**Faisal Sahito 1, Pan Zhiwen 1,\*, Junaid Ahmed 2 and Raheel Ahmed Memon 3**

Received: 25 April 2019; Accepted: 14 May 2019; Published: 17 May 2019

**Abstract:** We propose a scale-invariant deep neural network model based on wavelets for single image super-resolution (SISR). The wavelet approximation images and their corresponding wavelet sub-bands across all predefined scale factors are combined to form a big training data set. Then, mappings are determined between the wavelet sub-band images and their corresponding approximation images. Finally, the gradient clipping process is used to boost the training speed of the algorithm. Furthermore, stationary wavelet transform (SWT) is used instead of a discrete wavelet transform (DWT), due to its up-scaling property. In this way, we can preserve more information about the images. In the proposed model, the high-resolution image is recovered with detailed features, due to redundancy (across the scale) property of wavelets. Experimental results show that the proposed model outperforms state-of-the algorithms in terms of peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM).

**Keywords:** wavelet analysis; deep learning; super-resolution; deep neural architecture; pattern mining; multi-scale analysis

### **1. Introduction**

Single image super-resolution (SISR) is generally posed as an inverse problem in the image processing field. Here, the task is to recover the original high-resolution (HR) image from a single observation of the low-resolution (LR) image. This method is generally used in applications where the HR images are of importance, such as brain image enhancement [1], biometric image enhancement [2], face image enhancement [3], and standard-definition television (SDTV) and high definition television (HDTV) applications [4]. The problem of SISR is considered a highly ill-posed problem, because the number of unknown variables from an HR image is much higher compared to the known ones from an LR image.

In the literature for SISR, a number of algorithms have been proposed for the solution of this problem. They can be categorized as including an interpolation algorithm [5], edge-based algorithm [6], and example-based algorithms [7–9]. The interpolation and edge-based algorithms provide reasonable results. However; their performance severely degrades with the increase in an up-scale factor. Recently, the neural network-based algorithms have captured the eye of researchers for the task of SISR [10–12]. The main reasons can be the huge capacity of the neural network models and end-to-end learning, which helps researchers to get rid of the features used in the previous approaches.

However, the algorithms proposed so far are unable to achieve better performance for higher scale-ups. The proposed algorithm is a wavelet domain-based algorithm inspired by the category of the SISR algorithms in the wavelet domain [13–17]. Most of these algorithms give state-of-the-art results. However, their computational cost is quite high. With the advances in deep-learning algorithms, the task of computational cost is much reduced with acceptable quality.

Authors in [16], proposed a wavelet domain-based deep learning algorithm with three layers, inspired by the super-resolution convolution neural network (SRCNN) [8] and using a discrete wavelet transform (DWT), and achieved good results. However, the authors fail to capture the full potential of deep learning and wavelets. In this paper, we propose a wavelet domain-based algorithm for the task of SISR. We incorporate the merits of neural network-based end-to-end learning and large model capacity [18], along with the properties of the wavelet domain, such as sparsity, redundancy, and directionality [19,20]. We propose the use of stationary wavelet transform (SWT) for the wavelet domain analysis and synthesis, owing to its up-sampling property over the DWT down-sampling. By doing so, we want to preserve more contextual information about the images. Moreover, we propose the use of deep neural network architecture in the wavelet domain.

More specifically, we train our network between the wavelet approximation images and their corresponding wavelet sub-band images for the task of SISR. By experimental analysis, we show that the proposed deep-network architecture in the wavelet domain can improve performance for the task of SISR with a reasonable computational cost. The proposed algorithm is compared with recent and state-of-the-art algorithms in terms of peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) over the publicly available data sets of "Set5", "Set14", "BSD100", and "Urban100" for different scale factors.

The rest of the paper is organized as follow. Section 2 describes the details about related work. Section 3 describes the details about the proposed method. Section 4 gives an experimental discussion about the properties of the proposed model. Section 5 given the discussion about the experiments and comparative analysis, and Section 6 concludes the paper.

### **2. Related Work**

The proposed algorithm falls into the category of wavelet domain-based SISR algorithms. Authors in [13] proposed a dictionary learning-based algorithm in the wavelet domain. The proposed algorithm learns compact dictionaries for the task of SISR. A similar approach utilizing dictionary learning is proposed in [14], utilizing the DWT. Authors in [15] proposed coupled dictionary learning in the wavelet domain, utilizing the properties of the wavelets with the coupled dictionary learning approach. Another algorithm that utilizes the dual-tree complex wavelet transform (DT-CWT), along with the coupled dictionary and mapping learning for the task of SISR, is proposed in [17]. Authors in [16] utilize the convolution neural networks in the wavelet domain using the DWT, and propose an efficient model for the task of SISR.

In the wavelet-based SISR approaches [13–16], the main point to note is that they assume the LR image as the level-1 approximation image of the wavelet decomposition. Here, to recover the HR image, the task is to estimate the wavelet sub-band images representing this approximation image, and finally doing one-level inverse wavelet transform. By doing so, authors induce sparsity and directionality along with compactness in the algorithms, which helps boosts the performance of the algorithms as well as improve their convergence speed.

Dong et al. [8] exploited a fully convolution neural network (CNN). In this method, they proposed a three-layer network where complex non-linear mappings are learned between the HR and LR image patches. Authors in [18] propose deep network architecture for the task of SISR. Instead of using the HR and LR images for training, they utilized the residual images, and to boost the convergence of their algorithm, they utilized adjustable gradient clipping. Authors in [8] further propose the sped-up version of the super-resolution convolution neural network (SRCNN) algorithm, called a fast super-resolution convolution neural network (FSRCNN) [21] algorithm. They achieve this by learning the mappings between the HR and LR images without interpolations, along with shrinking the mappings in the feature learning step. Also, the authors decrease the size of filters and increase the

number of layers. Authors in [22] propose a deep residual learning network with batch normalizations for the task of SISR, called a deep-network convolution neural network (DnCNN) algorithm. Authors in [23] propose an information distillation network (IDN) algorithm for the task of SISR. They propose a compact network that utilizes the mixing of features and compression to infer more information for the SISR problem. Authors in [24] propose a super-resolution with multiple degradations (SRMD) algorithm for the problem of SISR. They propose the deep network model for SR, utilizing the degradation maps achieved using the dimensionality reduction of principle component analysis (PCA) and then stretching. By doing so, they learned a single network model for multiple scale-ups.

There are several applications related to single image super-resolution, pattern recognition, neural networks, etc., which can be applied in our human's daily life as well as in human biology. In [25,26], authors have applied different algorithms of neural networks that focus on magnetic resonance imaging (MRI), while in [27–29], authors have applied different algorithms of neural networks that focus on human motion and character control. Likewise, our proposed work can be applied in different applications: brain image enhancement, face image enhancement, and SDTV and HDTV applications. The proposed model can be effectively extended to other image processing and pattern recognition applications.

### **3. Proposed Method**

We propose a deep neural network model based on wavelets and gradient clipping for SISR. The wavelet domain-based algorithm was chosen because of the unique properties of the wavelets: they exploit multi-scale modeling, and wavelet sub-bands are significantly sparse. Moreover, instead of DWT, we propose the use of SWT. DWT is a down-sampling process and SWT is an up-sampling process, so the size of the wavelet approximation and sub-bands remains the same, while preserving all the essential properties of the wavelets.

The DWT and SWT decompositions are shown in Figure 1. Further, the wavelet domain-based algorithms consider the LR image as the wavelet approximation image of the corresponding HR image. The task is to estimate its detailed coefficients, as done in [30–33].

$$\mathbf{A\_{q}}\ (\mathbf{m}, \mathbf{n}) = \sum\_{\mathbf{l}=\mathbf{j}}^{\mathbf{M}} \sum\_{\mathbf{j}=\mathbf{l}}^{\mathbf{N}} \mathbf{h}\_{\mathbf{l}=1}^{\mathbf{1}} \mathbf{h}\_{\mathbf{j}=1}^{2} \mathbf{A\_{q}}(\mathbf{l}, \mathbf{j}),\tag{1}$$

$$\mathbf{H}\_{\mathbf{q}}\left(\mathbf{m},\mathbf{n}\right) = \sum\_{\mathbf{l}=\mathbf{j}}^{\mathcal{M}} \sum\_{\mathbf{j}=\mathbf{l}}^{\mathcal{N}} \mathbf{h}\_{\mathbf{l}=\mathbf{l}}^{\mathbf{l}} \mathbf{h}\_{\mathbf{j}=\mathbf{l}}^{2} \mathbf{A}\_{\mathbf{q}}(\mathbf{l},\mathbf{j}),\tag{2}$$

$$\mathbf{V\_{q}}\ (\mathbf{m},\mathbf{n}) = \sum\_{\mathbf{l}=\mathbf{j}}^{\mathbf{M}} \sum\_{\mathbf{j}=1}^{\mathbf{N}} \mathbf{g}\_{\mathbf{l}=1}^{\mathbf{l}} \mathbf{h}\_{\mathbf{j}=1}^{2} \mathbf{A\_{q}}(\mathbf{l},\mathbf{j}),\tag{3}$$

$$\mathbf{D}\_{\mathbf{q}}\left(\mathbf{m},\mathbf{n}\right) = \sum\_{\mathbf{l}=\mathbf{j}}^{\mathbf{M}} \sum\_{\mathbf{j}=\mathbf{l}}^{\mathbf{N}} \mathbf{g}\_{\mathbf{l}-1}^{\mathbf{1}} \mathbf{g}\_{\mathbf{j}=\mathbf{l}}^{2} \mathbf{A}\_{\mathbf{q}}(\mathbf{l},\mathbf{j}),\tag{4}$$

where h1 m, h2 n, g1 m, and g2 n are the wavelet analysis filters for the SWT. Aq−1(m, n), Hq−1(m, n), Vq−1(m, n), and Dq−1(m, n) are the wavelet approximation image, horizontal sub-band image, vertical sub-band image, and diagonal sub-band image, respectively. The practical decomposition is shown in Figure 2. In the experimental analysis, we have chosen the

sym29 wavelet filters, following the convention from [13,15,17]. The wavelet synthesis equation can be given as

