Typical crack detection processes in digital images produce a binary-segmented image that constitutes the basis for all of the following analyses. Binary images are, however, an unsatisfactory data format for advanced crack analysis algorithms due to their sparse nature and lack of significant data structuring. Therefore, this work instead proposes a new approach based on Euclidean graphs as functional crack pattern descriptors for all post-detection analyses. Conveying both geometrical and topological information in an integrated representation, Euclidean graphs are an ideal structure for efficient crack path description, as they precisely locate the cracks on the original image and capture salient crack skeleton features. Several Euclidean graph-based algorithms for autonomous crack refining, correlation and analysis are described, with significant advantages in both their capabilities and implementation convenience over the traditional, binary image-based approach. Moreover, Euclidean graphs allow the autonomous selection of specific cracks or crack parts based on objective criteria. Well-known performance metrics, namely precision, recall, intersection over union and F1-score, have been adapted for use with Euclidean graphs. The automated generation of Euclidean graphs from binary-segmented images is also reported, enabling the application of this technique to most existing detection methods  for cracks and other curvilinear features in digital images. Surface crack monitoring is of primary importance in the structural assessment of structures made from concrete ,2 or othThe analysis of a crack image is typically subdivided into a first detection phase, where the possible surface cracks are identified through a specific image segmentation process, and a subsequent post-detection phase, where the recognized cracks are refined, selected and analyzed. Several methods were studied for automatic and semiautomatic crack detection, from traditional image processing techniques such as threshold segmentation or edge detection ,27,28, tBinary images, however, are not the best data format for the implementation of advanced crack refining and analysis algorithms, due to their very sparse nature and the lack of any meaningful data structuring (aside from the Cartesian coordinates of each identified pixel). This results in the necessity to identify each needed crack feature by direct search on the binary image itself . MoreoveAn ideal data structure for crack description should instead capture the essentials of the crack pattern, ensuring an effective computational availability of the main crack path features for direct analysis . At the same time, such structure should provide for a quick and precise localization of the crack path and the related features on the original grayscale image when this is required for specific measurements.A weighted graph is a set of vertices (nodes) connected by edges (links), each of the latter having a numerical value (weight) associated with it. An Euclidean graph (EG) is a weighted graph where each vertex corresponds to a point in an Euclidean space . Most crack analyses, such as length , tortuosIn this work, it is therefore proposed to use an EG-based description of the crack pattern for all of the post-detection refinement and analysis processes instead of using the binary-segmented image. The EG is obtained from the latter through a skeletonization step that reduces all of the detected cracks to their single-pixel-wide medial line.The skeletonized crack image is explored only once during the EG generation, then all of the related information is recorded in the EG, ensuring a very wide computational availability for following processes.The topological and geometrical information conveyed by EGs allows the implementation of tailored algorithms for the refinement of the detected cracks and for their selection, classification, processing and analysis.Particular cracks and crack zones can be algorithmically identified and classified on the EG itself according to specific requirements .The position information associated with each EG vertex allows a precise crack localization on the original image for specific measurement tasks .The EG can constitute the foundation of a machine-readable, high-resolution crack pattern documentation for archiving and later analysis .This approach offers, among the others, the following advantages:Furthermore, EGs allow for easy manipulation for the refinement of a crack pattern, such as edge insertion and deletion for crack merging and separation. EGs can also be modified for smoothing  and on the original grayscale image by direction of crack EG (crack width) are described alongside an image-to-image crack correlation analysis in the whole time-series image set. The advantages obtained in the refinement of the crack paths and in the following crack analyses are discussed and compared with the traditional implementation based on the direct analysis of the binary segmented image.It is worth noting that the EG representation of a crack network can be handled with a wide variety of methods thanks to its compact description of both topological and geometrical crack skeleton features, allowing the development of a broad family of procedures for accurate crack pattern refining and analysis. Some of these are described in the present work, but this is only a small set of possible processing strategies made available by this approach, which allows to merge the large collection of algorithms developed for graph processing with the extensive variety of digital image analysis methods reported in the literature.Moreover, an EG representation of a curvilinear feature can be easily derived from any binary-segmented image. EG-mediated analyses can therefore be applied to any detection process that results in a binary segmentation, such as threshold-based methods or pixel-wise CNN-based algorithms.The implementation of an EG-based pattern