any adiabatic order. The adiabatic condition usually required in this context carries over to a condition on the solution of the Ermakov equation for each mode. This in turn can be directly related to specific properties of the unitary map corresponding to the time-dependent canonical transformation between the time-dependent and time-indepdendent harmonic oscillator. Hence, there is an interesting interplay between the characteristic properties of the unitary map and the choice of adiabatic vacua. Considering this and the fact that we set our initial condition at the limit of conformal past infinity, the Lewis-Riesenfeld method leads to mode functions that can be interpreted as a non-squeezed adiabatic vacuum of non-linear order, that is without performing any truncation. The property of being non-squeezed reflects our freedom of choice of mapping to a target frequency *ω*(0) **k** = *k* that causes no residual squeezing if we apply the unitary operator to an already time-independent harmonic oscillator. Furthermore, the time rescaling involved in the mode function becomes *e*−*ikη* in the limit of large (negative) conformal times, showing that the mode function obtained here are compatible with the condition used in the Bunch-Davies case.

Finally, in Section 6 we have illustrated how the formalism we used throughout this work can be used in terms of computing eigenstates of the Lewis-Riesenfeld invariant associated to a particular system. In our case, this was a time-dependent harmonic oscillator corresponding to the

Mukhanov-Sasaki equation on a quasi-de Sitter spacetime for a single mode. Together with the construction of these eigenstates via Γˆ *ξ* , we outlined how to find a solution *ξ*(*η*) of the Ermakov equation with this particular time-dependent frequency *ω*(*η*) corresponding to the background geometry of quasi-de Sitter. This was done by using the asymptotic behavior of the Hankel functions (which solve the Mukhanov-Sasaki equation on quasi-de Sitter analytically) and the fact that the Wronskian of two linearly independent solutions of this equation is a constant. Finally, we provided a visualization of the time-dependent squeezing operation Γˆ *ξ* in terms of the probability densities of two time-dependent eigenstates of ˆ*ILR* for different values of the slow-roll parameters, which precisely correspond to the probability densities of solutions of the Schrödinger equation of the associated time-dependent Hamiltonian *H*(*t*). As far as the computation of the power spectrum is concerned, we do not expect new insights from our obtained results because what enters into the computation is the final Fourier mode that we constructed in both cases in such a way that the results agree with the standard result for the Mukhanov-Sasaki mode. Our results however, give new insights on whether there exists a time-independent harmonic oscillator Hamiltonian associated with the Mukhanov-Sasaki Hamiltonian that is unitarily equivalent in the field theory context. In future work we want to analyze applications of this formalism to other than quasi de Sitter spacetimes. This requires in particular to find solutions of the Ermakov equation in this more general case and analyze whether the corresponding transformation can be implemented unitarily. Furthermore, we plan to investigate in future research how the transformation in the classical theory on the extended phase space can be lifted to the field theory context. This might be realizable in the framework of the Gaussian dust model presented in Reference [26] where the dust fields can be used as reference fields for physical temporal and spatial coordinates.

**Author Contributions:** All authors contributed equally to this work.

**Funding:** This research was partly funded by the Heinrich-Böll Foundation.

**Acknowledgments:** M.K. and K.G. would like to thank Hanno Sahlmann for illuminating and productive discussions during the project as well as Beatriz Elizaga Navascués and Thomas Thiemann for fruitful discussions towards the end of this work.

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


**2. Mechanisms of estrogen receptor induced cell proliferation**

ERα and ERβ are transcribed from distinct genes located on separate chromosomes (6 and 14, respectively) (Green et al., 1986; Kuiper et al., 1996). These receptors differ in their tissue distribution, with ERα being highly expressed in the pituitary gland, ovaries (thecal and interstitial cells), uterus, liver, kidneys, adrenals and the mammary glands while ERβ is found mainly in the prostate, bone, ovaries (granulosa cells), lungs and in various parts of the central and peripheral nervous system (Emmen et al., 2005; Kuiper et al., 1997). Nevertheless, ERα and ERβ do overlap in their expression in some tissues (Zilli et al., 2009). More importantly, the two receptors have different roles in breast development. Only ERα appears to be essential for ductal growth although both receptors are present in the breast. ERα-knockout mice show very little growth of mammary ducts, while ERβ-knockout mice develop a normal mammary gland with regular ductal branching (Förster et al., 2002; Lubahn et al., 1993). This suggests that ERβ might be exerting pro-differentiative and antiproliferative functions. In addition, increased ERα/ERβ ratio in breast cancer as compared with benign tumours and normal tissues suggest that ERα is most closely associated with breast cancer pathogenesis, while ERβ can protect against the mitogenic activity of estrogens in pre-malignant lesions (Roger et al., 2001; Shaw et al., 2002). It has even been suggested that the estrogen-induced proliferation of ER+ breast cancer cells can be inhibited by ERβ over-expression (Ström et al., 2004; Williams et al., 2008). Thus ERα remains the main focus of attention in studies on breast cancer. Unless otherwise specified, 'ER' in this review will refer to ERα.