$$\begin{array}{rcl} \mathbf{A}\_{\mathbf{q}+2}(\mathbf{m},\mathbf{n}) & = & \sum\_{\mathbf{l}=\mathbf{j}}^{\mathbf{M}} \sum\_{\mathbf{h}\_{\mathbf{l}}-\mathbf{m}}^{\mathbf{\tilde{m}}-\mathbf{1}} \mathbf{h}\_{\mathbf{l}-\mathbf{m}}^{\mathbf{\tilde{m}}} \mathbf{A}\_{\mathbf{q}}(\mathbf{l},\mathbf{j}) \mathbf{A}\_{\mathbf{q}+2}(\mathbf{m},\mathbf{n}) \\ & + \sum\_{\mathbf{l}=\mathbf{j}}^{\mathbf{M}} \sum\_{\mathbf{h}\_{\mathbf{l}}-\mathbf{m}}^{\mathbf{\tilde{m}}} \mathbf{h}\_{\mathbf{l}-\mathbf{m}}^{\mathbf{\tilde{m}}} \mathbf{\tilde{m}}\_{\mathbf{q}}(\mathbf{l},\mathbf{j}) \sum\_{\mathbf{l}=\mathbf{j}}^{\mathbf{M}} \sum\_{\mathbf{\tilde{m}}}^{\mathbf{\tilde{m}}} \mathbf{\tilde{g}}\_{\mathbf{l}-\mathbf{m}}^{\mathbf{\tilde{m}}} \mathbf{\tilde{h}}\_{\mathbf{l}-\mathbf{n}}^{\mathbf{\tilde{m}}} \mathbf{\tilde{V}}\_{\mathbf{q}}(\mathbf{l},\mathbf{j}) \\ & + \sum\_{\mathbf{l}=1}^{\mathbf{M}} \sum\_{\mathbf{l}=1}^{\mathbf{\tilde{m}}} \mathbf{\tilde{g}}\_{\mathbf{l}-\mathbf{m}}^{\mathbf{\tilde{m}}} \mathbf{\tilde{h}}\_{\mathbf{l}-\mathbf{n}}^{\mathbf{\tilde{m}}} \mathbf{\tilde{D}}\_{\mathbf{q}}(\mathbf{l},\mathbf{j}). \end{array} \tag{5}$$

**Figure 1.** (**a**) Discrete wavelet transform (DWT) decomposition and (**b**) stationary wavelet transform (SWT) decomposition.

**Figure 2.** Wavelet decomposition. (**a**) Original image; (**b**) from left to right and top to bottom: approximation, horizontal, vertical, and diagonal images.

After getting the desired unknown wavelet coefficients, one-level inverse wavelet transform is required to get the desired HR output. Figure 2 shows the wavelet decomposition at level one of the hibiscus image. It can be seen from the image that a strong dependency is present between the wavelet coefficients at the given level and its sub-bands.

There have been several attempts to handle the problem of dimensionality reduction. In [34], authors propose a local linear embedded (LLE) approach that computes low-dimensional, neighborhood-preserving embeddings of high-dimensional inputs. The LLE approach maps its inputs into a single global coordinate system of lower dimensionality, and its optimizations do not involve local minima. LLE is able to learn the global structure of nonlinear manifolds, such as those generated by images of faces or documents of text. In [35], the authors describe an approach that combines

the classical techniques of dimensionality reduction, such as principal component analysis (PCA) and multidimensional scaling (MDS) features. This approach is capable of discovering the nonlinear degrees of freedom that underlie complex natural observations, such as human handwriting or images of a face under different viewing conditions. In [36], authors have compared PCA, kernel principal component analysis (KPCA), and independent component analysis (ICA) to a support vector machine (SVM) for feature extraction. Furthermore, the authors described that the KPCA method is best among three for feature extraction. In [37], authors have proposed a geometrically motivated algorithm for representing the high-dimensional data, which provides a computational approach to dimensionality reduction compared to previous classical methods like PCA and MDS. The algorithm proposed learns a single network model for multiple scale-ups. However, the proposed algorithm utilizes the wavelet domain decomposition before the training of the network, and the wavelet sub-band images are used as the input the training. As can be seen from Figure 2, which shows the wavelet decomposition of a single image, the wavelet sub-band images are significantly sparse, and represent the directional fine features of the images. Further implying the dimensionality results will result in the loss of such directional fine features.

However, in spite of the sparsity property of the wavelets, the assumption of independence of wavelet coefficients at consecutive levels is somewhat limited for the task of SISR. This assumption fails to take into account the intra-scale dependency of the wavelet coefficients that capture the useful structures from the given images.

We make use of this dependency on the task of SISR. The proposed algorithm is different from the previous neural network- and wavelet domain-based methods in the following aspects.

For the WIDN, the deep-network architecture is inspired by the Simonyan and Zisserman [38]. The network configuration can be found in Figure 3.

**Figure 3.** The wavelet deep network configuration.

In our network model, we utilize D layers. All the layers in our network are the same except the first and the last. In our network, the first layer has a total of 64 filters. The size of each filter is 1 × 3 × 3 × 64. These filters operate at a 3 × 3 spatial size on 64 channels. These channels are also called feature maps. The first layer is used for the LR input image, and the last layer reconstructs the output image. As the last layer is used for the output image reconstruction, it has three filters, each of size 3 × 3 × 3 × 64. Our network is trained between the input LR image and its corresponding wavelet coefficients. Thus, given an input LR image, the network can predict the corresponding wavelet coefficients for HR

image reconstruction. Modeling the image details in the wavelet domain has certain usefulness for the task of SISR [13–15]. The proposed model shows that by using wavelet details, the performance of SISR is highly improved. One of the problems pertaining to the deep convolution networks is that size of the output feature maps get reduced after each layer as the convolution operation is performed.

The problem is maintaining the same output size after each convolution operation is performed. Some authors suggest the use of surrounding pixels can give information about the center pixel [8]. This is quite handy when it comes to the problem of SISR. However, for the boundary of the image this can fail; cropping may be utilized to solve this problem. To alleviate the problem of size reduction and boundary condition, we employed zero paddings before the convolution operation. We find that by doing so, the size of the features remains constant, and the boundary condition problem is also solved. Once the three wavelet sub-bands are predicted, we add back the LR input image and do one-level wavelet reconstruction to get the HR image estimate.

Data preprocessing is a very important step to make features invariant to input scale and reduce dimensionality in the machine learning process (a restricted Boltzmann machine, or RBM), which is likely to be used for preprocess the input data. In [39], the authors note that the RBM is an undirected graphical model with hidden variables and visible variables along with a feature learning approach, which is used to train an RBM model separately for audio and video. After learning the RBM, the posteriors of the hidden variables given the visible variables can be used as a new representation of the data. This model is used for multimodal learning as well as for pre-training the deep networks. In [40], the authors present the sparse feature representation method based on unsupervised feature learning. By using the RBM graphical model, which consists of visible nodes and hidden nodes, the visible nodes represent input vectors, while hidden nodes are feature-learned by training the RBM. This method helps to pre-process the data. In [41], the authors present a method in which a number of motion features computed by a character's hand is considered. The motion features are preprocessed using restricted Boltzmann machines (RBMs). RBM pre-processing performs a transformation of the feature space based on an unsupervised learning step. In our proposed model, we have utilized the data augmentation technique for pre-processing the data, inspired by VDSR [18] and FSRCNN [21] algorithms. However, implementing the RBMs will definitely be considered as a future task of our approach.

### *3.1. Training*

For the training of our model, we require a set of HR images. As we train our model between the wavelet approximation image and its corresponding sub-band coefficient images, we do a one-level wavelet decomposition on the HR images from the training data set. The wavelets have a very unique property of redundancy across the scale.

Given the wavelet approximation image at a certain scale and its coefficients, one can perfectly reconstruct the preceding approximation image. Thus, the wavelet coefficient contains all the information about the preceding approximation image. We utilize this property of the wavelet and learn the mappings between the wavelet approximation image and its corresponding coefficients for the task of SISR. Let X denotes the level1 wavelet LR image and Y denote the detail sub-band images. The task is to learn the relationship between the LR approximation image and its corresponding same-level wavelet sub-band images (horizontal, vertical, and diagonal).

In the algorithm SRCNN [8], one problem is that the network has to preserve the information about input details as the output is obtained, using these learned features alone, and the input image is not utilized and discarded. If the network is deep, having many weight layers, this corresponds to an end-to-end learning problem, which requires a huge memory.

Due to this reason, the problem of the vanishing/exploding gradient [42] arises and needs to be solved. We can solve this problem by wavelet coefficient learning. As we assume the dependency between the wavelet LR approximation image and its corresponding same-level detailed coefficients, we define the loss function as

$$\mathcal{L}(\Theta) = \frac{1}{k} \sum\_{\mathbf{i}=1}^{k} (\sum\_{\mathbf{b}=1}^{\mathbf{\hat{3}}} \|\mathbf{f}(\mathbf{X}\_{\mathbf{i}} \Theta)^{\mathbf{b}} - \mathbf{y}\_{\mathbf{i}}^{\mathbf{b}}\|), \tag{6}$$

where k is the number of training samples, X is the tensor containing the LR approximation images, and Y is the tensor containing the wavelet sub-band images (horizontal, vertical, and diagonal). T represents the network parameters, and b represents the sub-band index. For the training, we use the gradient descent-based algorithm from [43]. This algorithm works on the mini-batch of images and utilizes the back-propagation approach to optimize the objective function. In our model, we set the momentum parameter to be 0.9, with the regularizing penalty on the weight decay as 0.0001. Now, to boost the speed on training, one can use a high learning rate. However, if a high learning rate is utilized, the problem of vanishing/exploding gradients [42] becomes evident. To solve this, we utilize the adjustable gradient clipping.

### Gradient Clipping

Gradient clipping is generally used for training the recurrent neural networks [38]. However, it is seldom used in the CNN training. There are many ways in which gradients can be clipped. One of them can be to clip them in a pre-defined range (−θ, θ). In the process of clipping, the gradient lies in a specific range. If the stochastic gradient descent (SGD) algorithm is used for training, we multiply the gradient with the learning rate for step size adjustment. If we want our network to train much faster, we need a high rate of learning; to achieve this value, the gradient θ must be high.

However, high gradient values will cause the exploding gradients problem. We can avoid this problem by using a smaller learning rate. However, if the learning rate is made smaller, the effective gradient approaches zero, and the training may take a lot of time. For this purpose, we propose to clip the gradients to − θ γ , θ γ , where γ is the learning rate. By doing so, we observe that the convergence of our network becomes faster. It is worth mentioning here that our network converges within 3 h, just like in [44], while the SRCNN [16] takes several days to train. Despite the fact that the deep models proposed nowadays have greater performance capability, if we want to change the scale-up the parameter, the network is trained for that scale again, and hence for each scale, we need a different training model.

