Multiconnectivity allows user equipment/devices to connect to multiple radio access technologies simultaneously, including 5G, 4G (LTE), and WiFi. It is a necessity in meeting the increasing demand for mobile network services for the 5G and beyond wireless networks, while ensuring that mobile operators can still reap the benefits of their present investments. Multipath TCP (MPTCP) has been introduced to allow uninterrupted reliable data transmission over multiconnectivity links. However, energy consumption is a significant issue for multihomed wireless devices since most of them are battery-powered. This paper employs software-defined networking (SDN) and deep neural networks (DNNs) to manage the energy consumption of devices with multiconnectivity running MPTCP. The proposed method involves two lightweight algorithms implemented on an SDN controller, using a real hardware testbed of dual-homed wireless nodes connected to WiFi and cellular networks. The first algorithm determines whether a node should connect to a specific network or both networks. The second algorithm improves the selection made by the first by using a DNN trained on different scenarios, such as various network sizes and MPTCP congestion control algorithms. The results of our extensive experimentation show that this approach effectively reduces energy consumption while providing better network throughput performance compared to using single-path TCP or MPTCP Cubic or BALIA for all nodes. The massive increase in the data traffic volume and the user demand for high-speed data rates and high-quality services has created a requirement for innovative and adaptable network implementations in the existing wireless technologies. The machine-to-machine (M2M) and the Internet of Things (IoT) paradigms  presume The fifth-generation (5G) wireless network standard came with radio enhancements (new radio) to provide users/devices with communication services such as ultra-reliable and low-latency (URLLC) communication, high-throughput mobile broadband (eMBB), and the massive support of machine-type communication (mMTC). However, the increasing demand for wireless bandwidth may negatively impact the performance of these services. Thus, the 3GPP introduced a method known as dual connectivity/multiconnectivity, in which a user device can send and receive data concurrently to and from two or multiple nodes using the same  or different technologies  ,3. This At the same time, the emergence of the multipath transmission control protocol (MPTCP)  can aid Using devices with dual or multiconnectivity can be challenging due to energy consumption, especially with battery-powered wireless devices used in emerging technologies like IoT. It is crucial for wireless devices to be energy-efficient while providing optimal performance. Higher energy consumption leads to increased battery capacity and a larger device size and weight. Therefore, minimizing energy consumption is crucial to extend the battery life (for the same form factor) and maintain a small carbon footprint. When using two wireless interfaces simultaneously, it is essential to ensure that the overall energy consumed by both interfaces does not significantly exceed that of a single interface.The operation of the MPTCP protocol relies on two main components, namely a scheduler and a congestion control algorithm. The scheduler selects the traffic path (the wireless interface) for each packet, whereas the congestion control algorithm estimates the amount of data to be sent over each path in order to avoid congestion. The execution of both components controls the traffic share of each interface, which directly affects the energy consumed by each interface, as the more data sent, the longer the time that the interface will be used and hence more energy is consumed. For the first component (the scheduler), the MPTCP Linux kernel implementation uses the default scheduler, which splits the traffic on each path based on the round-trip time (RTT) experienced over that path. However, for the second component , there are five different algorithms available as Linux kernel implementations, namely OLIA, LIA, wVegas, Cubic, and BALIA ,7,8,9,10Therefore, this paper proposes the usage of SDN accompanied by a deep neural network (DNN) to reduce the energy consumption for devices with dual or multiconnectivity. SDN  is an evThus, we propose a scheme employing the SDN concept to control the traffic flows received by each node wireless network interface to minimize the downlink energy consumption. In this scheme, the SDN controller decides on steering the flow of data packets to the receiving nodes based on a lightweight interface selection algorithm relying on the measured achievable throughputs of each node’s wireless interfaces. Moreover, the proposed scheme offers another algorithm that also runs on the SDN controller to fine-tune its interface selection based on energy consumption information provided by a trained DNN.This paper offers two main contributions. Firstly, it provides a comparative experimental study of the data transfer throughput and energy consumption of different MPTCP congestion control algorithms, namely LIA, OLIA, BALIA, Cubic, and wVegas, which are all available as Linux kernel implementations. Secondly, it presents two algorithms that select which wireless interface should operate in each network node to minimize the overall network energy consumption. These algorithms are implemented using a Ryu-based SDN controller, which manages an Open vSwitch-based switch via the OpenFlow protocol. Based on the comparative study results, the first algorithm selects the operating radio interfaces of each node mainly based on their probed achievable throughput. The second algorithm uses a trained DNN to make an informed decision about whether the interfaces selected by the first algorithm are the best selection in terms of energy consumption or need further tuning. Both algorithms are tested on a real hardware testbed that fully implements a single-cell LTE network  and a WiFi network using dual-homed single-board computers as sending/receiving nodes.The rest of the paper is organized as follows. Several previous research works address the management of wireless MPTCP connections using an SDN framework. The works propose the usage of SDN to manage MPTCP mainly focusing on routing, controlling the path, and path resilience. For instance, the WRR MPTCP scheduler is used for multipath routing in . A dynamSeveral research works address the reduction of MPTCP energy consumption by devising a new scheduling scheme. An energy-aware MPTCP (eMPTCP) model is proposed by  and testMoreover, the authors in  address A few researchers discuss minimizing MPTCP energy consumption by proposing congestion control schemes different from the Linux kernel implementation ones. For example, the authors of  suggest Other authors target MPTCP energy consumption analysis and modeling. For instance, the authors of  analyze Thus, the previously mentioned research works addressing MPTCP energy consumption mainly aim at changing the current MPTCP Linux kernel implementations by modifying the scheduler ,32,33,34To the best of our knowledge, no research work in the literature experimentally introduce SDN combined with DNN to manage the energy consumption of multiconnectivity wireless nodes running MPTCP, which avoids the need to make any changes in the MPTCP Linux kernel implementation.The MPTCP protocol contains a scheduler to select the traffic path for each packet and a congestion control algorithm to estimate the amount of data to be sent over each path in order to avoid congestion. The default scheduler of the Linux kernel implementation splits the traffic on each path based on the round-trip time (RTT) experienced over that path. In this section, we provide a basic background of the congestion control algorithms available as a Linux kernel implementation, namely LIA, OLIA, Cubic, BALIA, and wVegas.x,This algorithm utilizes the RTT and congestion window size of all subflows to determine the congestion window of a subflow, which increases until congestion is detected. When congestion is detected, the transmission rate is reduced to alleviate the issue. The LIA algorithm strikes a balance between the rate of increasing and decreasing the congestion window to ensure a stable transmission rate. It is highly suitable for fluctuating network conditions as it facilitates smooth and stable data transfer while making the most of available resources. LIA utilizes the same algorithms as TCP-Reno, including slow start, fast retransmit, and fast recovery. During the congestion avoidance phase, LIA also employs an additive increase multiplicative decrease (AIMD) algorithm, which increases the congestion window CiRTThe first term in  incorporiciently .The Cubic algorithm  controlsThe increase in the congestion window size in Cubic is calculated asS is the scaling constant. T and Here, BALIA is a congestion control algorithm that prioritizes both friendly flow behavior and responsiveness to changing network conditions. It dynamically adjusts the sending rate based on the available bandwidth and loss rate, while also balancing the sending rate across multiple subflows. BALIA has proven to be more effective than traditional TCP algorithms, especially in high-bandwidth and high-latency networks.The BALIA algorithm enhances the effectiveness of TCP’s congestion avoidance algorithm in contemporary network settings that have multiple paths and changing network conditions. BALIA alters both the increase and decrease phases of the AIMD algorithm employed in TCP.i is determined usingThe BALIA algorithm relies solely on the congestion window size and RTT of the subflow paths. Upon receiving an ACK, the increase in congestion window size for subflow i in the range of  using  as(7)CWThis reduces the size of the congestion window by a factor of 2 multiplied by the minimum of th share . The val is used .wVegas  is desigSince MPTCP is applied with dual or multiconnectivity, where more than one wireless interface is used in data transfer, energy consumption remains a significant issue, especially for devices with limited energy supply .Consider a scenario where several stationary devices are receiving data traffic from some sending nodes via a communication backbone using MPTCP. The receiving nodes can connect to this backbone through dual connectivity via the simultaneous usage of different radio access technologies (RATs), such as WiFi and LTE/5G. This implies that the receiving nodes are under the overlapped coverage of a WiFi access point (AP) and an eNB or a gNB as shown in In this section, the experimental setups used in this research are presented along with the experimental procedures. It is worth noting that due to budget limitations, the cellular configuration of the dual connectivity realization in the testbed is implemented with a reasonable scale using LTE (4G) technology, which can be achieved using communication modems of affordable cost, in contrast to 5G technology.The experimental