In what is now referred to as the nuclear or genomic action of ER, binding of estrogen induces activation of the receptor by initiating its dissociation from cognate heat shock proteins, and leads to conformational changes, dimerisation and autophosphorylation (Osborne & Schiff, 2005). The activated ER binds to estrogen response elements (EREs) located in the promoter regions upstream of estrogen-regulated genes. Frasor et al., (2003) observed from microarray analysis of gene expression in MCF-7 cells that about 70% of such estrogen-regulated genes were actually down-regulated following treatment with estradiol. Many of these genes are transcriptional repressors, or genes with anti-proliferative or proapoptotic function. On the other hand, there is increased expression of genes inducing cell proliferation and survival. Up-regulation of gene expression is mediated through two domains; activating function-1 (AF-1) and activating function-2 (AF-2). AF-1 is a hormone

Endocrine Resistance and Epithelial Mesenchymal Transition in Breast Cancer 455

pathways by these receptors down-regulates the expression of ER and PR causing reduction in estrogen dependency while activating the transcriptional function of ER, which suggests a contribution of this cross talk to the relative resistance to endocrine therapies in tumours with amplified ERBB2 expression (Bayliss et al., 2007; Brinkman and El-Ashry, 2009;

The two types of ER actions, genomic and non-genomic, are not mutually exclusive and do overlap. For example, ER induces the expression of transcripts for both TGFα and amphiregulin (Normanno et al., 1993; Saeki et al., 1991) which can both bind and activate EGFR resulting in activation of MAPK and AKT signaling which are also activated by direct interaction with ER (Salomon et al., 1995). ER binding to membrane caveolin-1 leads to the activation of specific G proteins resulting in the activation of SRC and in turn of matrix metalloproteinases that cleave transmembrane precursors of the EGFR ligand, heparin binding-EGF (HB-EGF) (Levin, 2003; Razandi et al., 2003). Fig 2 illustrates the major

It should be noted that most tumours are heterogeneously composed and a biphasic response to treatment could reflect the survival and eventual clonal outgrowth of an

Since all endocrine therapies target ER, the expression of the latter is the main predictor of the outcome of such therapies. The *de novo* resistance is clearly caused by the lack of ER expression which can be due to histone deacetylation (Parl, 2003) or associated with aberrant methylation of ER CpG islands that deactivates chromatin (Ottaviano et al., 1994; Weigel & deConinck, 1993 ). Interestingly, ER expression can be restored in ER-ve breast cancer following co-treatment with DNMT1 and HDAC inhibitors (Robertson et

It was initially thought that acquired resistance might be due to missing or non-functional variants of ER. However, only 17–28% of patients with acquired endocrine resistance lack ER expression (Gutierrez et al., 2005; Johnston et al., 1995 ). Furthermore, approximately 20% of tamoxifen-resistant patients will eventually respond to second-line treatment with aromatase inhibitors or fulvestrant (Howell et al., 2005; Osborne et al., 2002). Although a number of exon-deleted receptor isoforms have been described, their frequency is

Furthermore, these mutations have been detected in ER-ve tumours (Herynk & Fuqua 2004). A mutation that results in a hypersensitive receptor that shows enhanced binding of coactivators in the presence of low estrogen levels (a single amino acid substitution changing lysine 303 to arginine) was found in 20 of 59 hyperplastic breast lesions (Fuqua et al., 2000). However, the role and frequency of such mutations in primary breast carcinomas and their

Patients carrying inactive alleles of cytochrome P450 2D6 (CYP2D6) (approximately 8% of Caucasian women) fail to convert tamoxifen to its active metabolite, endoxifen (4-hydroxy-N-desmethyl-tamoxifen), and are consequently less responsive to tamoxifen, which is considered to be a significant factor in resistance to therapy (Hoskins et al, 2009). The baseline levels of endoxifen are elevated in patients carrying the wild-type CYP2D6 and who

relation to endocrine resistance needs to be exploredin a larger number of patients.