Considering the fact that the scale factor is used often and is important, we need to find a way across this problem. To tackle this problem, we propose to train a multi-scale model. By doing so, we can utilize the parameters and features from all scales jointly. To do so, we combine all the approximation images and their corresponding wavelet sub-bands across all predefined scale factors, and form a big data set of training images.

### **4. Properties of the Proposed Model**

Here we discuss the properties of the proposed model. First, we say that the large depth networks can give good performance for the task of SISR. Very deep networks make use of the contextual information of an image, and can model complex functions with many non-linear layers. We experimentally validate our claim. Second, we argue that the proposed network gives a significant boost in performance, with an approximately similar convergence speed to VDSR.

### *4.1. Deep Network*

Convolution neural networks make use of the spatial–local correlation property. They enforce the connecting patterns between the neurons of adjacent layers in the network model. In other words, for the case of hidden units, the output from the layer m − 1 is an input to the layer m in the network model. By doing so, a receptive field is formed that is spatially contagious. In this network model, the corresponding hidden unit in the network only corresponds to the receptive field, and is invariant to the changes outside its receptive field. Due to this fact, the filters learned can efficiently represent the local spatial patterns in the vicinity of the receptive field.

However, if we stack a number of such layers to form a network model, the output ends up being global—i.e., it corresponds to bigger pixel space. The other way around, a filter having large spatial support can be broken into a number of filters with smaller spatial support. Here we use 3 × 3 size filters to learn the wavelet domain mappings. The filter size is kept the same for all corresponding layers. This means that the receptive field for the layer has the 3 × 3 filter size. For the corresponding proceeding layer, this size is increased by a factor of two. The depth of the receptive field in our model has the size of (2D + 1) × (2D + 1). For the task of SISR, if one has more contextual information about the high-frequency components, it can be used to infer and generate a high-quality image. In this paradigm of neural networks, a bigger receptive field can serve the purpose of extracting more contextual information. As the problem of super-resolution is highly ill-posed, using more contextual information is bound to give better results.

Another advantage of using deep networks is that they can model non-linearity very well. In our proposed network architecture, we utilize 19 ReLUs, which allows our network to model highly complex non-linear functions. We experimentally evaluated the performance of deep networks by calculating the network's PSNR as depth values increased from 5 to 20, only counting the weight layers and excluding the non-linearity layers. The results are shown in Figure 4. In most cases, the performance increases as depth increases.

**Figure 4.** Depth performance of the network on dataset Set5: (**a**) at scale 2, (**b**) at scale 3, and (**c**) at scale 4.

There are a number of different techniques in machine learning to solve computational problems. Some of them we discuss here and compare with our proposed WIDN. In [45], authors have proposed a recurrent neural network (acRNN), which synthesizes highly complex human motion variations of arbitrary styles, like dance or martial arts, without asking from the database. In [46], the authors have proposed dilated convolutional neural network for capturing temporal dependencies in the context of driver maneuver anticipation. In [47], authors have proposed CNN for speech recognition within the framework of a hybrid NNHMM model. Hidden Markov models (HMMs) are used in state-of-the-art automatic speech recognition (ASR) to model the sequential structure of speech signals, where each HMM state uses a Gaussian mixture model (GMM) to model a short-time spectral representation of the speech signal. In [48], authors have briefly explained in detail the number of graphical models that can be used to express speech recognition systems. The main idea of the proposed work is the wavelet domain-based deep-network algorithm. In our proposed model, we use the wavelet sub-band images as the input to the network, and learn a single model for multiple degradations. One can try such an implementation with other DNN-based algorithms, but the first one needs to investigate whether the DNN will be compatible with the wavelet sub-band images or itself. One also has to account for the sparsity and directionality of the wavelet sub-band images. We have proposed the DNN model of the

VDSR [18] algorithms, as it utilizes the residual images obtained by subtracting the LR from HR images for the training of the network. The wavelet sub-band images possess quite similar properties as the residual images for the task of SISR. Experimental analysis validated our assumption, and comparative analysis proved the efficacy of the proposed model.

### *4.2. Wavelet Learning*

In this work, we propose a network structure that learns wavelet sub-band images. We now study this modification to the VDSR approach. First, we show that for approximately similar convergence, the network gives better performance. We use a depth of 20(weight layers) and the scale parameter is 2. Performance curves for various learning rates are shown in Figure 5. All use the same learning rate scheduling. It can be seen that the proposed algorithm gives superior performance.

**Figure 5.** Performance comparison with VDSR and bicubic algorithms based on learning rates: (**a**) 0.1, (**b**) 0.01, and (**c**) 0.001.

### **5. Experiments and Results**

Here we give the details about the experiments and results. Data preparation in our case is similar to SRCNN [8], with a minute difference. In our model, the patch size of the input image is made the same as the receptive field of the network. We do not utilize the overlap condition while extracting the patches to form a mini-batch. A single mini-batch in our model has a total of 64 sub-images. Also, the sub-images corresponding to the difference scales can also be combined to form a mini-batch. We implement our model using the publicly available MatConvNet package [44]. For the training data set, we used the 291 images with augmentation (rotations), as done in [21].

For the test data sets, we used the most commonly used data sets of "Set5", "Set14", "Urban100", and "BSD100", as used in previous works [18,21,23,24]. The depth of our network model is 20. The batch size used is 64. The momentum used is 0.9 with the decay rate of 0.0001. The network was trained for 80 epochs, and initially, the learning rate was set to 0.1; after every 20 iterations, we decreased it by a factor of 10. The training of our model normally takes about 3 h using the GPU Titan Z. However, if we use a small training set like that in [49], we can increase the speed of learning. Table 1 shows the average PSNR values of the proposed algorithm with increasing numbers of epochs and on different learning rates. It can be seen from the Table 1 that the proposed algorithm provides good results by employing the deep neural network architecture in the wavelet domain.

**Table 1.** Performance table (peak signal-to-noise ratio, or PSNR) for the proposed and VDSR [18] networks ("Set5" dataset, ×2).

The visual results are shown in Figures 6–11. Figures 6 and 7 show the comparative results for the scale-up parameter of 2. Almost all the algorithms perform better. However, the proposed wavelet domain-based algorithm provides more sharp edges and textures. Figures 8 and 9 show the comparative results from the BSD100 test set images for the scale-up parameter of 3.

**Figure 6.** Visual comparison for a baboon image at the scale-up factor of 2.

**Figure 7.** Visual comparison for the Barbara image at the scale-up factor of 2.

**Figure 8.** Visual comparison for the tiger image at the scale-up factor of 3.

**Figure 9.** Visual comparison for the man image at the scale-up factor of 3.

**Figure 11.** Visual comparison for the Urban73 image at the scale-up factor of 4.

Here the algorithms under comparison fail to provide good results; however, the proposed algorithm provides better results. Figures 10 and 11 are taken from a more challenging image data set of Urban100. Here, the scale-up parameter used is 4. Looking at Figures 10 and 11, the proposed algorithm is able to recover the sharp edges and texture where other algorithms fail.

The quantitative analysis based on PSNR and SSIM is shown in Table 2. The algorithms under comparison include the bicubic technique, SRCNN algorithm [8], SCN algorithm [11], VDSR algorithm [18], FSRCNN algorithm [21], DnCNN algorithm [22], IDN algorithm [23], and SRMD algorithm [24]. In the comparative analysis, the trained models used for these algorithms are provided by the authors. The proposed algorithm gives better results than the algorithms under comparison.

**Table 2.** Comparative results based on PSNR (left) and the structural similarity index measure (SSIM) (right).

### **6. Conclusions**

A scale-invariant, wavelet-integrated deep-network model is proposed for the task of SISR. To improve the training speed of the algorithm, the adjustable gradient clipping is used. Useful properties of the convolution neural networks, such as large model capacity, end-to-end learning, and high performance, are exploited in the wavelet domain for the task of SISR. The up-sampling SWT is proposed instead of the down-sampling DWT, to avoid the data loss. Experimental analysis is carried out to validate the efficacy of the proposed model. Quantitative results based on the PSNR and SSIM indicate that the proposed algorithm performs better in comparison with the recent state-of-the-art algorithm. Visual results also validate the quantitative ones. The proposed algorithm can be extended and modified for other super-resolution applications, such as face and brain image enhancement. Also, the proposed algorithm can be tested with other wavelet transforms, such as dual-tree complex wavelet transforms (DT-CWT).

**Author Contributions:** Conceptualization, F.S.; Data curation, J.A.; Formal analysis, R.A.M.; Funding acquisition, P.Z.; Investigation, P.Z.; Methodology, F.S.; Project administration, P.Z.; Resources, P.Z.; Software, F.S.; Supervision, P.Z.; Validation, J.A.; Visualization, R.A.M.; Writing—original draft, F.S.; Writing—review & editing, J.A.

**Funding:** This work is partially supported by national major project under Grants 2017ZX03001002-004 and 333 Program of Jiangsu under Grants [BRA2017366].

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

### **References**

© 2019 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/).


**7. Study design and methodology**

A mixed-methods longitudinal research methodology with a qualitative focus was undertaken. The research design involved a 2 phased approach to the study- whereby data would be gathered from the same participants on two occasions; Phase 1 of data collection was designed to take place while schools were closed in June 2020 and it was intended that Phase 2 of data collection would be undertaken when schools re-opened. Schools re-opened in September 2020 and the data for phase 2 was collected in December 2020. Both phases of data collection involved a semi-structured interview, whereby participants could reflect on their experiences of education and schooling since schools were closed on March 12th 2020. The impact of this experience on personal well-being was the key focus of the interview. In the interview in phase 2 the focus again was on participant well-being, involving reflection on personal well-being since return to school. Prior to completion of the interviews in both phases of data collection, participants were asked to complete two short questionnaires; The Emotion Regulation Questionnaire (ERQ ) [28] and the Copenhagen Burnout Inventory adapted for teachers (CBI) [32]. These measures were intended to assess the impact of the pandemic on the teachers' and principals' perceptions of burnout and emotional regulation. Details of phase 1 and 2 of data collection are summarised in **Figure 1** below.