setup imitates the system model using a testbed based on a real scenario, which enables dual connectivity by transmitting data packets over two wireless networks of different technologies. The wireless nodes employed in the lab experiments are single-board computers (SBCs), which can simultaneously connect to an LTE network via attached LTE universal serial bus (USB) modems and connect to the WiFi network through attached USB WiFi adapters. Due to budget and space limitations, the experiment engages only 10 SBCs: one acts as a sender and the rest are receivers. All SBCs run the Ubuntu Linux server with the Linux kernel implementation of MPTCP, supporting five congestion control algorithms, namely, OLIA, LIA, Cubic, BALIA, and wVegas. The receiving nodes are connected to a WiFi router, which is directly connected to another WiFi router serving the sending node. The two routers run on two different WiFi frequency channels. Moreover, the receiving nodes are connected to a real (not simulated) single-cell LTE network, which consists of a real eNodeB implemented using software-defined radio (SDR) connected to a real evolved packet core (EPC) system implementing the mobility management entity (MME), serving gateway SGW, packet data network gateway (PGW), and home subscriber server (HSS). The LTE network uses the iperf traffic generation tool, which is also used to measure the data transfer throughput. The downlink energy consumption is measured during data transfer using an energy meter, as depicted in The experimental procedure is performed by transferring a certain amount of data from the sending to the receiving nodes using the MPTCP protocol. The data are generated using the The results of using experimental setup I to measure the energy consumption of dual connectivity receivers running MPTCP with different congestion control algorithms such as OLIA, LIA, BALIA, Cubic, and wVegas are revealed in this section.The energy consumed in the downlink of the receiving nodes when transferring some data volume (60 MB) by the sending node is measured in a scenario where the receiving nodes are varied from one to nine. Moreover, from Furthermore, we analyze the energy behavior of different congestion control algorithms while varying the number of receiving nodes, as depicted in This setup uses a similar configuration to setup I. However, it additionally incorporates an SDN controller and uses a multi-Ethernet interface computer running Open vSwitch (OVS), instead of a normal Ethernet switch. Both WiFi routers (for the sending and receiving nodes) and the EPC system are connected to the OVS switch. The SDN controller is implemented using Ryu for simplicity. It employs the standard OpenFlow protocol  to managThe OVS switch can monitor the incoming packets to each receiving node and record the packet arrival rate, packet size, and transmission duration. By collecting this information, the switch can measure the throughput value of each receiving node and communicate it to the SDN controller. Once the SDN controller receives the throughput measurements from the OVS switch, it utilizes this information to make an informed decision about the interface to be used to transmit the packets.Consequently, the controller manages the data flows by dynamically changing the flow table rules in the switch. For instance, if the data are required to be received only over the WiFi interface of a receiving node, the SDN controller commands the OVS switch to stop forwarding the data of the LTE flow. Similarly, the OVS switch can allow only the LTE flow by dropping the WiFi route from the flow table. The flows through both interfaces are also provided in the flow table of the OVS switch. Ultimately, the entirety of setup II, as shown in The proposed algorithms aim to achieve the lowest overall network energy consumption by sending the data packets through the wireless interface(s) of each node that can achieve this. Thus, the outcome of the proposed algorithms is a combination of interfaces. Here, the term "combination" refers to the mix of interfaces through which the data transfer occurs for each number of nodes. For instance, if three nodes are used, the interface combination that gives the lowest energy consumption may be WiFi for Node 1, LTE for Node 2, both interfaces for Node 3, or the treble . We propose two algorithms. The first selects a combination of interfaces by using SDN (the SDN controller and OVS switch) based on the achieved throughput, whereas the second algorithm performs fine-tuning of the outcome of the first algorithm with the help of neural networks.The SDN controller runs the developed algorithms as Ryu applications after measuring the achievable channel throughput via the information received from the OVS switch using the OpenFlow protocol. The SDN controller and algorithms are intended to be lightweight. This is easily achieved using the Ryu framework, which also allows seamless integration with machine-learning Python libraries. The SDN controller runs the interface selection algorithm initially and collects the throughputs of the resultant combination of interfaces obtained. Furthermore, these throughputs are given to the trained DNN, and the tuning algorithm runs, as mentioned in the following.In this algorithm, the SDN controller probes the achievable throughputs of each interface by sending some traffic via the OVS switch through this interface separately for each node. Indeed, every node has specific achievable throughput values for each interface based on its channel condition.The IS algorithm compares these achievable throughputs for each interface of each node. The interface that achieves significantly higher throughput than the other is selected to receive the traffic. If the channel conditions of both interfaces lead to slightly different throughput values  of data is transferred from one sender node to a varying number of receiving nodes (from 1 to 9) with different congestion control algorithms, such as OLIA, LIA, BALIA, Cubic, and wVegas. For each case , the average throughput and corresponding energy consumption are measured when a single interface (WiFi or LTE) is used or both interfaces are. To train the DNN, 30 samples are used for each case. Similarly, 15 samples are used for testing with the DNN. The regressor used is based on a DNN following a multilayer perceptron (MLP) architecture with five hidden layers and 200 neurons in each layer. The ’ReLU’ activation function is used for the hidden layer. The DNN is trained for a large number of iterations on the generated dataset to obtain accurate results. The neural network model is depicted in Since the IS algorithm mainly depends on the achievable throughput to select the interface combination of the receiving nodes, the Tuning algorithm tries to tune or ensure this selection. This is done mainly for the nodes where the achievable throughput of both of their interfaces are slightly different  of the controller processing time needed to calculate the energy consumption of each node using the pre-trained DNN model, where The following steps compose the Tuning algorithm.Step 1: Train the DNN (an offline step).Step 2: Feed the output of the IS algorithm for all network nodes to the trained DNN.Step 3: Calculate the sum of the energy consumption of all network nodes using the trained DNN based on the measured throughput values.Step 4: For the nodes with both interfaces selected by the IS algorithm, select only the interface with the highest achievable throughput.Step 5: Measure the throughput by the SDN controller based on the newly tuned selection and feed it to the DNN.Step 6: Obtain the energy values of all nodes from the DNN.Step 7: Compare the energy values from Step 3 and Step 6; if the energy sum after tuning is greater, use the interfaces as chosen by the IS algorithm for the data transfer. Otherwise, use the interfaces as chosen by the Tuning algorithm.The addition of the SDN in experimental setup II is realized by inserting the OVS switch in the data path between the sending node and the receiving nodes. This allows the SDN controller to execute the proposed algorithms, which run as a Ryu application, select the energy-optimized combination of interfaces, and communicate the selection to the OVS to implement it.The proposed algorithms can enhance both the network energy consumption and average throughput because they produce a mixed combination of the scenarios shown in Consequently, based on both algorithms, the SDN controller oversees and makes informed decisions about which interface(s) should be used at each node. This makes the proposed SDN-based scheme able to reduce the energy consumption by This paper addresses the reduction of the energy consumption of multihomed wireless devices using multiconnectivity via heterogeneous radio access technologies to receive MPTCP data packets. We propose an SDN-based approach supported by a DNN to select which wireless interface(s) a network node should use to reduce the overall network energy consumption. The scheme employs two algorithms. One initially selects the wireless interface(s) that should operate on each network node based on the achievable throughput. After this, the other algorithm fine-tunes the selection of the first by applying a DNN to select the interface(s), leading to the lowest overall energy consumption. Both algorithms run at the SDN controller, which implies that no change in the MPTCP implementation, either in the scheduler or the congestion control algorithm, is required. This preserves the features and throughput performance of the currently available MPTCP Linux kernel implementations while retaining operation compatibility.Two experimental setups mimicking realistic settings are utilized in this research. As the congestion control algorithm used by MPTCP manages the amount of data sent over a wireless interface, affecting its energy consumption, the first setup is used to conduct experimental testing and build a dataset for the energy consumption performance of different MPTCP congestion control algorithms available as Linux kernel implementations, namely LIA, OLIA, Cubic, BALIA, and wVegas. The experimental results show that Cubic and BALIA achieve the lowest energy consumption and the highest throughput among the other MPTCP congestion control algorithms available as Linux kernel implementations. Thus, the second setup tests the proposed scheme algorithms by implementing them on a Ryu-based SDN controller managing an OVS switch via the OpenFlow protocol when using either MPTCP BALIA or Cubic on the sender and receiving nodes.Extensive experimental results with a variable number of network nodes show that the proposed scheme is efficient in reducing network energy consumption by The future directions for this research include predicting the throughput values and energy consumption of fast-moving mobile network nodes using machine learning via the SDN controller. This prediction can be integrated with the proposed algorithms to cope with the fast-changing network topology and node connection status.