description can therefore provide great advantages in the image processing of cracks and other line-shaped features, leading to a unified approach for all post-detection refinements and analyses and allowing the full exploitation of the potentials given by most of the classic and advanced detection methods.The application of EGs in the analysis of crack images is illustrated in the present work by studying the cracks developed during the tensile strength test of reinforced cementitious renders used as a base coat for building thermal insulation systems. The cracks were generated by applying a controlled strain on a 600 × 100 mm strip sample using a static uniaxial tensile testing machine, generating a sequence of up to five images recorded at an increasing strain level.f/2 lens . The illumination source used to optimize the crack detection was a 180 mm diffused side annular red LED light . A lens-mounted 660 nm passband filter centered on LED emission band  ensured negligible disturbance by ambient light.All images were recorded with a 6576 × 4384 pixel CCD monochromatic camera  equipped with a 50 mm, The acquisition system was installed on a tensile testing machine with a geometry optimized in order to image a 10 × 10 cm sample surface with maximizing resolution. The resulting sample-image sensor distance was 344 mm, with 23.8 μm/px nominal reproduction scale at the sample surface. The actual reproduction scale can vary slightly in each setup because of sample positioning tolerances on the testing machine and must be evaluated each time by means of a calibrated target. The illumination angle was chosen as a compromise between the need to maximize crack contrast (that requires a large angle of incidence) and to minimize the shading due to the sample surface roughness . In this work, the annular illumination system was positioned at a 50 mm distance from the sample surface.f/8) in order to optimize resolution and depth of field. Images were recorded as grayscale, uncompressed files  with 8 bits per pixel using the manufacturer’s acquisition software . Illumination source power and exposure time were adjusted in order to optimize the image intensity histogram.All images are recorded at medium lens aperture  that were recorded on the image as a low-contrast, 1-pixel-wide feature. The actual EG representation was generated by software, tracking the crack path between closely spaced points visually identified on a high-magnification representation of the sample image.The software used for EG-based crack image analysis was developed in-house in C language using the Xcode 9.2 (LLVM/Clang) development system . Camera image files (.bmp file format) were read with custom routines and stored internally as an 8-bit grayscale representation. Images for illustrations were saved as PDF or PNG file using operating system routines . Figures and illustrations were created with Affinity Designer 1.10 .The whole analysis process is depicted in the flowchart of The binary segmented image is then skeletonized . A raw, primal EG is directly derived from the skeletonized image with complete information retention. The primal EG is then processed in order to obtain the final EG, which is a functional description of the crack pattern captured in the original image. This latter step is depicted in detail in The potential of EG-based analysis will be illustrated using a simple automated crack image analysis process as example. The reported process is based on a threshold binarization detection that results in a relatively low-quality binary segmentation, which is ideal for demonstrating various EG-based refinement techniques. The finished crack description will then be used to demonstrate several EG-based fracture analyses.All of the reported results were obtained by studying the cracking of reinforced cementitious render samples under a tensile strength test . The speEven with the quite simple algorithms presented in this work, the adoption of an EG-based crack pattern description can provide interesting enough results that are illustrated and commented on in the following sections. In particular, the advantages are discussed in comparison with the usual implementation based on the direct analysis of the binary-segmented image.In the present work, the sole grayscale image preprocessing step is the cutting of original image edges in order to include the sample surface only. It is, however, important to note that image preprocessing methods that can interfere with particular crack measurements (such as crack width) may be safely used here because critical quantifications requiring image access will be carried out later on the original image, using the obtained EG as a guide for accurate crack localization.3 pixels versus 18.1 × 106 total pixel count). While demonstrating a reasonable compromise between crack capture and noise rejection, the binarized image retains a significant portion of the noise and, at the same time, exhibits a notable crack fragmentation.A 4136 × 4384-pixel, 8-bit grayscale image of a 10 × 10 cm sample area is cut from the original 6576 × 4384-pixel image of a reinforced render sample strip loaded with 1.5% strain a. The imIn this work, the segmentation is implemented with threshold binarization, a classical and well-known process with a wide coverage in the literature ,43. The The whole process thus appears quite robust in respect to the binary thresholding alone, relaxing to some extent the criticality of the latter and allowing to obtain a final, neat crack EG description that is less dependent on the selected threshold level.An example is given in Given the above considerations, in the present study a simple global binarization threshold level is thus used for EG generation, and it is computed as 65% of the central value of the most significant peak in the whole image histogram. This results in a fairly complete but noisy and somewhat fragmented crack capture represented by a