Contents

Preface

Forests absorb carbon from the atmosphere and store it in the tissues of the plants. Because forest soils typically have a lot of soil organic matter, they are one of the most important carbon sinks. However, in our rush to develop and produce more food, we have reduced the amount of forest cover. Reduced forest cover has resulted in increased global warming and climate change, both of which are impacting crop production and human life. Cyclones, polluted air, receding glaciers, and erratic rainfall are all common occurrences. Agricultural production is necessary, but it must be done in harmony with the environment. This is possible if we can use agroforestry to mimic the forest on farmlands. Agroforestry is the production of food, fodder, timber, fiber, and other products in a cost-effective and environmentally sustainable manner. These systems are also appropriate for small landholders who are primarily cultivators. This book was designed to share success stories and agroforestry techniques for small landholders for climate change resiliency and mitigation. This book is divided into six chapters, each of which discusses climate change and agroforestry from the perspective of various authors from around the

The first chapter discusses *Dusung*, a humid tropic traditional agroforestry practiced in Indonesia. The researchers estimated the traditional agroforestry system's sustainability index and divided it into four categories/sustainability indices. Traditional agroforestry is used for economic, ecological, and socio-cultural purposes as well as for greenhouse gas mitigation and adaptation through carbon sequestration. These sustainability indices can assist in the development of agroforests. The development

The second chapter discusses traditional agroforestry systems and their contribution to biomass and carbon stock at various altitudes. The research was conducted at altitudes ranging from 286 to 2800 meters above mean sea level. Agrisilviculture, agrihorticulture, and agri-horti-silviculture are three common agroforestry systems that have been studied. The chapter authors quantify the biomass and carbon stock of each component and system. They also summarize the best agroforestry system

and trees for biomass production and carbon stock based on their research.

nature-based intervention against climate change.

livestock farmers.

The role of Zimbabwe's small landholder's agroforests is the subject of the third chapter. The chapter discusses the depletion of forest resources because of deforestation in Zimbabwe, as well as its impact on the climate. The chapter promotes the use of a landscape approach to climate change adaptation. According to the author, agroforestry is a compelling option available to small landholders in Zimbabwe as a

The fourth chapter looks at potential climate-smart farming practices that could help farmers adapt to local climate change and variability in South Africa's Limpopo Province. The chapter also discusses field studies on Moringa oleifera and Vachellia karroo conducted in the province, as well as their potential as a feed source for

of agroforests with low sustainability index values can be prioritized.

world.


Meet the editors

Dr. Serban C. Moldoveanu is a senior principal scientist at R. J. Reynolds Tobacco Company. His research activity is focused on various aspects of chromatography including GC/MS, HPLC, LC/MS/MS, and pyrolysis, with applications mainly to natural products. He is the author of more than 150 original papers, 12 books, and several book chapters. He is a member of the editorial board of *Analytical Methods in Chemistry.*

Professor Victor David was the head of the Analytical Chemistry Department, University of Bucharest, Romania, between 2007 and 2019, and is now an Emeritus Professor. His main field of research is separation science. He is the author of 5 books, 11 chapters in books and encyclopedias, and 150 scientific articles in ISI journals. He was an associate editor of the Journal of Liquid Chromatography & Related Technologies and

is a member of the editorial board of *Biomedical Chromatography, Molecules, Journal of Chemistry, Journal of Essential Oil-Bearing Plants, Revue Roumaine de Chimie*, and *Current Chromatography.*

## Contents


**Quantum-Mechanical Assessment of the Energetics of Silver Decahedron Nanoparticles**

#### **Svatava Polsterová 1, Martin Friák 2,3,\*, Monika Všianská 1,2 and Mojmír Šob 1,3,4**

Received: 14 February 2020; Accepted: 7 April 2020; Published: 16 April 2020

**Abstract:** We present a quantum-mechanical study of silver decahedral nanoclusters and nanoparticles containing from 1 to 181 atoms in their static atomic configurations corresponding to the minimum of the *ab initio* computed total energies. Our thermodynamic analysis compares T = 0 K excess energies (without any excitations) obtained from a phenomenological approach, which mostly uses bulk-related properties, with excess energies from *ab initio* calculations of actual nanoclusters/nanoparticles. The phenomenological thermodynamic modeling employs (i) the bulk reference energy, (ii) surface energies obtained for infinite planar (bulk-related) surfaces and (iii) the bulk atomic volume. We show that it can predict the excess energy (per atom) of nanoclusters/nanoparticles containing as few as 7 atoms with the error lower than 3%. The only information related to the nanoclusters/nanoparticles of interest, which enters the phenomenological modeling, is the number of atoms in the nanocluster/nanoparticle, the shape and the crystallographic orientation(s) of facets. The agreement between both approaches is conditioned by computing the bulk-related properties with the same computational parameters as in the case of the nanoclusters/nanoparticles but, importantly, the phenomenological approach is much less computationally demanding. Our work thus indicates that it is possible to substantially reduce computational demands when computing excess energies of nanoclusters and nanoparticles by *ab initio* methods.

**Keywords:** nanoparticles; thermodynamics; silver; decahedron; excess energy; *ab initio* calculations

#### **1. Introduction**

The silver nanoparticles are widely used as antiviral agents [1,2], sensors [3,4], catalysts [5], as nanoparticle solders [6,7] as well as in numerous others application. Nanoclusters, as extreme cases of nanoparticles, have a yet greater surface/volume ratio and different geometries and electronic structures when compared with their bulk counterparts. Theoretical computations constitute a very advantageous tool when studying nanoclusters as they can accurately determine many of their characteristics, such as their surface type, strain energies [8,9], phase diagrams [10] or information on their catalytic activity. Many studies reported that modifications of the surface energy can change the shape of a (nano-)particle and/or its melting temperature [11–13]. The surface energy of a nanoparticle is often considered as the most important factor in catalysis, crystal growth, sintering and other surface-related processes. The most stable surface geometry for nanoparticles of pure fcc transition metals is the {111} facet [14] but the situation can differ in multi-component cases [15].

Relative to the bulk, the {111} facet exhibits the highest density of atoms and the highest coordination number of surface atoms. The most stable structures of fcc nanoclusters include the icosahedron, cuboctahedron and decahedron [8]. Another energy contribution is that related to strain. The strain energy of the particle can be affected by many factors. As the ratio of surface to volume decreases, the effect of surface stress is more significant and leads to the compression of particles [8].

Our study is focused on decahedral particles which have very interesting plasmonic and optical properties [16] as well as catalytic possibilities due to high strain energy [9]. The decahedron and icosahedron are inherently strained due to twinning and unfilled volume [17]. In particular, the decahedral nanoclusters are balancing the surface stability of five tetrahedrons (see Figure 1), which exhibit the {111} facets, against the strain energy related to an internal unfilled gap of 7.35◦ and distortion induced by their twinned internal structure [9]. The actual shape of the studied nanoparticles can deviate from a prediction by the Wulff construction due to the influence of the internal strain and strain-associated strain energy (in particular in the case of intermediate states [18,19]).

**Figure 1.** Schematic visualizations of (**a**) five tetrahedrons forming an imperfect decahedron with a gap of 7.35◦ and (**b**) one of the studied decahedral nanoclusters/nanoparticles (see below) without the gap. A characteristic length *a* defined here is used below when defining the shape factor.

#### **2. Methods**

The energies of studied decahedral nanoclusters and nanoparticles were calculated in two different ways which are both connected with quantum-mechanical Density Functional Theory (DFT) [20,21] calculations. The first method is a phenomenological thermodynamic modeling based on the CALPHAD method when the energy of nanoclusters and nanoparticles is approximated by a sum of relevant energy contributions corresponding (i) to a defect-free bulk material and (ii) surface energies and stresses (related to surfaces of a bulk, not nanoparticles) [22–26]. It is customary now that some or all energy contributions used in CALPHAD approach are computed using quantum-mechanical methods. Let us note that the idea of connecting the CALPHAD method and *ab initio* calculations is not trivial. It was presented first before the end and at the beginning of the new millennium in papers [27–32] and has been used many times since then (see e.g., [33–42]), also in studies of nanoalloys and nanoparticles, as mentioned above.

Our second approach is represented by direct *ab initio* calculation of electronic structure of decahedrons, schematically shown in Figure 2. The quantum-mechanical calculations are very computationally demanding in this case but still feasible for systems of a few hundred of atoms such as the studied decahedral nanoparticles/nanoclusters. Each of the computed nanoclusters/nanoparticles was treated inside a larger computational supercell where it was surrounded by vacuum, but the periodic boundary apply to these supercells. The positions of atoms in the nanoclusters were optimized so as to minimize the total energy which is provided by our *ab initio* software package (see Section 2.2). The total energy includes electronic-structure energy terms such as the Hartree energy, exchange-correlation energy, local ionic pseudopotential energy or kinetic energy as well as Madelung energy of the ions. The total energy is essentially related to T=0K without any entropy contributions and its minimum corresponds to the ground state of each nanocluster/nanoparticle.

**Figure 2.** A schematic visualization of studied decahedron nanoclusters and nanoparticles (for higher number of atoms) with each of them accompanied by the number of atoms.

#### *2.1. Phenomenological Thermodynamic Modeling*

The phenomenological thermodynamic approach based on the CALPHAD method is very often used for calculations of the total energy of particles as well as for the prediction of phase diagrams [22–26,43]. The computations use an approximation when bulk variables are applied in the case of nanoparticles but not all properties of the (nano-)particles are included (for example, a structural disorder is sometimes omitted). The molar total Gibbs energy *G*tot is decomposed into a sum of relevant contributions [24]:

$$\mathbf{G\_{tot}} = \mathbf{G\_{ref}} + \mathbf{G\_{id}} + \mathbf{G\_{E}} + \mathbf{G\_{mag}} + \mathbf{G\_{P}} + \mathbf{G\_{surr}} \tag{1}$$

where *G*ref is the molar reference Gibbs energy, *G*id is the molar energy of ideal mixing of an alloy, *G*E is the molar excess Gibbs energy, *G*mag is the molar contribution related to magnetism (which could be particularly complicated in the case of magnetic nanoparticles, including spin and orbital moment contributions as discussed, e.g., in Ref. [44]), *G*P accounts for the influence of pressure *P* and *G*sur for the molar contribution of surface energy. When adapting the Equation (1) to the studied case of silver nanoclusters/nanoparticles, i.e., an unary non-magnetic metal at the temperature T = 0 K, only the reference Gibbs energy *G*ref and the surface Gibbs energy *G*sur remain:

$$G\_{\rm tot} = G\_{\rm ref} + G\_{\rm sur}.\tag{2}$$

The surface energy contribution is in the case of spherical nanoparticles equal to:

$$G\_{\rm surf} = \frac{A\_{\rm sph}}{n} \cdot \sigma\_{\rm sur} = \frac{A\_{\rm sph}}{n} \cdot \frac{V\_{\rm sph}}{V\_{\rm sph}} \cdot \sigma\_{\rm sur} = 3 \cdot \frac{V\_{\rm m}}{r} \cdot \sigma\_{\rm sur} \tag{3}$$

where *σ*sur is surface energy, *A*sph = 4*πr*2 is the surface area of a spherical nanoparticle with the volume *V*sph = (4/3)*πr*3, *n* is is the number of moles and the *V*m is the molar volume. As the volume of nanoclusters/nanoparticle is ill-defined, we below discuss three different ways of assigning the (molar) volume to the studied nanoclusters/nanoparticles. The radius *r* is then set equal to the radius of a sphere, which has the volume equal to the product of the number of particles in the nanocluster/nanoparticle and the (specifically assigned) volume (per atom). The surface area (to be multiplied by *σ*sur) is then put equal to the surface of a sphere with the radius equal to the above discussed radius *r*. The fact, that the shape of studied nanoclusters/nanoparticle is non-spherical, decahedral, is taken into account by a shape factor *C* is introduced [25,43,45] into the Equation (3):

$$\mathbf{G}\_{\rm sur} = \mathbf{3} \cdot \mathbf{C} \cdot \frac{V\_{\rm m}}{r} \cdot \sigma\_{\rm s} \quad \mathbf{C} = A\_{\rm shape} / A\_{\rm sph} \tag{4}$$

where the shape factor *C* is defined as the ratio of the surface area of the calculated nanoparticle *A*shape to the surface area of a spherical particle with the same volume. For the decahedron we use

$$A\_{\rm dec} = a^2 \cdot 5 \cdot \sqrt{3} \cdot \sin 36^\circ \cdot \sqrt{1 - 0.75 \cdot (\sin 36^\circ)^2} \quad \text{and} \quad V\_{\rm dec} = a^3 \cdot (5/4) \cdot \sin 36^\circ \cdot \cos 36^\circ \tag{5}$$

with the length parameter *a* defined in Figure 1 (also equal to the height of the decahedron, a pentagonal dipyramid). The values for a few commonly occurring shapes of (nano-)particles are listed in Table 1. Importantly, following the procedure described above we do not need a Tolman length to define the surface of particle [46] as it is defined by molar volume and radius of a spherical particle.

**Table 1.** Shape factors for different shapes of (nano-)particles as collected from selected literature sources. By a liquid spherical shape we mean an ideal sphere (without any atomic structure manifesting itself) while solid spherical shape represents a spherical nanoparticle with its atomic structure which is making its surface not ideally spherical.

Analogous to the Equations (2) and (4) is the total Gibbs energy of cluster, *g*tot equal to:

$$g\_{\rm tot} = \frac{G\_{\rm tot}}{N\_{\rm A}} \cdot N = g\_{\rm ref} + g\_{\rm sur} \text{ where } \; g\_{\rm ref} = N \cdot g\_{\rm Ag}^{\phi} \tag{6}$$

where *N* is the number of atoms in a studied nanocluster/nanoparticle, *N*A is the Avogadro constant and the *g φ* Ag is the atomic Gibbs energy of pure constituent Ag. As far as the Gibbs energy g*φ* Ag is concerned, we use the Gibbs energy of the bulk fcc Ag per atom *E*bulk, calculated by DFT.

The equation of surface contribution for one nanocluster/nanoparticle is then changed to:

$$\mathcal{g}\_{\rm sur} = N \cdot \mathfrak{Z} \cdot \mathbb{C} \cdot \frac{V\_{\rm at}}{r} \cdot \sigma\_{\rm sur} = N \cdot \mathfrak{Z} \cdot \mathbb{C} \cdot \frac{V\_{\rm m}}{r \cdot N\_{\rm A}} \cdot \sigma\_{\rm sur}.\tag{7}$$

where *V*at corresponds to the volume of one atom. One of the consequences of a high surface Gibbs energy is a surface strain [17]. It is caused by the minimization of the surface energy of the studied (nano-)particles and it leads to the reduction of the mean molar volume of the nanoparticle. As an extreme case, a particle without any surface energy exhibits zero surface strain and its volume is equal to that of the bulk.

Our phenomenological approach of calculating thermodynamic properties of silver nanoclusters/nanoparticles consisting of *N* atoms at temperature T = 0 K is based on the following procedure. First, the Gibbs energy of the studied nanoparticle has the two contributions mentioned in Equation (6), i.e., *g*tot = *g*ref + *g*sur. Importantly, when evaluating the reference energy *g*ref = *N* · *g φ* Ag of the Ag nanoparticles we put the *g φ* Ag equal to the reference Gibbs energy of the bulk *E*bulk (per atom), here fcc Ag, which we get from *ab initio* calculations.

All the changes, which are related to the fact, that we assess nanoparticles (and not the bulk), are included in the molar volume of the studied nanoparticles *V*m and the surface stress *P*sur, i.e., in the surface energy term *G*sur:

$$\mathbf{G\_{sur}} = P\_{\rm sur} \cdot V\_{\rm m} \quad \text{where} \quad P\_{\rm sur} = \frac{\mathbf{G\_{sur}}}{V\_{\rm m}} = \frac{\mathbf{3} \cdot \mathbf{C} \cdot \sigma\_{\rm sur}}{r} . \tag{8}$$

Two further approximations are made. First, the surface stress *P*sur is evaluated for each relevant surface orientation, i.e., those existing on the facets of the studied nanoparticles, from the DFT calculations of infinite planar surfaces of the bulk system—see its schematic visualization in Figure 3. It means that we use a bulk-related property, the surface stress, instead of the surface stress (or surface energy) which would be related to any actual nanoparticles (there the surfaces contain edges and vertices where individual facets meet). In our particular case of decahedral nanoparticles, which have only {111} facets, our DFT calculations were performed for the (111) surface of fcc Ag.

**Figure 3.** A schematic visualization of a computational cell, so-called slab, used for calculations of surface energy and surface stress in fcc-structure Ag (the visualization shows a 5 × 5 multiple of the studied primitive cell within the surface plane, a side view on the left, and a top view on the right). The surface is formed by the (111) crystallographic plane (see it in the middle also visualized inside a bulk fcc structure elementary cell).

The second important approximative step is related to the evaluation of the molar volume of the studied nanocluster/nanoparticle. In order to assign it to a particular decahedral nanoparticle, we put the surface stress *P*sur equal to a fictitious hydrostatic pressure *p* which would be acting on every atom of the studied nanoclusters/nanoparticles. We thus do not take into account any elastic strains and stresses which are inside of decahedral nanoparticles due to the unfilled gap of 7.35◦. Instead, we apply the surface stress to all particles as if it were a hydrostatic pressure *p* acting upon all atoms in the nanoparticle. For calculations of the molar volume of the particle (from the known molar volume of a bulk system) we apply the following three methods.

First, we use the Murnaghan equation [50,51] applied to the bulk:

$$p(V\_{\rm m}) = \frac{B\_0}{B\_0'} \cdot \left[ \left(\frac{V\_{\rm m,0}}{V\_{\rm m}}\right)^{B\_0'} - 1 \right] \quad \text{and we put} \quad p(V\_{\rm m}) = P\_{\rm sur}.\tag{9}$$

The Murnaghan equation of state above contains the following (bulk-related) quatities: *B*0 is the bulk modulus, *B* 0 is its pressure derivative and *V*m,0 is the molar volume of the bulk material. The values of *B*0, *B* 0 and *V*m,0 are obtained from energy-volume curve of *ab initio* calculation of the bulk fcc Ag. The equation allows to assign the molar volume *V*m to the studied nanocluster/nanoparticle.

The second way of assigning a volume to the studied nanoclusters/nanoparticles is based on the definition of the bulk modulus *B*0 [52] where we use finite differences instead of derivatives:

$$B\_0 = -V\_{\rm m} \cdot \frac{dp}{dV\_{\rm m}} \approx -V\_{\rm m} \cdot \frac{\Delta p}{\Delta V\_{\rm m}} = -V \text{m} \cdot \frac{0 - p(V\_{\rm m})}{V\_{\rm m,0} - V\_{\rm m}}, \text{ and where we put} \quad p(V\_{\rm m}) = P\_{\rm sur} \tag{10}$$

and there is one state of the bulk for which *p*(*V*m) is equal to 0, Vm is the value of bulk molar volume and the second state is such that there is a non-zero pressure *p*(*V*m) applied on the particle. Instead of extrapolating from *V*m,0 using *B* from the Murnaghan equation as in Equation (9), we put *p*(*V*m) equal to *P*sur and determine the volume directly from Equation (10). Again, the bulk-related quantities, such as the bulk modulus *B*0 and the molar volume of the bulk material *V*m,0 are determined from quantum-mechanical calculations of bulk fcc Ag.

Third, in the following section we also consider the case when the volume of the atoms in the studies nanoclusters/nanoparticles is simply set to be equal to the volume of atoms in the bulk fcc Ag, i.e., the molar volume is not affected by the fact that we study a nanocluster/nanoparticle system.

The above described series of approximative steps, which we apply as a part of our phenomenological thermodynamic approach to nanoparticles, is tested by direct quantum-mechanical calculations of energies of static (T = 0 K) atomic configurations of a series of nanoclusters/nanoparticles visualized in Figure 2. The energy of these nanoclusters/nanoparticles is computed directly and compared to the results of the phenomenological thermodynamic approach described above (including three different ways of assigning the molar volume to the studied nanoparticle).

#### *2.2. Parameters of Our DFT Calculations*

All our DFT calculations were performed using the Vienna Ab-initio Simulation Package (VASP) [53,54]. The exchange and correlation energy was treated in the generalized gradient approximation (GGA) as parametrized by Perdew, Burke and Ernzerhof (PBE-96) [55]. The used Ag pseudopotential contains 1 *s* electron and 10 *d* electrons. We prefer the GGA-PBE exchange-correlation approximation over the the local density approximation (LDA) [21] because the former gives the value of the bulk modulus of silver closer to the experimental value (see the discussion below). Consequently, we assumed a better description of strained/stressed states. The cut-off plane-wave energy was equal to 550 eV and the employed spacing between k-points amounted to 0.11 Å−1. When minimizing the total energy, the forces acting upon atoms of the surface slabs were reduced under 0.01 meV/Å while those acting upon atoms of the nanoparticles were minimized under 0.1 meV/Å.