The adaptive mutation phenomenon has been drawing the attention of biologists for several decades in evolutionist community. In this study, we propose a quantum mechanical model of adaptive mutation based on the implications of the theory of open quantum systems. We survey a new framework that explain how random point mutations can be stabilized and directed to be adapted with the stresses introduced by the environments according to the microscopic rules dictated by constraints of quantum mechanics. We consider a pair of entangled qubits consist of DNA and mRNA pair, each coupled to a distinct reservoir for analyzing the spreed of entanglement using time-dependent perturbation theory. The reservoirs are physical demonstrations of the cytoplasm and nucleoplasm and surrounding environments of mRNA and DNA, respectively. Our predictions confirm the role of the environmental-assisted quantum progression of adaptive mutations. Computing the concurrence as a measure that determines to what extent the bipartite DNA-mRNA can be correlated through entanglement, is given. Preventing the entanglement loss is crucial for controlling unfavorable point mutations under environmental influences. We explore which physical parameters may affect the preservation of entanglement between DNA and mRNA pair systems, despite the destructive role of interaction with the environments. Thus far, researchers have considered two different Darwinian and Lamarckian mechanisms for evolution process. Darwinian evolution mode occurs at low-stress levels, where random mutations seem to be a dominant source for evolution6. In contrast, the Lamarckian mechanism happens at high-stress levels, where the adaptive mutations are dominant and environmental factors introduce genomic changes. Here, the mutations target are specific genes and causes of adaptation to the original motive. Through the phenomenon of adaptive or directed mutations individual organisms show suitable plasticity to contribute directly into the evolutionary process by changing their genome. Adaptive mutations are time-dependent and appear only after the cell exposion to a selective substrate8. For several decades, people have tried to explain how cells can selectively mutate a specific gene in response to environmental signals. Quantum studies of the evolution suggest that adaptive mutations may be generated by environment-induced collapse of the quantum wave function describing DNA in a superposition9 of mutated and unmutated states10. Proton tunneling is the way that DNA can become in superposition. Löwdin considering the proton tunneling between two adjacent sites within the H-bonded DNA bases proposed a quantum model for gene mutations12. The proton tunneling in DNA can cause the transformation like C-G 13. For describing the adaptive mutation with such a mechanism, the evolving DNA wave function must remain coherent for sufficiently long time to interact with the cell’s environment. The coherence must be maintained during the separation of the two strands of the DNA via helicase18. There is an intense debate on if both forms of tautomers can exist and dynamically be stable. The strengths of hydrogen bonds within DNA due to the inherently quantum mechanical nature of hydrogen bonding can be affected by nuclear quantum effects21. Moreover, the unzipping DNA is a complex biological process and involves strong interactions from several proteins22. It has been hotly debated for decades if the coherence of tautomers can survive the unzipping helicase25. McFadden and Al-khalili modeled a specific mutational process involving proton tunneling and investigated the possibility of the coherence to be maintained. They estimate the rate of decoherence for the protons initiating mutational events within DNA using the Zurek model26. Accordingly, for a system of mass m in a superposition of two position states separated spatially by a distance T, dependent, and 7. More recently, Slocombe et al. investigations demonstrated that the quantum rate of tautomeric lifetime is significantly higher than the classical rate for a wide range of bath coupling strengths. The proton transfer processes and interconversion between the normal and tautomeric forms occur remarkably quicker than the helicase cleavage timescale19. These evidences for surviving coherence between tautomers allowed scientists to hire quantum approaches of evolution on the genome7 and cellular level8 for describing the various aspects of adaptive mutations30. Both approaches inspect the situation in which the system under consideration fluctuates between two quantum states labeled as mutated and unmutated states due to the proton tansfer13. In the absence of a selective substrate, the mutated and unmutated states are not distinguishable by the environment8. In such situations the state is said to be stable. The application of the selective substrate destabilizes the fluctuating state that can lead to the generation of the mutant colony. The addition of a specific substrate may result in the collapse of the superposition by rapid decoherence, which corresponds to consecutive monitoring of the state of the system with its environment34.As the frontiers of quantum biology predicted, one of the most debating topics in relation to quantum origins of life is the evolution story35. Where the term R-error refers to synthesis of a mutated strand of mRNA due to the recognition of a tautomeric form of a base along the gene by RNA-polymerase. Also, the term D-error specifies a similar mistake made by DNA-polymerase 37. Here, a related question arises as to what extent this kind of non-classical correlation in the cell is prone to survive from the EID. In different words, how decoherence can play a positive role in stabilizing some non-classical correlations in the macroscopic object of living cell?Taking non-classical correlations between two different parts of the cell into account reveals a prominent feature of quantum mechanics, namely the entanglementAfter transcription and replication processes within the nucleus and before translation, the daughter DNA and mRNA separate from each other and lie in different places. The daughter DNA remains in the nucleoplasm, and mRNA migrates to the cytoplasm according to their biological tasks. From now on, daughter DNA will be referred to as DNA for simplicity. For such a bipartite system of DNA and mRNA, it is desirable to describe what occurs for the available information of two separated parts after they have correlated for a while. Putting in quantum language, entanglement implies dealing with just a single composite system, instead of two isolated ones. Therefore any change to one subsystem, regardless of the distance between two parts, would influence the other.38 for tackling macroscopic quantum tunneling in the presence of the environments. By calculating concurrence of the two entangled qubits, as a measure of entanglement propagation, we comment on the extent of dispersing of entanglement on the whole system. Our approach opens a new perspective to study genetic errors and adaptive mutations through the distinct framework of quantum mechanics39.In this investigation, we consider a model consisting of the pair of DNA and mRNA located in nucleoplasm and cytoplasm, respectively. Both DNA and mRNA are two-level systems created due to the base tautomerizatio. We use this model to study their correlation and the related entanglement dynamics. The correlation between DNA and mRNA is a primary correlation after the replication and transcription of error containing DNA. Correlation between daughter DNA and amino acids is a secondary correlation and is a consequence of the correlation between mRNA and DNA. We mainly focus on the time-evolution study of the entanglement between DNA and mRNA while they interact with the corresponding environments. We analyze the interaction between DNA and mRNA subsystems and the environments using a framework proposed by Takagi inThe paper is organized as follows. In Sect. "38:ith system, ith environment bosonic mode. ith environmental mode. Here, we use a linearly coupled harmonic environment model, named ’separable interaction’ in which 38, noting that M to pass the distance Consider a bipartite system We aim to study the sources of genetic errors and genetic mutations using quantum-mechanical formalism. Thus, we describe the quantum state of the entangled bipartite DNA and mRNA systems which alluded to each other by quantum correlation due to the replication and transcription of tow-state mother DNA strand with H defined in Eq.  for the calculated expression of the cuncurrence. Figure E(C) with time for different values of E(C) shows a similar behavior to the concurrence which is demonstrated in Fig. Let us now attend to another measure of entanglement. For a given mixed state In the present work, we studied the environment-induced decoherence for mRNA-DNA-error correllation created due to the base tautomery, considering the mRNA-DNA system as entangled bipartite system, where each part coupled to a different bosonic environments. The time-evolution of the energy states of the pair has been studied entangled biomolecules has been studied using time-dependent perturbation theory. The concurrence of these systems calculated in order to determine how extent the components are entangled. We have found that the mRNA-DNA-error correlation depends on the interaction strength of the each component and the corresponding environment. The parameters Supplementary Information.