Creighton et al., 2010; Lopez-Tarruella and Schiff, 2007).

identified downstream events involving ER activation.

**3. Mechanisms of endocrine resistance**

intrinsically resistant minor sub-population.

**3.1 Alterations in ER expression or function**

al., 2000; Rountree et al., 2000;Yang et al., 2001).

insufficient to account for resistance.

independent domain located at the N-terminus of the receptor with its function regulated by phosphorylation. AF-2 is the site where ligand-binding actually occurs and is therefore hormone dependant. Almost all gene promoters are activated through both AF-1 and AF-2, though some are activated independently by AF-1 or AF-2 (Gronemeyer 1991; Osborne et al., 2001). Subsequent to formation of the ER-ligand complex, binding of co-regulatory molecules such as nuclear-receptor co-activator 1 (NCOA1 or SRC1), NCOA2 (TIF2) and NCOA3 (AIB1, TRAM1, RAC3 or ACTR) (Leo & Chen 2000; McKenna et al., 1999) enhance the transcriptional activity of ER accompanied by increased activity of histoneacetyltransferase (HAT) at the promoter site. Other co-regulatory molecules can also partly suppress the transcriptional activity of ER by recruitment of histone-deacetylase complexes such as nuclear-receptor co-repressor 1 (NCOR1) and NCOR2 that influence ER-induced transcription (Chen & Evans, 1995; Horlein et al., 1995). Several of these groups of molecules have been reported to have prominent roles in cancer. AIB1 (SRC-3) is over-expressed in almost two thirds of all breast cancers and associated with a shorter disease-free survival in patients receiving tamoxifen as adjuvant treatment (Osborne et al., 2003). In untreated patients, high levels of AIB1 were associated with improved outcome, consistent with studies that suggest the possibility of an association between an enhanced agonistic effect of tamoxifen and the high levels of co-activators. However, ER can also co-operate with FOS/JUN and bind with other transcription factors such as AP-1 (activator protein-1) and SP-1 (specificity protein-1) at their specific sites on DNA (Kushner et al., 2000; Ray et al., 1997; Safe 2001) commonly designated as serum response elements (SRE).

In addition to its classical mode of action through a nuclear-located receptor, estrogen has also been reported to interact with membrane associated receptors, leading to a more rapid reaction than would be expected from a transcriptionally mediated response, such as initiation of cAMP production (Rosner et al., 1999; Zivadinovic et al., 2005) and activation of intrinsic kinases present in other plasma membrane receptors such as insulin-like growth factor-1 receptor (IGF-1R), epidermal growth factor receptor (EGFR) and ERBB2 (Bunone et al., 1996; Campbell et al., 2001; Font de Mora & Brown 2000) as well as receptors for fibroblast growth factor (FGF), platelet-derived growth factor (PDGF), vascular endothelial growth factor (VEGF) and hepatocyte growth factor (HGF). It has been suggested that interaction of SERMs including tamoxifen with such membrane associated receptors may be responsible for their agonist behaviour. There is however much controversy over this issue, with other studies discounting the involvement of such postulated receptors as G proteincoupled receptor as targets of estrogen action (Otto et al., 2008). However this may be, any non-genomic interactions of estrogen would depend on the levels of the above-mentioned kinases, and they will likely be modest in ER+ breast cancer cells that express low levels of tyrosine kinase receptors such as EGFR and ERBB2 (Normanno et al., 2005).

Ligand independent activation of ER can occur via the downstream signaling cascades transmitted through membrane receptor tyrosine kinases such as EGFR, ERBB2, and IGF1R In particular. MAPK/ERK, PI3K/AKT, p90RSK and p38 MAPK pathways can specifically activate ER at key positions (serine 118 and 167 and threonine 311) in the AF-1 domain and in other domains (Bunone et al., 1996; Campbell et al., 2001; Joel et al., 1998; Kato et al., 1995). Expression of ligands and receptors such as transforming growth factor-α (TGFα), IGF1 and IGF1R can be increased by estrogen and those can then initiate signalling while expression of other receptors such as EGFR and ERBB2 is decreased by estrogen signaling (Kushner et al., 2000; Massarweh et al., 2008; Umayahara et al., 1994; Vyhlidal et al., 2000; Yarden et al., 2001). In addition, activation of the PI3K/AKT and the p42/44 MAPK pathways by these receptors down-regulates the expression of ER and PR causing reduction in estrogen dependency while activating the transcriptional function of ER, which suggests a contribution of this cross talk to the relative resistance to endocrine therapies in tumours with amplified ERBB2 expression (Bayliss et al., 2007; Brinkman and El-Ashry, 2009; Creighton et al., 2010; Lopez-Tarruella and Schiff, 2007).