The surface energies and stresses were determined from DFT calculations employing computational supercells with so-called slab geometry, see an example for the (111) surface [56] in Figure 3. The surface energy of an infinite slab *σ*hkl (where {hkl} are mainly {111}, {100} and {110} for fcc-structure faces) was calculated as a difference of the relaxed surface energy *E*sur(*N*) and the relaxed bulk *E*bulk(*N*) per surface area *S*:

$$
\sigma\_{\rm hkl} = E\_{\rm sur}(N) - E\_{\rm bulk}(N) / 2 \cdot S\_{\prime} \tag{11}
$$

with both energies being related to systems with the same number of atoms *N*.

Due to various shape of nanoparticles, the mean surface energy of nanoclusters/nanoparticles is computed according to the approach suggested by Guisbiers and Abudukelimu in [57]

$$
\sigma\_{\rm sur} = \left(\sum \mathbf{A}\_{\rm hkl} \cdot \sigma\_{\rm hkl}\right) / \sum \mathbf{A}\_{\rm hkl} \tag{12}
$$

where Ahkl are areas of facets with different {hkl} crystallographic orientation on the surface of a nanocluster/nanoparticle. In the following, we put the energy *σ*{111} equal to the surface energy *σ*sur of the whole decahedron particle as its surface contains only the {111} facets.

Next to the energy we also make an attempt to determine the molar volume of the studied nanoparticles from our quantum-mechanical calculations by the following steps. We first compute the mean radius as a half of the average inter-atomic distance between all the atoms and all their nearest neighbors—see Figure 4. Second, we put this mean radius equal to a radius of equally sized touching spheres in a fcc bulk crystal (as when computing the atomic packing factor, for fcc equal to 0.74). Third, we assign the atomic volume in such a fcc bulk crystal to each atom in our nanocluster.

**Figure 4.** Computed bond lengths between pairs of nearest neighbors in the studied nanoclusters/nanoparticles. Blue symbols represent all inter-atomic distances in calculated nanoparticles, orange color marks the mean inter-atomic distances and the black dashed line shows the inter-atomic distance of bulk fcc structure of Ag.

The figure neatly shows that the studied nanoclusters/nanoparticles are highly strained. The majority of bond lengths (interatomic distances) is well below the bulk value of fcc Ag (see the horizontal black dashed line in Figure 4). In particular, this is true for the two nanoclusters with the number of atoms equal to 7 and 23. The mean (average) interatomic distance (see the orange data points) clearly demonstrates this reduction of the interatomic distances. It is worth noting that internal elastic strains (and the corresponding energies) are not included in our approximative phenomenological thermodynamic description of nanoclusters/nanoparticles (as described in the subsection above) but all particles are subject to a fictitious hydrostatic pressure (which we put equal to the surface stress value).

#### **3. Results and Discussion**

The molar volumes determined from direct quantum-mechanical calculations using the procedure of averaging the interatomic distances (see Figure 4) are compared with those determined from the Murhaghan equation and the definition of the bulk modulus within our thermormodynamic approach in Figure 5a. The volumes obtained from the direct calculations of the electronic structure of nanoclusters/nanoparticles are represented by the DFT black data points, and the molar volumes from our phenomenological thermodynamic approach are continuous blue and red lines for the volumes based on the Murnaghan equation and the definition of the bulk modulus, respectively. It is evident that the volumes from direct DFT calculations of nanoclusters/nanoparticles agree very well with those based on the definition of the bulk modulus (Equation (10)).

**Figure 5.** The dependencies of (**a**) the molar volume and (**b**) the ratio of coordination numbers of nanocluster surface atoms with respect to that of {111} surface of the bulk (which is equal to 9) as functions of the number of atoms in the studied nanoclusters/nanoparticles. The green dashed lines in parts (**a**,**b**) are the values corresponding to the bulk (or its {111} surface), blue and red lines represent volumes assigned to nanoparticles using Murnaghan equation and the definition of the bulk modulus, respectively. The full black circles represent results of direct DFT calculations of nanoparticles. The part (**c**) shows absolute (and part (**d**) also relative) differences of excess energies per atom determined by our phenomenological thermodynamic approach w.r.t. to the excess energies of the direct DFT calculations of nanoparticles when the volume of nanoparticles in the phenomenological thermodynamic modeling is determined from the Murnaghan equation (blue curves and blue data points in part (**d**)), from the definition of the bulk modulus (red curves and red data points) and from determining the volume of the nanoparticles from the volume of bulk fcc Ag (green lines and green data points). Also added is the experimental molar volume (the horizontal brown dashed line in (**a**)).

In order to determine the molar volumes from the Murnaghan equation of state and the definition of the bulk modulus (shown in Figure 5a) we used the hydrostatic pressure equal to the surface stress *p* = *P*sur which was found from the calculations of the surface energy of Ag for T = 0 K for the {111} and {100} terminations of the bulk fcc Ag. The obtained value of the surface energy for the {111} facet is equal to 0.80 Jm−2 and for the {100} surface orientation to 1.14 Jm−2. Our values agree quite well with the experimental mean surface energy of 1.1–1.3 Jm−2 (see Table 2), reported for much higher temperature of 1073 K in Ref. [58], or with the theoretical values obtained using the LDA approximation in Ref. [59].

**Table 2.** Our computed surface energies for Ag surfaces with different crystallographic orientations in comparison with available experimental data [58].

Our calculations also reproduce fairly well the lattice constant and the bulk modulus of the bulk fcc Ag. Our theoretical lattice constant of fcc Ag is equal to 4.1555 Å in an acceptable agreement with the experimental value of 4.0853 Å. Our computed bulk modulus of 90 GPa lies between the experimental values of 84 GPa and 118 GPa [60].

In a similar way we analyze also the ratio of the coordination number of surface atoms of the studied nanoparticles, the coordination number of an fcc bulk lattice is 12. The coordination number of the surface atoms is lower. For an infinite surface of a bulk fcc (see the schematics in Figure 3) it is equal to 9 and so the ratio of the coordination numbers of surface atoms of the bulk with respect to the coordination number of atoms in the fcc bulk is 0.75 (see this value as the horizontal green dashed line Figure 5b). The coordination numbers of surface atoms at the {111} facets of the studied nanoclusters/nanoparticles apparently converge to the coordination number of surface atoms at the {111} surface of the bulk only very slowly as a function of the number of atoms in the nanoparticle.

Using our computational approaches it is now possible to evaluate an energy contribution related to the fact that the studied systems are nanoclusters/nanoparticles (with respect to the energy of the bulk). As this energy has a character of an excess energy *E*ex (the total energy of nanoclusters/nanoparticles without the cohesion energy of the bulk):

$$E\_{\rm ex} = \frac{E\_{\rm tot} - N \cdot E\_{\rm bulk}}{N} \tag{13}$$

we show it (per atom) in Figure 5c as a function of the number of atoms in the studied nanoclusters/nanoparticles. The excess energy per atom decreases with increasing radius of nanoparticles. Let us note that this excess energy is different from the excess Gibbs energy *G*E employed in Equation 1, similarly as in other papers dealing with nanoparticles, e.g., Ref. [61].

While Figure 5c clearly shows that the absolute values of the excess energies (per atom) as determined using (i) our phenomenological thermodynamic approach based on bulk-related properties (obtained by DFT calculations) very well match (ii) those from direct DFT calculations of actual nanoclusters/nanoparticles *E*DFT ex , it is important to evaluate the differences more precisely. Therefore, we analyze the excess energy differences as relative values:

$$D = \frac{E\_{\rm ex} - E\_{\rm ex}^{\rm DFT}}{E\_{\rm ex}^{\rm DFT}} \cdot 100\%. \tag{14}$$

The results are presented in Figure 5d again for differently defined volumes of nanoclusters/nanoparticles. Importantly, the Figure 5d clearly demonstrates that when using the phenomenological thermodynamic approach based on (i) the bulk reference energy, (ii) the bulk surface stress (slab calculations in Figure 3) and (iii) the bulk atomic volume, then the relative differences with respect to the energies obtained from direct DFT calculations of nanoclusters are only a few %, see the green data points in Figure 5d. The only exception from this nice agreement is the limiting case of a single silver atom (the relative error of the excess energy is over −22%). The actual values of the relative differences of the excess energy are summarized in Table 3.

The agreement can be interpreted so that that the surface-related energy of the phenomenological thermodynamic model of static configuration of atoms in a nanocluster/nanoparticle at T=0K (blue, red and green data points in Figure 5d) covers a vast majority of the excess energy which is determined by the DFT calculations of the actual nanoclusters (black horizontal dashed line in Figure 5d). We thus demonstrate that, in the case of the total energy of static atomic configurations of nanoparticles, the top-down phenomenological approach can be extended from the bulk down to nanoclusters containing essentially only a few atoms. The only necessary information related to the nanoparticle of interest is then (i) the number of atoms, (ii) the type of surface facets (their crystallographic orientation) and (iii) the shape of the nanocluster/nanoparticle.

The last aspect enters our phenomenological approach via the shape factor *C* (see Equation (4) and Table 1). Its importance is demonstrated in Figure 6 where the predictions of the phenomenological thermodynamic modeling are visualized for the same set of DFT values related to the bulk but for different values of the shape factor *C* corresponding to differently shaped nanoparticles. For a spherical nanoparticle, when the surface is not formed by planar {111} facets as in the case of decahedron, the surface energy was put equal to the average of surfaces energies obtained by DFT calculations of {100} and {111} surfaces.

**Figure 6.** The computed excess energies of the studied nanoclusters/nanoparticles (per atom and as functions of the nanoparticle radius) as obtained from the phenomenological thermodynamic modeling when considering different shapes of the nanoparticles with the same number of atoms. The absolute excess energies are shown in part (**a**) and compared with the excess energies from the direct DFT calculations of the actual decahedral nanoparticles (shown as black symbols in part (**a**)). The differences of the excess energies are presented also relatively in part (**b**) with respect to the DFT values (horizontal black dashed line). The blue curve in part (**a**) and blue data points in part (**b**) correspond to the spherical shape, red to the decahedral shape and brown to the tetrahedral shape.

**Table 3.** Relative differences (Equation (14)) of the excess energy per atom (Equation (13)) shown in Figures 5 and 6.