Thyroid cancer is the most common endocrine neoplasm . BesidesHigh-risk patients and undifferentiated tumors loose the capacity of trapping iodine-131, making not only the diagnosis but also the treatment of those patients a challenge. Even when conventional imaging is not able to localize the recurrence besides the rise of the serum thyroglobulin (Tg) levels, it is clinically valuable to pursue other alternatives to localize the sites of recurrent disease. Actually, neck ultrasound and chest computed tomography are efficient to detect the most common sites of recurrent thyroid tumor .PET-CT emerged as a molecular imaging tool, where the disease is detected more due to the molecular profile and/or metabolic cellular signaling than structural or functional abnormalities. The high rate of anaerobic glycolysis is one of the main features of various malignant tumors, and that is the reason for using fluordesoxyglucose labeled with fluoride-18 (FDG), a common positron emitter produced on Cyclotrons . DediffeArchives of Endocrinology and Metabolism (AE&M) by Yang and cols. (A very interesting paper published in this issue of nd cols.  is the fnd cols. . The firIn the group IB, many patients showed alterations on conventional imaging at the same location seen of FDG-PET. If the location was the same of FDG-PET, and not compatible with the WBS, could we assume that the CT or MRI finding was enough to confirm the recurrence? Moreover, it is very well know that CT has a better detection rate of lung metastasis compared to PET, since size of the nodule is a limitation factor for the resolution of the modern PET scanners . Even thThe same issues can be discussed for the Group 2. Many patients showed abnormalities on lungs by CT and also by PET. Has PET also provided real incremental value towards the CT findings or just confirmed the CT abnormalities as related to the thyroid cancer recurrence?Another limitation is the small number of patients regarding each group with unfavorable histology, a limitation that is expected considering the low prevalence of those histological types. There is no data in the literature evaluating the GLUT and HK-II expression in the various aggressive histology thyroid tumors. So, some conclusions must be taken with caution regarding the power of sample and considering some methodological aspects inherent to a retrospective study. Nevertheless, this is the first large cohort Brazilian study evaluating the clinical value of PET-CT in high-risk thyroid cancer patients, and hopefully will stimulate other groups to replicate that study to confirm the very interesting findings published in this issue of the AE&M.


Trump supporting Twitter posting activity from right-wing Russian trolls active during the 2016 United States presidential election was analyzed at multiple timescales using a recently developed procedure for separating linear and nonlinear components of time series. Trump supporting topics were extracted with DynEGA  and analyzed with Hankel Alternative View of Koopman (HAVOK) procedure. HAVOK is an exploratory and predictive technique that extracts a linear model for the time series and a corresponding nonlinear time series that is used as a forcing term for the linear model. Together, this forced linear model can produce surprisingly accurate reconstructions of nonlinear and chaotic dynamics. Using the R package havok, Russian troll data yielded well-fitting models at several timescales, not producing well-fitting models at others, suggesting that only a few timescales were important for representing the dynamics of the troll factory. We identified system features that were timescale-universal versus timescale-specific. Timescale-universal features included cycles inherent to troll factory governance, which identified their work-day and work-week organization, later confirmed from published insider interviews. Cycles were captured by eigen-vector basis components resembling Fourier modes, rather than Legendre polynomials typical for HAVOK. This may be interpreted as the troll factory having intrinsic dynamics that are highly coupled to nearly stationary cycles. Forcing terms were timescale-specific. They represented external events that precipitated major changes in the time series and aligned with major events during the political campaign. HAVOK models specified interactions between the discovered components allowing to reverse-engineer the operation of Russian troll factory. Steps and decision points in the HAVOK analysis are presented and the results are described in detail. Strategic misinformation has been spiraling out of control with intranational and international actors attempting to manipulate social media users for political and commercial reasons. Fortunately, social media platforms keep records that can be aggregated into publicly available datasets and subjected to quantitative analysis. Modern quantitative techniques can be a key to extracting, understanding, and predicting misinformation for regulation and prevention.In the United States, online activities were used to influence public opinion and voters during the 2016 presidential campaign, with attacks occurring before and during the electoral process. Twitter accounts linked to the Russian state-sponsored Internet Research Agency (IRA) were used to try to divide voters on a wide range of issues and data from these accounts were released by the United States Congress after an investigation . A largeRecent literature on Twitter disinformation is vast, but still insufficient. Different aspects of online social media disinformation have been actively researched over the recent years through qualitative and quantitative methods with the purpose of the detection of malevolent accounts and their discernment from one another. The most studied troll characteristics include linguistic profiles .HAVOK analysis was performed using the  package . The hav1 In short, dynamics of a system exist in a high dimensional space. We measure the system along one of the dominant axes in time and obtain a measured time series of the system. In psychology, this is what we have and where we startŮwe measure the time series of a phenomenon of interest. In the current case, we use the average network scores of the 3 Trump supporting topics in the right-wing troll tweets.How exactly does HAVOK operate?First we arrange our measured time series into a Hankel matrix, equivalent to the transpose of a time-delay-embedded matrix with lag 1 , where eThe next step consists of applying singular value decomposition (SVD) to the Hankel matrix Columns of The diffeomorphic to the first three dimensions of the true system attractor. In this context, diffeomorphic means that the true attractor is analogous in its behavior patterns at each corresponding time point to the reconstructed attractor.By plotting the first three of these latent time series on mutually orthogonal axes  and r (model degree/truncation parameter) hyperparameter space where stackmax ranged from 3 to 120, and r included all the possible model degrees within each stackmax . Derivatives of the truncated HAVOK analysis was applied to the preprocessed time series through the havok R package . 7,021 Hλ, of the hyperparameter space along with stackmax and r.Models with squared correlation r of 4 or higher were considered, with higher model degrees preferred within a cluster of well-fitting models , to possess a forcing term that was distinctly different from the forcing terms of the other 3 models, and to belong to the dominant forcing term cluster in the corresponding timescale range.Four models were then selected from the models that met the above criteria. Each of the models was selected to be representative of a distinct timescale  of the extracted forcing term events was the most appropriate for alignment with relevant political events.The forcing term had identifiable directionality that aligned with the context, i.e., the peaks identified forcing events that increased Twitter troll activity on selected topics, while troughs identified forcing events that potentially decreased it.stackmax. As you can see, the higher is the stackmax and, correspondingly, the number of days in the kernel, the more smoothed the time series are, and in turn the slower is the time scale of events that the model focused on. For instance, a stackmax of 36, given that we have 4 measurements per day is equivalent to 9 days. So it means that the model with such stackmax identifies systematic patterns in shifting 9-day long kernels. The longer the kernel, the more prominent and lower frequency events the HAVOK model will focus on, with longer kernels resulting in more smoothing and more focus on slower time scales.Application of HAVOK analysis to the preprocessed time series resulted in a number of well-fitting . The model with The , λ=.002  had R2 b λ=.1242  had R2 b06 model  had R2 b04 model  had R2 bstackmax and, accordingly, the length of the timescale and the level of smoothing increase, the These estimates are low due to the high frequency intraday fluctuations being smoothed over and discounted in the major latent component of the time series. As the Many well-fitting models were available at different time-scales. At some timescales no well-fitting models were available, potentially showing that those particular timescales were not aligned with the timescale of events that forced the system. In the context of the troll data, those would be the time-scales of events that did not incite troll tweets. On the other hand some timescale ranges had multiple well-fitting models available, implying that those time-scale ranges align with the frequencies of the most prominent events that affected the system.Out of these 4 models, the one with the kernel of length 16 days was surrounded by the densest cluster of well-fitting models in the hyperparameter space implying that this model is potentially appropriately capturing the time-scale of the most influential