binary image segmentation b.The obtained binarized image is then skeletonized , which is a key step in order to allow the computation of the crack EG. Skeletonization algorithms are of central importance in image processing and computer vision, with numerous approaches described in the literature ,48,49,50From the 8-connected skeleton, it is possible to generate a primal EG that completely describes the skeleton path, retaining all the related information. In the primal EG, each vertex corresponds to a skeleton pixel and each edge corresponds to a neighboring pixel connection .A graph generation process constituted by a scan routine that looks for foreground pixel clusters in the skeletonized image and a subgraph building algorithm see . Moreove3 . The resulting primal EG, directly derived from the skeletonized image, retains all skeleton features yielding a graph with 157 × 103 vertices distributed in 59 × 103 subgraphs  are now readily available for all of the following processes without any further exploration of the skeletonized image. This is a distinctive advantage of the EG representation in comparison to the direct analysis of the binary image, where this information must be retrieved each time by scanning the image itself.The quality of the crack pattern description given by the primal EG  is strictly dependent on the upstream segmentation and skeletonization processes. Moreover, specific analyses may have particular quality requirements . In order to provide an effective functional description of the cracks appearing in the image, the primal EG must therefore be refined with a specific finishing process which includes, among the other things, noise filtering, artefacts elimination and crack merging . Primal EG elaboration is thus of central importance, and for the purposes of this work, an automated process is developed based on a series of successive noise elimination and crack correlation steps that take advantage of both the geometrical and the topological properties of crack EG b. In parNoise removal is the first step of the primal EG refining process. As previously discussed, the binarization of noisy images inevitably produces a considerable number of false positives , which can be challenging to avoid in the first place and to filter out in the post-binarization process. False positive foreground clusters subsequently translate to crack-unrelated subgraphs in the resulting EG that must be identified and removed.−1. This remarkably simple process effectively removes the most part of noise artefacts (An example of a noisy sample is given in rtefacts c. A subsrtefacts d.3 vertices (>69%) and >58 × 103 subgraphs (>99.3%), leading to a near complete noise elimination but substantially retaining almost all crack features . Therefore, calculating both the subgraph diameter and the diameter/vertex count ratio is a relatively inexpensive process. The same analysis carried out directly on the skeletonized image instead requires, for each foreground pixel cluster, its localization on the image itself, the localization of all the related end pixels by tracking the cluster path and the computation of the total pixel count. This is a relevant consideration due to the high number of subgraphs (tens of thousands) typically present in the primal EG of large images.A possible alternative to the specific search for noise-related pixels is to process the whole binary segmented image directly with morphological operators  in order to eliminate small isolated pixel clusters and then reconstruct the original shape of the remaining image objects . The maiTypically, the same tradeoff in the binarization process between complete crack description and background noise removal also leads to an incomplete crack capture in the binarized image, resulting in a fragmented crack graph. Separated subgraphs belonging to a single crack must then be identified and joined. This latter task is accomplished by the introduction of new edges between the relevant vertices in the involved subgraphs. There are several ways to identify the subgraphs to be joined. As an example, Ammouche et al.  developeAn example of incomplete capture of crack pattern is reported in As in the noise removal step, the EG representation eases the process’ computational requirements thanks to the quick localization of end vertices in the graph structure in contrast with the specific pixel search needed when operating on the binary segmented image. Moreover, the EG description allows a straightforward merging of subgraphs by means of edge insertion instead of the morphological manipulations needed for connecting discontinuities in pixel clusters directly on the segmented image .During the noise removal process, several small subgraphs that belong to genuine cracks are inevitably filtered out. Subsequently, the formerly described subgraph merging step introduces large distal edges in place of the removed subgraphs. The latter can then be recovered by performing a specific search on the primal EG, looking for eligible subgraphs located in the corresponding surroundings of each distal edge. Details of the implemented algorithm are reported in A particularly severe example of subgraph loss is depicted in 3 vertices (+5.0%) previously present in the EG.In the sample depicted in As in the previous examples, the EG crack description allows an easier implementation of the subgraph recovery algorithm that, in the case of the analysis carried out on the skeletonized image, should instead be implemented with searching processes at the pixel level and image manipulations. A possible alternative is to operate directly on the whole segmented binary image with morphological operations to fill discontinuities in proximal pixel clusters . HoweverAfter the merging and recovering procedures, the EG is composed of an array of subgraphs, each one related to a significant crack in the original image. Some noise artefacts that are undetected by the