The two types of ER actions, genomic and non-genomic, are not mutually exclusive and do overlap. For example, ER induces the expression of transcripts for both TGFα and amphiregulin (Normanno et al., 1993; Saeki et al., 1991) which can both bind and activate EGFR resulting in activation of MAPK and AKT signaling which are also activated by direct interaction with ER (Salomon et al., 1995). ER binding to membrane caveolin-1 leads to the activation of specific G proteins resulting in the activation of SRC and in turn of matrix metalloproteinases that cleave transmembrane precursors of the EGFR ligand, heparin binding-EGF (HB-EGF) (Levin, 2003; Razandi et al., 2003). Fig 2 illustrates the major identified downstream events involving ER activation.


**7.4 Left ventricular functional indexes changes pre and post-surgery (MRI parameters)**

Figure 12 shows typical short-axis and long-axis magnetic resonance images of patient preand post-SVR and how to calculate shape, eccentricity and sphericity index. It is noted that the long-axis decreased more dramatically compared with short-axis dimension, thereby producing a more spherical LV. Figure 13 shows typical 3-dimensional modeling of LV from CMR images using LVtools pre and post SVR.

The intraobserver and interobserver data for EDV, ESV and mass for pre- and post-surgery groups are shown in Table 9. Table 10 summarizes the mean LV functional indexes pre and post-SVR. Following SVR, there was a significant decrease in the dimensions of both the long- and short-axes of the LV. However, the long-axis dimension of the LV decreased more than the short-axis dimension, resulting in a more spherical ventricle post-SVR. There was a significantly reduction in end-diastolic volume index (EDVI), end-systolic volume index (ESVI), LV stroke volume index (SVI), LV mass index, and peak normalized wall stress after

All 40 patients were treated with CABG and SVR (endoventricular circular patch plasty). The age of the patients averaged 69 years (range, 52-84 years). Among them, 19 patients had severe mitral regurgitation and received additional MVS. 28 patients had CHF. The baseline

Variables Value Male : female 36:4 Age (years) 69 ± 9 Body surface area (m2) 1.98 ± 0.18 Coronary artery disease 39 (98%) Hypertension 19 (48%) Diabetes mellitus 13 (33%) Tobacco 23 (58%) Congestive heart failure 28 (70%) Peripheral arterial disease 3 (8%) Stroke 2 (5%) Creatinine (mg/dL) 1.17 ± 0.29 Prior cardiac surgery 19 (48%)

 I-II 26 (65%) III-IV 14 (35%)

Table 8. Patients' characteristics and clinical data (n=40). This table is related to our work in

**7.4 Left ventricular functional indexes changes pre and post-surgery (MRI parameters)**  Figure 12 shows typical short-axis and long-axis magnetic resonance images of patient preand post-SVR and how to calculate shape, eccentricity and sphericity index. It is noted that the long-axis decreased more dramatically compared with short-axis dimension, thereby producing a more spherical LV. Figure 13 shows typical 3-dimensional modeling of LV from

The intraobserver and interobserver data for EDV, ESV and mass for pre- and post-surgery groups are shown in Table 9. Table 10 summarizes the mean LV functional indexes pre and post-SVR. Following SVR, there was a significant decrease in the dimensions of both the long- and short-axes of the LV. However, the long-axis dimension of the LV decreased more than the short-axis dimension, resulting in a more spherical ventricle post-SVR. There was a significantly reduction in end-diastolic volume index (EDVI), end-systolic volume index (ESVI), LV stroke volume index (SVI), LV mass index, and peak normalized wall stress after

21 (52%)

19 (48%)

Surgical ventricular restoration + coronary artery bypass

Surgical ventricular restoration + coronary artery bypass

Values are mean ± SD or numbers of patients (percentages).

**7.3 Clinical results**

patient characteristics are summarized in Table 8.