events that incited active troll tweets.In this particular system the peaks correspond to the events that forced active Trump promotion on Twitter , while troughs correspond to sharply decreased Trump promotion activity . This interpretation is relevant only to this particular system, and will not necessarily be the case in other systems or even models of the same system. The meaning of the forcing term directions depends on the shape of the U-mode of the forcing term, its relationship to the other U-modes, as well the structure of the system’s attractor.It is noteworthy that the forcing peaks and troughs exhibit a different alignment pattern during the presidential debates. Forcing is active immediately before and right after each debate, but not during the debates, as might have been expected from the alignment of other events.st, 4th and 5th embedded dimensions  of the original time series. Atypically for HAVOK models, however, none of the following sequential derivatives representing U-modes are present. Instead, U-modes 2 through 5 possess phase-shifted sinusoidal shapes that resemble Fourier modes. U-modes 2 and 3 possess sinusoidal shapes of the same frequency lagged by The U-modes of the selected model are presented in th U-mode, which represents the kernel of the forcing term, is unique to the selected model (and the neighboring models clustered in the hyperparameter space). Its shape resembles a logistic curve with sinusoidal daily oscillations that oscillate in the opposite direction from the daily sinusoids in U-modes 2 and 3 in the first rd of the kernel, in the same direction as the daily sinusoids in U-modes 2 and 3 in the last rd of the kernel, and phase transition between the two in the middle rd of the kernel (see The 6rnel see . This keThe relationships between the latent time series components stackmax) regions that contain the largest and densest well-fitting model clusters are likely the most representative of the internal troll factory functioning and/or the timescales of external events that incited troll posting activity. Analogously, timescale regions that contain few well-fitting models are likely to be indicative of timescales that had no particular importance for the troll operation. When the models in low density timescale regions contained little similarity to the nearest dominant clusters, they were likely to indicate the transitions between dominant model structures at distinct timescales.Many well-fitting HAVOK models were found, representing different timescales. These models were clustered across and within different timescales in the Model a focused on the timescale equivalent to 3.5 days , and the manner in which the trolls tended to initiate and terminate their posting activity. Increased posting activity sometimes dissipated gradually as it lost relevance whereas sometimes the troll posting volume declined due to a second forcing event. In Insight into features of the troll operation can be gained from the dominant patterns of U-modes and model structures. U-mode structures that pervade clusters of well-fitting models are likely to have a meaningful structure that is representative of either the internal functioning of the troll factories, or the influence of external events on the troll activity patterns. For instance, U-modes can capture cyclicity and patterns of the rate of change in the troll activity. Repeating elements of the model structures that define the relationships between the U-modes can further inform us on the nature of connections between the different types of cyclicities and rates of change, as well as their stability and relationship to the external forcing. Distribution of the dominant U-modes across different timescales can also distinguish those that are timescale independent from those that are timescale specific.Model c suggest that day-night and four-day cycles were the most important dynamics, suggesting coupling with daily and weekly cycles rather than intrinsic dynamics of the troll postings. That is to say, there was less evidence that one posting led to the next in a deterministic way (intrinsic dynamics) than there was evidence that the postings were coupled to day-night cycles and four-day cycles. Day-night cycles and four-day cycles were present among the U-modes of all four models at four different timescales pictured in Model c, U-modes 2 & 3 are aligned with day-night cycles and modes 4 & 5 are aligned with four-day cycles. As can be seen in The U-modes of ynomials . Due to We explored this hypothesis by locating information from troll factory insider interviews. There is an 8 to 12 hour difference in time zones between the Moscow area in Russia and the USA. To be able to realistically align their tweet patterns with waking time in the USA, Russian trolls would need to work at night, which was confirmed by insiders , 2021a. irregularities in the cycles representing 12-hour shifts. The directional flip in the forcing kernel shape in the second half might indicate the normalization of the regular daily work schedule after a panic posting episode.The forcing term is out of sync (fluctuating in the opposite direction) with the 3rd U-mode daily cycles for the first one third  were all detected and interactions between them were explored.When applied across a range of hyperparameters, HAVOK has been shown to reveal the multi-timescale nature of the troll tweeting system with evidence that events forced the system at different timescales. HAVOK was able to determine many well-fitting models across all timescales of interest. It exhibited model fit patterns that distinguished the timescales that were representative of the troll factory functioning from the timescales that held no particular importance for the troll operation. The distribution of model features in the hyperparameter space allowed identification of features of the system that were timescale-universal from those that were timescale-specific. HAVOK’s separation of linear and nonlinear model features also allowed observation of the evolution of the interactions between timescale-specific external nonlinear forcing events and internal linear troll functioning patterns across timescales, making it possible to identify differences between trolls’ reactions to events at different time-scales.HAVOK identified the timing of nonlinear events that forced troll activity at different timescales. These nonlinear forcing events aligned with real world politically relevant events with striking precision. The forcing events precipitated changes in the measured time series of topical troll tweeting activity. The precipitation feature of the forcing events allowed determination of troll reaction speed patterns , and the manner in which the trolls tended to initiate and terminate their posting activity. The dominant model provided directional meaning for the forcing eventsŮforcing peaks preceded surges in troll tweeting activity, and forcing troughs preceded ebbs in the troll tweeting activity. The combined knowledge of the timing, the real world event alignment, and the precipitation and directionality of the forcing events permitted realistic explanations of the mechanisms underlying governance of the troll factory operation.HAVOK analysis provides a mathematically elegant state-space model of this system’s functioning. The model contained meaningfully interpretable structural components that could be mapped onto corresponding components of the real world troll operation system. The U-mode components, which typically extract the patterns of the rates of change in a form of sequential derivatives as Legendre polynomials in HAVOK models governed by intrinsic dynamics, instead captured pairs of phase-shifted cyclic components analogous to Fourier modes. This is evidence that HAVOK possesses an inherent ability to detect cyclic bases in a form of Fourier modes, when the analyzed system is coupled to stationary external forcing. The domination of the cyclic components across Russian Twitter troll activity models at all timescales suggests that coupling with the detected cycles rather than intrinsic dynamics of the troll postings were the most important dynamics of the analyzed system. The alignment of the detected cycles with the Russian troll factory operation cycles was confirmed from insider interviews.Relationships between the cycles, the rates of change, and other basis elements were contained within the HAVOK models as coefficients connecting the latent time series This insight was achieved by reapplication of the HAVOK analysis across the hyperparameter space. It was surprising to us how reapplication of such a mathematically simple model provided a way to reverse engineer Russian manipulation strategies with impressive detail and alignment with the real world events. These results allow improved theoretical speculation about the future Russian troll activity and a method to quantitatively predict how future forcing events will manifest in the troll behavior. HAVOK models allow one to simulate a system’s response to hypothetical forcing events. Given that forcing events tend to precede events in the response time series, simulated responses generated by data from events in real time could allow for prediction and/or intervention. Simultaneous short-term forecasting of HAVOK components is also possible by the use of HAVOK forecasting extensions . All of Equally impressive results can be achieved by applying HAVOK across hyperparameter space to any intensive time series that meet the requirements listed in Supplement 1