former filtering process and some cracks that are too small to be significant can still be present in the EG, however. At this analysis stage, it can thus be useful to implement a further filtration step in order to fully clean up the crack EG. Considering that all of the relevant crack parts are already grouped into large subgraphs, at this stage a simple subgraph filtering step based on the vertex count is applied, eliminating all subgraphs with fewer than 200 vertices.This yields in the example given in Depending on the objective of the whole analysis, it can be useful to identify the main path and the secondary branches of each crack for separate evaluation or for morphological assessment. Moreover, the skeletonization process can generate artefacts due to local variations in crack thickness in the form of parasitic short branches that protrude from the skeleton path . These tIn the present case, all sample cracks are produced by the application of unidirectional loading and are therefore characterized by low branching and by the absence of random map, grid-like features . ConsequAs an example, a typical crack EG containing short parasitic side branches due to noise or local variability in crack width is shown in In the complete image analysis reported in The advantages of implementing the crack path description by EGs become apparent when considering alternative approaches based on the direct analysis of the binary-segmented image. A thorough description of the morphological separation of branching cracks in binary images is given by Arena et al. . In thisDepending on the specific purpose of the analysis, each identified crack can be considered as independent from the others, or it may be advisable to perform a search for possible correlations of contiguous cracks. As an example, in the laboratory samples measured in the present work, large cracks are typically generated perpendicularly to the strain vector at the reinforcing fibers. Consequently, it is of great convenience to consider all contiguous cracks formed along these preferential directions as parts of bigger cracks. The availability of an EG-based crack description allows the implementation of several algorithms for the evaluation of possible correlations between different cracks included in a single image. This study uses a correlation search algorithm based on the relative orientation (<45° angle) and distance (<10 mm) of subgraph end parts  is shown in In greater detail, the lower recall value in the final EG is due to missing crack parts related to very thin features mostly located on crack ends b. This iThe refined EG is then available as a basis for several different EG-based crack analyses, some of which are reported in the following sections.The obtained final EG gives an effective functional description of the crack pattern on the sample surface, with each crack individually represented by a connected sub-EG. As previously noted, with the implemented procedure, all the final EG vertices retain the strict correlation with the image pixel from which they are derived, and they are thus localized with single pixel precision. By describing the crack paths with a high resolution, the final EG allows direct EG analyses , EG-driven analyses on the original image  and crack correlation analyses in time-series images .In the analysis of cracked surfaces, it can be convenient to select particular cracks and even specific crack parts to be measured according to the objectives of the analysis itself. As an example, during crack width measurement, it is usually appropriate to avoid intersection zones. It is possible to eliminate these disturbing features directly on the binarized image by using a series of cleverly arranged morphological operations on the image itself, as described by Soroushian et al. . NeverthIn the present work, the position of each EG vertex is determined from the skeletonized image and never modified . Therefore, the actual positional precision of the crack pattern in the final EG depends directly on the implemented image segmentation and skeletonization procedures. Several algorithms were proposed in the literature both for binarization ,28,34 anAs mentioned above, all vertices in the final EG are bound to specific pixels in the original digital image and are therefore localized by discrete spatial coordinates. Consequently, even if the EG path of a horizontal, vertical or 45° diagonal line is constituted by a series of aligned vertices, paths at every other inclination generate rough EGs composed of a saw-edged succession of short segments. The EG of a generic curve is thus represented by a discrete approximation made from a jagging path through the image pixel grid. This can lead to errors in some measurements carried out on pristine EG . This problem can be addressed by using a smoothed EG in order to perform critical measurements with a more even path.In this work, a simple but effective iterative algorithm for EG smoothing  or the length of the shortest path between the most distant end points . Depending on the application, it may also be appropriate to include in the length determination all major branches excluding small cycles and minor features or even to evaluate the cumulative length of all crack parts exhibiting a width value greater than a given minimum. As previously discussed, the availability of EG crack description allows to fine-tune the crack parts to be measured according to well-defined selection rules.In the present work, the crack length is defined as the cumulative length of the whole crack path reported in the final EG  measured as the sum of Euclidean distances between connected vertices . Moreover, in order to minimize the errors due to the discrete nature of the image grid (from which the EG is derived), in the present study a three-cycle EG smoothing procedure  is used The analysis of crack branching can be directly derived from the final EG. As described in Besides