Regarding the tetrahedron, the {111} surface energy was used similarly as in the case of the decahedron. As seen in Figure 6a,b, the best agreement between the total energies of nanoparticles determined from phenomenological thermodynamic modeling and those obtained from direct DFT calculations of nanoparticles is found when the actual (decahedral) shape of nanoparticles is considered. Our calculations also confirm the previous findings that the surface energy and strain energy change rapidly with the change of structure (accompanying the change of temperature [8]). In agreement with results published by Vollath et al. in Ref. [62] our analysis also demonstrates that changes of surface energy are not noticeable for nanocluster/nanoparticles sizes less than 4 Å.

Finally, it is worth mentioning that our conclusion, that the energy of Ag nanoclusters and nanoparticles can be quite reliably assessed using the volume of the bulk fcc Ag, agrees well with the concept of so-called surface area correction [61,63] which is related to the expansion of the electronic cloud around the nanoclusters/nanoparticles. This phenomenon is specifically important for small nanoparticles and the resulting volume is, in the case of nano-sized systems, put equal to that of the bulk material. Our recommended choice of the volume in the case of nanoclusters/nanoparticles (to be set equal to the volume of the same number of atoms in the bulk) is thus neatly justified also by the electronic structure of the discussed nanoparticles.

#### **4. Conclusions**

With the help of first-principles calculations, we investigated properties of silver decahedral nanoclusters/nanoparticles containing 1–181 atoms in their static atomic configurations corresponding to the minimum of the quantum-mechanically computed total energies. Our T=0K thermodynamic analysis compares excess energies (per atom) obtained from a phenomenological approach, which is mostly based on bulk-related properties, with excess energies of direct quantum-mechanical DFT calculations of actual nanoclusters/nanoparticles. We show that the phenomenological thermodynamic modeling, which uses (i) the bulk reference energy, (ii) surface energies obtained for infinite planar (bulk-related) surfaces and (iii) the bulk atomic volume can predict the excess energy per atom of the studied nanoclusters/nanoparticles with the error lower than 3% with the only exception being the limiting case of a single silver atom. This agreement is achieved when the bulk-related properties (the bulk reference energy, the atomic volume and surface energy) are determined by the *ab initio* calculations performed as much as possible on equal footing with direct quantum-mechanical calculations of the studied nanoclusters/nanoparticles, i.e., with the same computational parameters (the same exchange-correlation functional, energy cut-off, k-point density, ... ). The only necessary information related to the nanoclusters/nanoparticles of interest, which enters the phenomenological thermodynamic modeling, is the number of atoms in the nanocluster/nanoparticle, their shape and the crystallographic orientations of facets. Importantly, the quantum-mechanical calculations of bulk-related properties are much less computationally demanding and we demonstrate that a top-down

phenomenological approach can be extended from the bulk down to nanoclusters containing only a few atoms.

Our work thus indicates that it is possible to substantially reduce computational demands when assessing thermodynamic properties of nanoclusters and nanoparticles by quantum-mechanical methods. We would also like to emphasize that, importantly, the agreement between (i) our phenomenological modelling and (ii) the DFT energies for the actual nanoclusters has not been found sensitive to minor deviations of the shape of the studied nanoclusters from a geometrically ideal decahedral case (due to atomic relaxations in our DFT calculations). On the other hand, it should be noted that (i) our study does not cover any excitations, such as phonons, and (ii) whenever the absolute value of the excess energy, i.e., not per atom, is needed when thermodynamically assessing the stability of nanoclusters/nanoparticles, the deviation of the absolute excess energies as obtained from our method may change with the number of atoms (with respect to absolute excess energies from direct *ab initio* calculations of the studied nanoclusters/nanoparticles).

**Author Contributions:** Conceptualization, S.P. and M.F.; methodology, S.P., M.F. and M.V.; formal analysis, M.V.; resources, M.Š.; writing—original draft preparation, S.P.; writing—review and editing, M.F., M.V. and M.Š.; visualization, S.P. and M.V.; supervision, M.F.; project administration, M.Š. and M.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Ministry of Education, Youth and Sports of the Czech Republic under the Project CEITEC 2020 (Project No. LQ1601) and by the Czech Science Foundation under the Projects "Stability and phase equilibria of bimetallic nanoparticles" (Project No. GA14-12653S) and "Structure and properties of selected nanocomposites" (Project No. GA 16-24711S).

**Acknowledgments:** We are very grateful to Jana Pavl ˚u from Masaryk University in Brno, Czech Republic, for many fruitful discussions related to the CALPHAD modeling. Computational resources were provided by the Ministry of Education, Youth and Sports of the Czech Republic under the Projects CESNET (Project No. LM2015042), the Project CERIT Scientific Cloud (Project No. LM2015085) and by IT4Innovations National Supercomputer Center (Project No. LM2015070) within the program Projects of Large Research, Development and Innovations Infrastructures. Figures 2 and 3 were visualized using the VESTA package [64–66].

**Conflicts of Interest:** The authors declare no conflict of interest.The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**

and CALPHAD methodology. *Calphad-Comput. Coupling Phase Diagrams Thermochem.* **2007**, *31*, 4–27. [CrossRef]

c 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/).


Sintering of Ceramics New Emerging Techniques

*Edited by Arunachalam Lakshmanan*

**SINTERING OF**

**NEW EMERGING**

Edited by **Arunachalam Lakshmanan**

**CERAMICS –**

**TECHNIQUES**

**INTECHOPEN.COM**


**1. Introduction**

Since its identification in 1885, *Escherichia coli* (*E. coli*) has become one of the most com‐ prehensively studied bacterial species. While *E. coli* is widely found in the environment and foods and is an important member of the commensal microbiota of mammals, some strains have evolved to include pathogenic mechanisms that cause significant diseases in humans and animals. In humans, *E. coli* strains can cause diverse enteric/diarrheagenic or extra‐intestinal infections by means of virulence factors that affect a wide range of cellular processes. Pathogenic *E. coli* associated with gastrointestinal illness have been divided into eight pathotypes based on their virulence profiles: (i) enteropathogenic *E. coli* (EPEC), (ii) enterohaemorrhagic *E. coli* (EHEC), (iii) enterotoxigenic *E. coli* (ETEC), (iv) enteroinvasive *E. coli* (EIEC), (v) enteroaggregative *E. coli* (EAEC), (vi) diffusely adherent *E. coli* (DAEC), (vii) adherent invasive *E. coli* (AIEC) and (viii) Shiga toxin‐producing enteroaggregative *E. coli* (STEAEC) [1]. This chapter will cover only two of them: ETEC and EHEC, which show opposite trends during their pathogenic processes. Even if in both cases human infections are primarily acquired through consumption of contaminated food products or drinking water, ETEC is a major cause of infantile diarrhea in developing countries, while EHEC is one of the main *E. coli* pathotypes associated with food poisoning outbreaks in the devel‐ oped world.

To cause human illness, pathogenic enteric *E. coli* must not only survive the passage through the human gastrointestinal (GI) tract but also accomplish their pathogenic process by a com‐ plex and coordinated multistage strategy, including adherence to the host intestine and toxin/ virulence protein production. The current chapter will provide a state of the art of ETEC and EHEC physiopathology, then focus on pathogen survival in the human digestive tract and regulation of virulence determinants by GI cues. As studies on humans are ethically incon‐ ceivable and small animal models do not recapitulate human pathogenesis, we will introduce the potential of dynamic *in vitro* digestion systems for increasing our understanding of ETEC and EHEC pathogenesis in a physiologically relevant GI environment.

ETEC cause approximately 280 million episodes of diarrhea worldwide, leading to hundreds of thousands of deaths per year [4]. With regard to EHEC, it is estimated that the pathogen is responsible for 2,801,000 acute illnesses, 3890 cases of haemolytic and uremic syndrome (HUS), 270 cases of permanent end‐stage renal disease, and 230 deaths worldwide [3]. For both pathogens, infants less than 5 years old are a high‐risk population. ETEC are respon‐ sible for 20–25% of diarrhea in young children, mostly in low‐income countries, and up to 40% of traveler's diarrhea [5]. In developing countries, children suffer from diarrhea attacks 7–8 times a year, with a peak incidence occurring between 6 and 18 months, and ETEC strains are responsible for one of each three attacks [6, 7]. In such countries, ETEC infections have then shown to play a significant part in the complex association between malnutrition and repeated bouts of diarrheal illness among young children. The impact of EHEC is also greater in infants and children, compared to other ages with 42% of cases of HUS and 29% of deaths

**Figure 1.** ETEC and EHEC pathogenesis including epidemiological data on the infections and at‐risk populations, reservoir, mode of transmission and virulence factors of the pathogen, and clinical signs are described. A/E: Attaching and effacing; CFTR: cystic fibrosis transmembrane regulator; GC‐C: guanylyl cyclase C; GM1: monosialoganglioside

Enterotoxigenic and Enterohemorrhagic *Escherichia coli*: Survival and Modulation of Virulence in the Human...

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While the lack of ongoing monitoring systems makes it difficult to understand ETEC pathogenesis worldwide, dedicated surveillance systems of human EHEC infections have been developed in most of the industrialized areas of the world [8]. In Europe, the surveillance of EHEC infections is embedded in the Food and Waterborne Diseases and Zoonoses (FWD) surveillance system coor‐ dinated by the European Center for Disease Prevention and Control (ECDC). FWD is a passive surveillance system, collecting data on EHEC infections including laboratory‐confirmed cases, probable cases, and possible cases. Cases of HUS are specifically recorded through a network of pediatric nephrologists and infection‐control practitioners on the basis of clinical diagnosis.

occurring in children between the ages of 0 and 4 years [3].

receptor; LT: heat‐labile enterotoxins; ST: heat‐stable enterotoxins; Stx: Shiga toxin.


*3.2. Wireless Sensing Test*

Next, we tested the wireless strain sensing, and compared with simulations using electromagnetic simulator. Figure 8 compares the wireless sensing results from the measurement and simulation when the transceiver was 10 mm away from the sensor. Among the two peaks, the right peak was chosen as the resonant frequency of the transceiver, because the changes in frequency of the right peak showed a higher sensitivity than that of the left peak. The measured and simulated results show that the resonant frequency decreased as the sensor strain increased. Overall, the simulated impedance magnitudes were higher than the measured values. It appears to be due to the relatively high DC resistance of the sensor in measurements, caused by the serpentine shape, which however was not included in the simplified simulation model. Nevertheless, the degree of changes in the peak frequency of the simulation was similar to that of the measured results, so that the simulation results could be used to predict the maximum wireless working distance of the sensor.