A novel multi-directional eddy current thermography (ECT) system is presented generating sets of directional phase images that have been fused with a processing pipeline allowing for an improved probability of detection (POD). Inhomogeneous electromagnetic Joule heating derived from the diversion of induced eddy currents provoked by cracks, altering its path around as well as under its bottom, is the principal phenomenon enabling its usage as a non-destructive-evaluation (NDE) technique. Most induction thermography systems employ inductors derived from old designs, optimized for localized heating with a fixed magnetic field direction. This provokes a directional detection blind-spot for surfaces with random crack orientations. In this paper we have observed that the pattern associated with the thermal response distribution can be geometrically correlated to the relative orientation of the magnetic field regarding the crack, conforming to a rotating feature that has not been described before. Extracting the apparent motion as an optical flow, with a phase-shifting interpolation of the intermediate orientations, generates a signal that enables a robust segmentation of a wide variety of defects in ferritic and austenitic alloys. Its performance has been evaluated with two ‘Hit/Miss’ POD studies TIG welds Inconel 718 and Haynes 282 alloys. Results show an increased detectability regarding the manual labelling of the defects in the same directional set, employing the same input. Industrial manufacturing processes such as welding, steel hot rolling or casting are prone to cracks and porosity defects. Yet these defective features act as a stress concentration site which negatively affect the fatigue life and tensile properties of as-built parts. Furthermore, when these faulty parts are subjected to large mechanical forces defects in these components could lead to fatal consequences. Therefore, it is crucial to identify these defective parts through a quality inspection process, on the one hand, to ensure product quality and, on the other hand, to enhance material circularity, requalifying it or reusing it in some other process, i.e., minimizing environmental footprint. The detection of cracks in manufactured metal alloys is conventionally performed with techniques such as the magnetic particle inspection (MPI) and fluorescent penetrant inspection (FPI).1, techniques are commonly used for 100 %-testing of components and for spot checks, though eddy current testing is limited to relatively simple geometries, fails to find large-scale defects as well as shallow inclined cracks, and does not allow to identify the cracks in thin materials. In this contribution, IT is featured as an interesting alternative to overcome these limitations.However, the detectability of cracks using MPI and FPI is limited and depends on the inspector’s skill, which reduces the reliability of these techniques. Additionally, these methods require the use of toxic chemicals and may require the removal of the component’s coating before inspection, which increases both the manufacturing and inspection times. Moreover, the manual and time-consuming nature of traditional inspection processes does not fit well with modern manufacturing lines. As manufacturing processes have become increasingly automated and faster, inspection processes must keep pace to avoid creating bottlenecks in the production line. In industrial practice, both eddy current and induction thermography (IT)IT uses a probe comprised of a coiled conductive piece of wire close to a test surface to generate eddy currents. In essence, exciting a time varying current on the coil to generate a magnetic field. In the proximity to the test surface, the magnetic field interacts with the test part inducing eddy currents running opposite to the currents in the probe. The phase and amplitude of these eddy currents depend on the conductivity, permeability, and homogeneity properties of the test part. Indeed, the non-zero resistivity of the material produces Joule heating radiation and in particular, test-parts discontinuities, such as cracks produce a noticeable change in the radiated heating distribution. The losses associated with hysteresis during induction heating have a measurable effect on ferromagnetic materials, as they result from the friction produced by the oscillation of the magnetic poles. However, the relative contribution of the hysteresis losses to the overall heating is comparatively small compared to the Joule heating losses associated with the induced eddy currents.4. These studies are mostly based on extensive empirical analysis from both laboratory and field investigations of faults and advanced diagnosis applications.There is already a large literature focused on identifying the optimum parameter definition in the IT technique, i.e. finding the most suitable lock-in regimes considering the skin depth, the thermal penetration depth, and the crack dimensions to be detectedUndoubtedly, the results and conclusions of such investigations are of particular interest for current induction thermographic inspection applications, however, the detection of these cracks is strongly conditioned by the relative orientation between the crack and the direction of the magnetic field produced by the inductor, which is indeed a non-predictable variable.6. The robust detection of the cracks, regardless of its orientation is indeed one of the main challenges of IT. There is though a very limited number of studies dedicated to overcoming this critical drawback in IT, indeed the majority of modern induction systems stem from functional old designs that have been subsequently optimized to enhance induction heating, have been inherited from welding and thermal treatment applications8, and thus the generated magnetic field shows a unique direction in most cases. This limitation of the inductor can be overcome by scanning the area considering different orientations relative to the inductor. This rotation would require an external intervention such as a robot gripper but it also increases the inspection time, its cost and makes it more complex. Angle-independent thermo-inductive system have been previously demonstrated, employing a pair of Helmholtz coils disposed in an orthogonal manner containing the inspected part, resulting in a varying magnetic field orientation derived from the vector addition associated to an induction frequency differential9. The required containment of the part limits the potential use-cases of the system to small parts. Other approaches have recurred to the circular polarization of the eddy currents employing a tetra-pole inductor11 which generates a rotating magnetic field.Using a customary inductor, such as a dipole or a pair of Helmholtz coils which are composed of two coils, produces a fixed magnetic field with a predominant direction. This limits the resulting thermal disparity in the vicinity of the cracks in certain configurations. The magnitude of this effect is minimized when both the direction of the crack and the resulting eddy currents associated to the magnetic field are alignedThe main contributions of this paper lie in: (1) the identification of a new type of rotational feature associated to the tips and narrow points of the cracks and defects, which can be geometrically correlated with the direction of the magnetic field; (2) the development of an interpolation method to approximate the intermediate orientations of the magnetic field, while canceling a large part of the noise present in the phase images, which is not affected by the variation of the orientation of the magnetic field. (3) The design of a processing algorithm that fuses the directional phase images of the thermography, on a pixel-wise basis, exploiting the apparent motion of the pattern associated to the cracks, which has demonstrated good results in different materials and defect types. (4)The rigorous evaluation of the performance for the automatic detection of the cracks, following the MIL-HDBK-1823A standard, in two distinct types of TIG weld defects on Inconel 718 and Haynes 282, with 218 and 337 cracks respectively. Obtaining the a90/95 crack size, that is the crack size that can be detected with 90% probability with a confidence level of 95%. The results demonstrate a probability of detection that is not dependent on the relative orientation, with an increased detectability regarding the manual identification of the cracks in their respective phase images.f, and the vacuum An inductive thermography inspection system consists of three main components: a wave generator, an infrared camera, and an inductor. During the inspection, the inductor, powered by an alternating current, generates a magnetic field. This magnetic field interacts with the material, inducing eddy currents beneath the surface. The density distribution of these currents shows an exponential decay as you move away from the surface, decreasing to 1/e (approximately 37%) at the skin depth, The skin effect has implications for thermographic inspections because it affects the depth at which thermal patterns are detected. Higher-frequency currents or fields have shallower skin depths, resulting in more surface-sensitive measurements. Conversely, lower-frequency currents or fields penetrate deeper into the material, allowing for the detection of thermal patterns at greater depths. Moreover, surface geometry, the isotropy of the material, and the presence of cracks, pores, and sharp edges strongly influence the distribution and path of the eddy currents and lead to localized Joule heating. This heating causes a localized increase of the emitted infrared radiation, which is typically captured and measured using an infrared camera. While this procedure is widely used, there remains a need for critical analysis of these measurements to accurately assess the presence or absence of defects. Interestingly, the design and configuration of the induction device significantly influence the distribution of the radiated field, thereby presenting additional challenges in the analysis process.10, though it features the ability to further control the induced magnetic field on it.Conventional inductor designs, including dipoles and Helmholtz coils, are commonly constructed with twin or single coils that generate a magnetic field with a fixed direction. Consequently, the induced eddy currents exhibit a