direct measurements, the EG-based description of a crack pattern, expressed in pixel coordinates, also allows a guided crack analysis on the original image. One of the most important applications is the measurement of crack width, that can greatly benefit from the EG description. In fact, such description allows to easily select relevant crack portions to be measured and to implement tailored algorithms for EG-driven width measurement on the original grayscale image .The crack width can be defined globally for the whole crack or locally at a given crack path point, with various image-based measurement procedures described in the literature. As an example, in the former case, the mean crack width may be evaluated by dividing the entire crack area by the measured crack length ,35. In aAll crack examples analyzed in this work are recorded in samples under tensile test . Consequently, the parallel lines approach is adopted, using fixed-length measurement lines oriented as the strain vector. The crack width determination along an arbitrary measurement line requires the extraction of the original image intensity values in a direction typically unrelated to an image axis . This can be achieved by locating a series of sampling points at constant intervals on the measurement line itself  and thenIn this study, the crack width measurements are carried out with parallel measurement lines oriented along the strain direction and separated by a constant 0.8-pixel distance. Each local width measurement is performed starting from the intersection of the respective measurement line with the crack EG  and takiWhile several examples of crack width determination carried out directly on the segmented binary image have been described in the literature ,22,36, tA usual requirement for field and laboratory damage evaluation is the assessment of the temporal evolution of the crack pattern. In these studies, crack images recorded at different times are typically compared in order to assess the progression of crack count and the evolution of length, width and branching of each detected crack.As an example, the typical render tensile test used in this study  producesIt is thus very convenient to describe the crack pattern evolution with a genealogy tree, where each crack in different images  is represented with a vertex and the crack relationships are represented by edges. This representation allows to model the evolution of the crack pattern, enabling the automated analysis of time-related crack properties. In order to build the crack genealogy tree, it is necessary to identify all crack correspondences in the whole image series. The actual crack association through different images can be carried out on the EG crack representations looking for the best correspondence of the crack patterns . Moreover, in the present work, the camera is secured to the test machine so the only recorded crack movements are due to sample deformation during the test. The latter causes the sample surface (and thus the cracks) to move in the strain direction and, considering that the sample bottom side is fixed and the strain is applied to the upper side, all apparent movements are always directed upwards. The search for the correlated cracks in image series is thus performed, seeking, for each crack, the nearest sub-EG in the following image, taking into account the expected movement of the sample surface. This results in an effective crack matching process that allows to reliably reconstruct the crack genealogy tree and to correlate the measured crack parameters to the test progression.The image reported in The analysis of the crack evolution results in a specific genealogy tree for each crack recorded in the final step image. The computed trees  show twoThe obtained representation enables the automated analysis of time-related crack properties. As an example, the progression of crack width with applied strain is reported in The previously described enhancements in crack pattern refinement and analysis made possible by the EG-based description allow to increase the reliability of such analyses with interesting potential in the development of systems for automated structural health monitoring. Moreover, the availability of crack EGs allows to perform an effective image-to-image crack correlation using polished path data, avoiding possible issues related to noise and image segmentation artefacts.This work proposes a new strategy for the automated analysis of crack images based on the use of EGs as crack pattern descriptors for all post-detection processes. EGs integrate both geometrical and topological information of the detected crack path in a compact representation, facilitating the development of effective algorithms for crack refining, selection, correlation and analyses. The repeated explorations of the bitmap image required with the traditional approach are then replaced by the single initial scan required to generate the primal EG, which then becomes the unique, highly accessible reference for all of the crack path information contained in the skeletonized image. After a finishing process, the required crack analyses can be carried out both directly on the resulting final EG and/or on the original grayscale image using the final EG as a guide (thus avoiding issues related to image manipulations during the identification process).The described approach offers several other advantages, including the easy manipulation and refinement of the crack pattern, the precise localization of the crack on the original image and the availability of a very accurate functional description of the crack path that is an invaluable resource for documentation and postponed analyses. The obtained EGs can also be evaluated with standard performance metrics, specifically adapted for use with EG crack representations.Moreover, the EG description allows the automated selection of particular cracks and crack features using objective criteria