**Figure 8.** Experimentally measured and simulated impedance magnitudes of the transceiver at 10 mm away from the sensor. The frequency of the right peak was shifted (**a**) from 15.01 MHz at 0% strain to 14.59 MHz at 100% strain in experiment, and (**b**) from 15.31 MHz at 0% strain to 14.47 MHz at 100% strain in simulation.

The shifted resonant frequencies and the gauge factors of strain sensing according to different strains and different distances are summarized in Figure 9. Figure 9a shows the measured resonant frequency modulation detected at the transceiver wirelessly, and Figure 9c shows the calculated gauge factors. As the strain of the sensor increased, the resonant frequency of the transceiver decreased gradually. This decreasing trend could be seen only up to 22.5 mm distance. When measured at farther distances, the frequency converged to the resonant frequency of the transceiver itself, indicating that no measurable changes were detected. At 100% strain, the gauge factor decreased from 0.028 to 0.011 at 10 mm to 22.5 mm distance, converging to 0 at farther distances. Figure 9b shows the simulated resonant frequency at the transceiver, and the calculated gauge factors are shown in Figure 9d. The simulated results also showed that as the distance increased, the frequency converged to the self-resonant frequency of the transceiver. The detectable distance was observed to be between 20 mm and 30 mm, in good agreement with the experimental results. However, unlike the measured results, the simulated results did not show that the resonant frequency first increased at strains up to 20% at distances greater than 20 mm. This appears to be because the simplified simulation model did not include the additional DC resistance caused by the serpentine pattern and therefore did not fully reflect the decrease of inductive coupling. Nonetheless, the simulation results showed that the used FEM model could predict the wirelessly measurable distance reasonably well.

**Figure 9.** Experimentally measured and simulated results of wireless strain sensing. (**a**) Measured and (**b**) simulated resonant frequency modulation as the strain applied to the sensor increased, and the gauge factor of the transceiver calculated based on (**c**) the measured and (**d**) simulated resonant frequency.


**7. Consolidation and maintenance therapies in MM**

Almost all patients with MM relapse after autologous HSCT. Hence, treatment given in the postautologous HSCT period is aimed at suppression of residual disease in order to prolong duration of response, OS and PFS while minimizing toxicity [125, 126].

The use of novel therapies in the consolidation phase following single or tandem autologous HSCT has been shown to enhance the rate as well as the quality of response thus contributing to improvements in clinical outcomes including prolongation of PFS [126]. Bortezomib-based regimens used as consolidation therapy after autologous HSCT in patients with MM have been shown to be effective in the improving PFS and decreasing relapse rate [127].

Maintenance therapy represents an important therapeutic strategy to delay disease progression and relapse [125, 126]. The following drugs have been used in postautologous HSCT maintenance: interferon, thalidomide, bortezomib and carfilzomib [125, 126, 128–130]. Bortezomib is safe, well tolerated and efficacious and it can be used with no risk of second malignancy till disease progression, but its disadvantages include cost and effects on quality of life (QoL) [126, 130].

In February 2017, the Food and Drug Administration in the USA approved the use of lenalidomide as maintenance therapy after autologous HSCT for patients with MM, after showing efficacy and safety in several studies [131]. Lenalidomide has tumoricidal and immunomodulatory activities against MM [132]. Several studies have shown the efficacy of lenalidomide maintenance after autologous HSCT as this therapy has been shown to be associated with significant improvements in OS, PFS and longer time to disease progression [133–136]. A multicenter, randomized double-blind study that included 306 patients with newly diagnosed MM ≥65 years of age and ineligible for autologous HSCT treated initially with melphalan, prednisolone and lenalidomide induction followed by lenalidomide versus placebo maintenance showed the following results: (1) significant prolongation of PFS, (2) maximum benefit was achieved in patients 65–75 years of age and (3) 3-year second primary tumor of 7% in the lenalidomide arm versus 3% in the placebo arm [132]. Other studies on lenalidomide maintenance have shown more toxicity and low rate of development of second tumors [133, 134]. Lenalidomide maintenance can be initiated as early as day 100 postautologous HSCT [133]. Duration of lenalidomide maintenance longer than 3 years has been associated with further improvement in survival [134]. Several studies performed in patients with newly diagnosed MM subjected to autologous HSCT have shown continuous therapy to be more effective in prolongation of OS and PFS that limited the duration of treatment [137–141].

kinesin motor proteins, aurora kinases, polo-like kinases and the anaphase-promoting complex/cyclosome [151]. The novel therapies that are used in the treatment of MM differ in their modes of action. Nevertheless, each drug has its own side effects that should be considered particularly once treating patients with comorbid medical conditions and once

**Table 1.** Novel agents and targeted therapies that are either currently used or under development for the treatment of

1. **Monoclonal antibodies:** Anti-CD 38 (daratumumab, elotuzumab, isatuximab, MOR202), anti-CD138 (indatuximab ravtansine), anti-interleukin-6 (siltuximab), anti-RANKL (denosumab), anti-KIR2DL1/2/4 (IPH2101)

Hematopoietic Stem Cell Transplantation in Multiple Myeloma in the Era of Novel Therapies

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2. **Immunomodulatory agents:** thalidomide, lenalidomide, pomalidomide

8. **BCL2 antagonists (BH3 mimetics):** venetoclax, obatoclax, navitoclax

13. **Phosphoinositide 3-kinase-Akt inhibitors:** perifosine, afuresertib

16. **Chimeric antigen receptor T cells (CAR T cells):** directed against:

4. **Histone deacetylase inhibitors:** panobinostat, vorinostat, romidepsin, ricolinostat

6. **Checkpoint (programmed cell death protein 1) inhibitors:** nivolumab, pembrolizumab

3. **Proteasome inhibitors:** bortezomib, carfilzomib, ixazomib

5. **mTOR inhibitors:** everolimus, temsirolimus

7. **Bruton's tyrosine kinase inhibitors:** ibrutinib

9. **Cyclin-dependent kinase inhibitors:** dinaciclib

11. **Kinesin spindle protein 1 inhibitors**: filanesib, array 520 12. **Selective inhibitors of nuclear transport**: selinexor

10. **MEK inhibitors:** selumetinib

14. **PIM kinase inhibitors:** LGH 447

**c.** B-cell maturation antigen **d.** Cell surface glycoprotein

15. **Vaccines:** PVH-410

**a.** CD-19 **b.** CD-38

multiple myeloma.

protein that is overexpressed in MM cells. It is given IV at a dose of 16 mg/kg weekly [153–156]. It induces death of MM cells by several mechanisms including (1) complement-dependent cytotoxicity, (2) antibody-dependent cell-mediated cytotoxicity, (3) antibody-dependent

Daratumumab has shown substantial efficacy as monotherapy in heavily pretreated patients with MM as well as in combination with bortezomib in patients with newly diagnosed MM [154]. Two phase III randomized clinical trials in R/R MM using daratumumab in combination with either bortezomib and dexamethasone or lenalidomide and dexamethasone showed

monoclonal antibody that targets CD38, which is a cell surface

these novel agents are used in combination with other drugs [152].

**8.1.


**5.1 Leak path**

The function of cement sheath in oil and gas wells is to seal formation fluids, support and suspend casing, protect the wellbore, and provide a certain alkaline environment to avoid casing corrosion and ensure wellbore integrity. However, after carbon dioxide is injected into the subsurface, it will corrode the cement sheath and casing under suitable humidity and pressure conditions cause problems, such as a decrease in the strength of the cement sheath and an increase in its permeability. Furthermore, the corrosion effect, cement hardening, and alternate injection processes will impact casing and cement sheath strength and stress distribution in the near-well region, exacerbating wellbore integrity failure. **Figure 10** shows the CO2 leak path due to wellbore integrity failure [45, 47].

**Figure 10.** *Schematic diagram of leak pathways related to wellbore integrity (reproduced from [46]).* (5) Leakage along formations damaged during drilling (#6)

(6) Casing-cement and cement-formation interface debonding resulting in microfractures (#7, #12)

(7) Poor cement consolidation quality with permeability (#8)

(8) Fractures or gas channels in cement (#10, #11)

#### **5.2 Chemical well integrity failure**

Silicate cement is usually used as a sealing material when completing a well. The reaction occurs when the cement comes into contact with CO2, resulting in the degradation of the cement. The continuous reaction of cement with CO2 increases the porosity of the cement matrix, which also allows chloride ions to pass through the matrix causing corrosion of the casing [48, 49].

However, the consequences of the reaction between cement and CO2 are not always harmful. The slight carbonation of CO2 can reduce the permeability and porosity of the cement without causing failure of well integrity if the cement consolidation quality is excellent. However, a high degree of carbonation will certainly lead to failure or fracturing of the cement structure, failing well integrity. The corrosive effect of CO2 will be more pronounced if the cement quality is poor with existing defects such as tiny pores or fractures [50, 51].

There are numerous mechanisms of chemical reactions impacting well integrity, and it is necessary to clarify the CO2 and formation properties, and then the various chemical changes during the interaction of cement materials, wellbore materials, and carbonic acid can be further investigated.

#### **5.3 Mechanical well integrity failure**

Geomechanics is a key factor impacting well integrity with effects throughout the life cycle of a GCS project. During the drilling, completion, and application of the well the stresses in the wellbore, the cement sheath, and the near-well area keep changing. The reasons include pore pressure changes due to injection, leakage, and diffusion, thermal stress changes due to temperature differences, and in-situ stress changes due to tectonic shifts or seismic activity. Among them, the stress change in the cement sheath is the most significant. After the cement is poured, it will go through two stages of hardening (liquid cement transforms into solid cement) and shrinkage (solid cement volume shrinks and continues to harden). The change in cement rheology is more obvious during the hardening process. However, in the post-hardening phase, the shrinkage of the cement not only has a large effect on the stresses (because it is a solid shrinkage), but also the shrinkage may lead to plastic deformation or cause debonding at the interface between the cement and the formation or casing. In addition, the casing position may offset from the center of the wellbore, resulting in uneven stresses on the casing and cement sheath, increasing the risk of casing deformation and interface debonding. Thermal stresses are particularly important when CO2 is injected into the subsurface, especially in the case of cyclic loading, causing coupling between thermal stresses and other stress fields, promoting fracture growth within the cement or debonding at the cement interface [46, 52, 53].

In conclusion, well integrity issues may be encountered during the entire GCS life cycle due to the influence of multiple factors such as coupled stress-thermal-chemical. Therefore, it is necessary to take into account the combined effect of these factors in GCS engineering for well integrity problems, which are generally studied using numerical simulation.