predominant direction aligned with the magnetic field. The interaction between the eddy currents and the defects is also influenced by the relative orientation of both, potentially causing the currents to flow around or beneath the defects. As previously stated, the presence of defects and the interplay with the eddy currents have been quantifiably observed in studies, particularly when the crack and the eddy currents are not parallel. Consequently, conventional inductors face significant limitations in consistently detecting defects in random crack samples. In contrast, a tunable induction system capable of rotating the induced magnetic field overcomes potential directional blind spots. A multidirectional inductor, capable of comprehensive coverage of all crack directions under examination, ensures that all cracks are subjected to the thermal stimulus. This capability becomes particularly important when dealing with complex shapes, irregular geometries, or components with varying thicknesses. With this regard, we devised a new tetra-polar inductor, based on the tetra-polar magnetic yoke reported inThe inductor, shown in Fig. i is one of the four orientations available using the proposed system. The specific orientations and their corresponding labels are presented in Table The resulting magnetic field of the 2 dipoles can be expressed as a vector addition in mentclass2pt{minim12. It incorporates a full-bridge inverter circuit with pulse-width modulation, operating within a continuous frequency range of 10 kHz to 60 kHz. And a switching device to alternate between the different states.The complete experimental setup is shown in Fig. 6.To demonstrate the multi-directional induction capability of the system, a set of experiments has been carried out to analyze this aspect. Previous research has empirically demonstrated the relation between the thermal response and the relative orientation between the longitudinal direction of the crack and the magnetic field1. Note that in this case, the carrier frequency is typically called lock-in frequency. This results in the most accepted metric to evaluate the thermal response for this type of application, defined as the absolute phase contrast13, subtracting the local maxima and minima of the pattern, denoted as This relation can be used to determine if the magnetic field is effectively rotating, by generating a similar thermal response by maintaining the same relative orientation of the magnetic field, mentclass2pt{minimThe measurements parameters are described in the first line of Table psi confirming an equivalent thermal response associated to the direction of the magnetic field.Note that both the inductor and the camera remain stationary for all the measurements, with the same recording and thermo-inductive parameters. Figure Another aspect to consider, that has not been previously exposed, is the apparent rotation of the pattern as a function of The resulting polar profile of each I, resulting in the following expression.15. In the current induction scheme shifting sequence, , a generalized method, such as the one exposed in16 has been employed, yielding the global solution, as a function of the pixel intensities.The shifted polar profiles shown in Fig. The amplitude, entclass1pt{minima17, which is based on two assumptions. The first one being a photometric consistency of the moving point formulated as a line constraint or direction, written as,The normalized rotational motion associated from the phase-shifted interpolation can be effectively described as an invariant feature of the cracks. The apparent motion between two images can be estimated with a method known as the optical flow (OF). The relative translation between two consecutive frames can be defined as 18, while modern approaches employ supervised Convolutional Neural Networks showing an improved performance19. OF thermographic use-cases have been mainly employed in image stabilization to generate pseudo-static sequences20, as well as an alternative thermal signal processing21.Other common methods, rely on image pyramids to extrapolate the flow regardless of the scale22, implemented in OpenCV, computing the consecutive synthetic images uniformly sampled with the expression , regarding the total number of defects, denoted as a. In many applications, the appraisal of an inspection technique is typically associated with the bigger defect to miss, and for this reason, the POD is generally expressed as a function of the defect size, defined as an ideal binary step function. In a realistic situation, the POD is typically described as an ascending sigmoid function, that can be modelled in many ways. The most accepted HM-POD model to fit the set of binary points associated to the experiments, is the log-logistic distribution25, written as:m and 26.In the previous section, a robust establishment of the ground-truth of the defects has been presented and all cracks have been measured. This characterization is necessary for a POD analysis to evaluate the performance of the method presented in this article, relative to existing ones. For the POD analysis, the “Hit and Miss” (HM-POD) model has been employed, following the MIL-HDBK-1823A standard. This procedure is considered the state of the art for conducting POD studies in many industries27, stating that a set of 60 cracks is the minimum required. The followed HM-POD, for both Haynes and Inconel sets, has consisted in the following steps.An enhanced FPI to stablish ground-truth and labelling of the defects and length.Phase-shifted induction thermography with a manual labelling of the butterfly pattern present in each phase image.The processing pipeline shown in Fig. Alignment and correlation of detected points with the ground-truth.Note that an added difficulty to the correlation of the detected points is the clustered distribution of some cracks, with a corresponding local maxima plateau covering multiple cracks, as it can be seen in Figs. In this scenario, the natural cracks arising from the TIG and Laser welds have been produced on two types of alloys, namely, Inconel 718 and Haynes 282. Since the materials have different types of cracks, as well as ferromagnetic properties and surface emissivity, affecting the perceived thermal response of the signal, it has been estimated that the POD analysis must be separated in two sets with their own distinct results. A set of 13 samples with 218 cracks for the Inconel case, and 14 samples with 337 cracks for the Haynes case, has been used to conduct both analyses according toBoth the Inconel and Haynes have a set of 4 hit and miss values corresponding to the manual labelling of the butterfly patterns for each direction, a 5th one associated to the union of the 4 phase images, and the 6th one linked to the phase-shifting. Since the manually labelled mono-directional phase-images are so sensible to the orientation, they generate a hit-miss distribution that is very difficult to reliably fit resulting in very poor results.24. The corresponding results of the analysis are summarized in Table To have a fair comparison, the union of the manual labelling of all the directions has been considered to effectively employ the same input as the phase-shifted method. The HM-POD curves are shown in Fig. In this paper, a novel multi-directional thermo-inductive system has been proposed which is able to generate thermographies with a discrete set of predominant eddy current directions. The multiple orientations of the eddy currents generate a varying path around the defect, resulting in a thermal response dependent on a directional component. The 4 directional observations produced by the exposed system enable the detection of cracks with an unknown orientation.The variation of the phase image pattern, regarding the magnetic field orientation, exhibits a new type of rotating feature that has not been described before. This differentiating feature has motivated the development of a processing technique, inspired by the phase-shifting, based on the integration of the relative motion of the thermal response. This directional thermal response has also been observed in a set of different samples and types of cracks.Note that the resulting thermal response of the pulses is based on the composition of the current and precedent ones. The separation of both effects could generate an improved thermal contrast, compared to a FFT of the raw thermogram, such as the one employed in this article for simplicity. The superposition of multiple induction modalities, combining discrete or continuous directional and temporal moneodulations remains an interesting topic, which could potentially yield to complementary information.The whole processing technique has exploited the rotating motion of the cracks in steel and superalloys such as Inconel 718, and Haynes 282, showing a strong correlation in all the exposed cases. The performance evaluation of this technique has been conducted with a ‘Hit/Miss’ Probability of Detection model, showing an increased sensitivity regarding the manual labelling of the phase-images butterfly patterns of the cracks. Future works should focus on the generalization of the technique to all types of defects, employing machine learning models, or neural networks, that would be able to carry out a fused training of the set of the discrete set of directional images. Multi-spectral and color-based Convolutional Neural Networks seem like good candidates to generalize the technique to enable an increased sensitivity of the phase-shifted induction thermography. Alternatively, the development of taylor made techniques that would focus on a sparse statistical reduction of the optical flow, into a set of trainable descriptors would also be a worthwhile option to explore in upcoming iterations. Ultimately, a rigorous physical modelling of the observed phenomena is necessary to further optimize the technique or develop new methods, as well as an eventual extrapolation to other use-cases.