New York Heart Association class

grafting + mitral valve surgery

CMR images using LVtools pre and post SVR.

Surgery

grafting

Ref [19].

SVR (Table 3). The values of LV EDVI, ESVI, LVEF and the contractility index *dσ\*/dtmax* preand post-SVR are also shown in the scatter plots of Figure 14.

Table 10 provides the sphericity index (SI) values in end-diastole and end-systole and its diastolic-systolic change, as well as the % shortening of the long- and short-axes. During a cardiac cycle, LV shape becomes less spherical in systole (SI smaller) than in diastole (SI closer to '1'). The diastolic-systolic change in SI (SIed-SIes) is significantly augmented by the operation, despite the LV chamber becoming more spherical. The % shortening of long-axis is not significantly altered, but the % shortening of the short-axis is significantly increased by the operation. Despite the seemingly unfavorable spherical LV shape post-SVR, the LV contractile function is significantly improved, as indicated by the increased value of *dσ\*/dtmax*.

The scatter plots of figure 14 graphically illustrate pre- and post-SVR values of ventricular end-diastolic volume, end-systolic volume, LVEF and contractility index *dσ\*/dtmax*. From Tables 9 and 10, we can note a significant reduction in end-diastolic volume (318 ± 63 ml vs. 206 ± 59 ml, p<0.01), end-systolic volume (228 ± 58 ml vs. 133 ± 61 ml, p<0.01), LV mass (204 ± 49 g vs. 187 ± 53 g, p<0.01), and peak normalized wall stress (PNWS) (4.64 ± 0.98 vs. 3.72 ± 0.87, p<0.01). Increased sphericity index SI (0.57 ± 0.094 vs. 0.67 ± 0.13, p<0.01) and increased shape factor (S) (0.44 ± 0.085 vs. 0.54 ± 0.089, p<0.01) during end-systole indicates that the LV became more spherical after SVR.

Table 9. Reproducibility data in patients pre- and post-SVR. This table is related to our work in Ref [19].

The prime effect of SVR may be viewed as: (i) effecting a decrease in myocardial oxygen consumption by reduction of LV peak normalized wall stress, resulting in improved functioning of LV, and (ii) augmentation of value of the contractility index *dσ\*/dtmax* (2.69 ± 0.74 s-1 vs. 3.23 ± 0.73 s-1, p<0.01). This improvement may be attributed to (i) increased maximal flow *dV/dtmax* with reduced LV mass, and (ii) improved regional contraction and contractility of the remote myocardium. The improvement in remote myocardial performance is likely due to reduced myocardial stress, along with effective and complete revascularization. This is because the SVR procedure reduces the volume by more dramatically reducing long-axis dimension compared with the short-axis dimension, and producing a more spherical ventricle.

Based on Table 10, increased LV contractile function *d*σ*\*/dtmax* can be not only associated with increased maximal flow *dV/dtmax*, reduced LV mass, and also increased maximal change rate of shape factor *dS/dtmax* (r=0.414, p<0.001). There was also good correlation between *d*σ*\*/dtmax* and LVEF (r=0.69, p<0.001, pre-SVR; r=0.77, p<0.001, post-SVR) (Figure 15).

Table 10. Patients' data pre- and post-SVR. This table is related to our work in Ref [19].

Cardiac Myocardial Disease States (Such as Myocardial Infarction) Cause Left Ventricular Remodeling with Decreased Contractility and Lead to Heart Failure; Interventions by Coronary … 811

810 Biomedical Science, Engineering and Technology

The prime effect of SVR may be viewed as: (i) effecting a decrease in myocardial oxygen consumption by reduction of LV peak normalized wall stress, resulting in improved functioning of LV, and (ii) augmentation of value of the contractility index *dσ\*/dtmax* (2.69 ± 0.74 s-1 vs. 3.23 ± 0.73 s-1, p<0.01). This improvement may be attributed to (i) increased maximal flow *dV/dtmax* with reduced LV mass, and (ii) improved regional contraction and contractility of the remote myocardium. The improvement in remote myocardial performance is likely due to reduced myocardial stress, along with effective and complete revascularization. This is because the SVR procedure reduces the volume by more dramatically reducing long-axis dimension compared with the short-axis dimension, and

increased maximal flow *dV/dtmax*, reduced LV mass, and also increased maximal change rate of