Electrical Impedance Tomography (EIT) is a low-cost imaging method which reconstructs two-dimensional cross-sectional images, visualising the impedance change within the thorax. However, the reconstruction of an EIT image is an ill-posed inverse problem. In addition, blurring, anatomical alignment, and reconstruction artefacts can hinder the interpretation of EIT images. In this contribution, we introduce a patient-specific structural prior mask into the EIT reconstruction process, with the aim of improving image interpretability. Such a prior mask ensures that only conductivity changes within the lung regions are reconstructed. To evaluate the influence of the introduced structural prior mask, we conducted numerical simulations with two scopes in terms of their different ventilation statuses and varying atelectasis scales. Quantitative analysis, including the reconstruction error and figures of merit, was applied in the evaluation procedure. The results show that the morphological structures of the lungs introduced by the mask are preserved in the EIT reconstructions and the reconstruction artefacts are decreased, reducing the reconstruction error by 25.9% and 17.7%, respectively, in the two EIT algorithms included in this contribution. The use of the structural prior mask conclusively improves the interpretability of the EIT images, which could facilitate better diagnosis and decision-making in clinical settings. Electrical Impedance Tomography (EIT) is a medical imaging modality which is mainly used to visualise the ventilation distribution of the lungs at the bedside . The estDespite all of these benefits, EIT reconstruction leads to a mathematically ill-posed inverse problem characterized by large degrees of freedom, mainly because of the nonlinear nature of the relation between conductivity changes and boundary voltage measurements ,9. ReconHowever, EIT images continue to be characterized by low spatial resolution, blurred anatomical alignment, and reconstruction-induced artefacts. These make them difficult to interpret in clinical settings. The combination of modalities as priors to improve image accuracy is a common concept, and can be applied to EIT. Several research groups have reported on the method of introducing structural prior information into the EIT reconstruction process ,18,19,20Additionally, it is common to incorporate data from one medical imaging technique into another in order to enhance the reconstruction or improve the interpretability of the results, e.g., PET-CT. There is a possibility of introducing patient-specific information obtained from, e.g., CT scans, into the EIT reconstruction process, such as through a structural prior mask . The masThe objective of this contribution is to investigate the influence of a personalized structural prior mask on EIT reconstructions, particularly using the Gauss–Newton (GN) EIT algorithm and DCT-based EIT algorithm. Two scopes of numerical simulations differing in terms of ventilation status and atelectasis scales were conducted. We reconstructed EIT images using the selected EIT algorithms with and without a structural prior mask. To analyse the influence of the structural prior mask, an evaluation of EIT reconstructions was conducted quantitatively in terms of the pixel-wise reconstruction error and figures of merit.An EIT algorithm reconstructs the variation of the electrical conductivity distribution i of j within the FEM. With these assumptions,  using the EIDORS toolbox . A 3D FEAs an example, ventilation pattern c is demonstrated in The second scope of simulation was designed as nine different increasing scales of atelectasis in the dorsal parts of both lungs, i.e., 10% to 90% with a step of 10%. These simulations are closer to a patient with a deteriorating status. Similar to the first simulation settings, the conductivity of the elements belonging to the ventilated lung region was changed to inverse crime’ [For each of the simulation settings, the boundary voltage measurement e crime’ . It is wIn this section, we introduce several evaluation parameters to quantitatively analyse the EIT reconstructions. These parameters are defined exclusively when the ground truth is known.reconstruction error (M rows and N columns.The one’ and the non-lung region as ‘zero’. The lung region of the ground truth in the simulation is the same as The figures of merit of the reconstructed image, which have been mentioned by several publications ,19,26, w as P in . IllustrDislocation is the figure of merit used to evaluate the reconstructed position error of the lungs:Shape deformation quantitatively evaluates the corresponding lung regions Ring effect is the ratio of the sum of the negative pixel values and the sum of the absolute pixel values in the reconstruction Amplitude response is defined as the ratio of the sum of the pixel values of the reconstruction amplitude response. It should ideally stay constant, which allows for a quantitative analysis, e.g., air distribution within the lung area.In general, a small value for the figures of merit represents a good reconstruction. The only exception is the The conductivity reconstructions for the four different ventilation patterns using the GN and DCT approaches are depicted in The reconstruction errors calculated using the pixel-wise The figures of merit of the reconstructions using the GN or DCT approaches with and without a structural prior mask are depicted in The results for the simulations in terms of different atelectasis scales are illustrated in The corresponding reconstruction errors are depicted in The figures of merit calculated from each EIT image in In this contribution, we implemented two scopes of numerical simulations to investigate the influence of a structural prior mask on EIT images using the GN and DCT approaches. In the first scope of simulations, four different ventilation patterns were simulated. A decreasing atelectasis scale of the dorsal lung was conducted in the second scope of our simulations. Overall, the EIT images reconstructed using the GN and DCT approaches benefited from the implemented structural prior thanks to improved interpretability. This result secures a more accurate EIT reconstruction as confirmed by different quantitative evaluations, including the reconstruction error and figures of merit.The structural prior mask considerably improves the accuracy and interpretability of the resulting EIT image. In It is common to combine data from different medical imaging methods to achieve better interpretability. However, it is worth noting that structural prior masks introduced to the EIT reconstruction process are usually derived from CT or MRI images representing the patient’s status at a certain time, while EIT is generally used to monitor a patient’s continuously changing status. In our simulation, the structural prior represents two healthy lungs without atelectasis, which means that the structural priors will not be accurate if there are atelectasis or non-ventilation areas in the simulation. Nevertheless, the majority of EIT images show benefits from the structural prior mask cf. . HoweverThe fact that this study only used simulation experiments to evaluate the impact of the structural prior mask is one of its limitations. Additional studies with phantoms and clinical data are necessary to validate this method. In this contribution, we introduced the structural prior through the application of a corresponding mask. There are further methods to include patient-specific structural prior information into EIT algorithms, e.g., through sub-domain based regularization or soft-prior regularization ,31. FutuNevertheless, reconstruction using the GN or DCT approaches can lead to enhanced interpretability if an accurate structural prior mask is implemented. The incorporation of structural information from a prior mask and functional data from EIT creates patient-specific EIT imaging. This enables a comprehensive understanding of pulmonary pathophysiology by preserving the anatomical structure of the lungs and correlating regional lung behavior with morphological structures.Simulations with two different scopes were used to evaluate the impact of a structural prior mask on the EIT images from two different EIT algorithms. In conclusion, using a structural prior mask can improve the accuracy of EIT images. This is confirmed by the reduced