Variables Pre SVR (n=40) Post SVR (n=40) Cardiac index (L/min/m2) 2.84 ± 0.74 2.59 ± 0.74 Mean arterial pressure (mmHg) 85 ± 14 84 ± 8 Systolic blood pressure (mmHg) 115 ± 20 113 ± 10 Diastolic blood pressure (mmHg) 71 ± 12 70 ± 8 End diastolic volume index (ml/m2) 156 ± 39 110 ± 33\* End systolic volume index (ml/ m2) 117 ± 39 77 ± 31\* Stroke volume index (ml/ m2) 39 ± 9 33 ± 8\* Left ventricular ejection fraction (%) 26 ± 7 31 ± 10\* LV mass index (g/m2) 112 ± 25 101 ± 23\* End-diastolic long axis, BAed(cm) 10.89 ± 1.16 8.31 ± 1.00\* End-diastolic short axis, APed(cm) 7.00 ± 0.80 6.64 ± 0.78\* End-systolic long axis, BAes(cm) 10.37 ± 1.20 7.87 ± 1.05\* End-systolic short axis, APes (cm) 5.86 ± 0.98 5.23 ± 1.06\* End-diastolic sphericity Index, SIed 0.65 ± 0.087 0.81 ± 0.11\* End-systolic sphericity index, SIes 0.57 ± 0.094 0.67 ± 0.13\*

Long axis shortening (%) 4.8 ± 3.6 5.4 ± 4.4 Short axis shortening (%) 16.4 ± 6.8 22 ± 9.7\* *dV/dtmax* (ml/s) 364 ± 83 401 ± 81\* Pressure normalized wall stress 4.30 ± 0.95 3.31 ± 0.75\* Stroke work (mmHg·L) 6.61 ± 1.96 5.46 ± 1.64\*

*\*/dtmax* (s-1) 2.69 ± 0.74 3.23 ± 0.73\*

Table 10. Patients' data pre- and post-SVR. This table is related to our work in Ref [19].

shape factor *dS/dtmax* (r=0.414, p<0.001). There was also good correlation between *d*

LVEF (r=0.69, p<0.001, pre-SVR; r=0.77, p<0.001, post-SVR) (Figure 15).

σ

*\*/dtmax* can be not only associated with

0.077 ± 0.043 0.14 ± 0.059\*

σ

*\*/dtmax* and

producing a more spherical ventricle.

Difference between end-diastolic and end-systolic sphericity index, SIed - SIes

*d*σ

\*p < 0.05.

Values are mean ± SD.

Based on Table 10, increased LV contractile function *d*

(b) Post-SVR ED & ES

Fig. 13. 3-dimensional reconstructions during end-diastole (panels A and C) and end-systole (panels B and D) phases before (panels A and B) and after (panels C and D) SVR using LVtools. It is created from the endocardial and epicardial contours, which were drawn for calculations of ventricular volumes and function from the multiple short-axis cines (Figure 12). This figure is based on our work presented in Ref. 19.

Fig. 14. Changes in end-diastolic volume (EDV), end-systolic volume (ESV), LVEF and contractility index *d*σ*\*/dtmax* after SVR. This figure is adopted from our work in Ref. 19.

Fig. 15. Association between *d*σ*\*/dtmax* and left ventricular (LV) ejection fraction (EF) pre- and post-SVR. (Solid line: *d*σ*\*/dtmax*=9.045×EF+1.091, r=0.69, p<0.001 for pre-SVR; dash line: *d*σ*\*/dtmax*=9.969×EF+1.337, r=0.77, p<0.001 for post-SVR). This figure is adopted from our work in Ref 19.


*2.5. UPLC-MS Analyses*

A UPLC system combined with a Q-Exactive Orbitrap mass spectrometer (Thermo Fisher Scientific, Waltham, MA, USA) equipped with a heated electrospray ionization (HESI) probe was used for lipidomic profiling as previously reported [13]. An XSelect CSH C18 column (100 × 2.1 mm, 2.5 μm) (Waters, Milford, MA, USA) was used for lipid separation. Mobile phase A was 3:2 ACN:H2O (*v*/*v*) and mobile phase B was 9:1 IPA:ACN (*v*/*v*), both of which contained 10 mM ammonium acetate. Previously published elution procedures and mass spectrometer parameters were used [16]. Data acquisition was performed in negative ionization mode with an *m*/*z* range of 200–2000. The resolutions of the full scan and fragment spectra were 70,000 and 17,500, respectively.