based on the geometrical and topological features of the EG path, enabling the autonomous execution of specific analyses on selected crack parts .Since EGs can be derived from any binary-segmented image, the described strategy can be applied to most crack detection approaches, allowing the implementation of sophisticated post-detection refinements and analyses that would be difficult or impossible to implement directly on the pristine segmented image. The EG representation of the crack pattern therefore constitutes an ideal interface between any crack detection algorithms resulting in a binary segmentation  and the following post-detection analysis processes.The effectiveness of the described approach is demonstrated by a challenging case based on the analysis of a laboratory render strip tensile strength test, characterized by a high noise level due to a very pronounced surface texture due to the sample roughness. Moreover, the simple crack detection algorithm adopted, based on the global threshold binary segmentation, provides a raw starting point that requires a substantial amount of EG refinement, illustrating the great potential of EG implementation for noise reduction, crack path reconstruction, artefact removal and crack classification and association. The implementation of an EG-based automated measurement of the evolution of crack length and width is also demonstrated by the unattended identification and avoidance of potentially disturbing features such as branching and end points.The illustrated procedures are, however, only examples of the possibilities offered by the compact description of geometrical and topological properties conveyed by EGs, and many other opportunities may arise from the combination of existing approaches for image processing with the vast collection of graph-related algorithms and from the development of specialized, EG-guided analyses on the original image. The implementation of EG-mediated analysis processes can thus allow to fully exploit the potential of most of the existing detection algorithms for cracks and other curvilinear features.


The traditional leader-follower Unmanned Aerial Vehicle (UAV) formation cooperative positioning (CP) algorithm, based on relative ranging, requires at least four leader UAV positions to be known accurately, using relative distance with leader UAVs to achieve the unknown position follower UAV’s high-precision positioning. When the number of the known position leader UAVs is limited, the traditional CP algorithm is not applicable. Aiming at the minimum cooperative unit, which consists of a known position leader UAV and an unknown position follower UAV, this paper proposes a CP method based on the follower UAV’s moving vector. Considering the follower UAV can only acquire the single distance with the leader UAV at each distance-sampling period, it is difficult to determine the follower UAV’s spatial location. The follower UAV’s moving vector is used to construct position observation of the follower UAV’s inertial navigation system (INS). High-precision positioning is achieved by combining the follower UAV’s moving vector. In the process of CP, the leader UAV obtains a high-precision position by an INS/Global Positioning System (GPS) loosely integrated navigation system and transmits its position information to the follower UAV. Based on accurate modeling of the follower UAV’s INS, the position, velocity and heading observation equation of the follower UAV’s INS are constructed. The improved extended Kalman filtering is designed to estimate the state vector to improve the follower UAV’s positioning accuracy. In addition, considering that the datalink system based on radio signals may be interfered with by the external environment, it is difficult for the follower UAV to obtain relative distance information from the leader UAV in real time. In this paper, the availability of the relative distance information is judged by a two-state Markov chain. Finally, a real flight test is conducted to validate the performance of the proposed algorithm. Over the past few decades, UAVs have been widely used in military and civilian fields. In the civilian field, they are mainly used for rescue missions , border INS is an autonomous, independent dead-reckoning system, that has been widely used in UAVs. However, the navigation accuracy is difficult to guarantee when only using the INS due to inertial measurement unit’s (IMU) error accumulation. When the satellite signals are available, the GPS receiver can provide the long-term reliable position information for the UAV. Thus, the INS/GPS loosely integrated navigation system is widely used in UAV formation ,6,7. In However, satellite signals may be interfered with by the external environment. Abundant external relative perception information among UAVs can effectively improve UAVs’ positioning accuracy. The airborne datalink system, as a communication system based on radio data transmission and receiving, is widely used in the field of collaborative navigation . Under tAiming at the minimum cooperative unit, which consists of a known position leader UAV and an unknown position follower UAV, there is little literature on only using the single relative distance to achieve follower UAV high-precision positioning, but there are a few applications in Autonomous Underwater Vehicles (AUVs). Considering the single relative distance between the AUV and a known position beacon, it is difficult to determine an AUV’s spatial position. Many researchers have constructed the virtual beacon arrays as known position beacons to achieve the AUV’s positioning ,17. HoweAiming at the minimum cooperative unit, which consists of a known position leader UAV and an unknown position follower UAV, this paper proposes a CP algorithm based on follower the UAV’s moving vector.High-precision positioning of the follower UAV is achieved by using the single relative distance information and the follower UAV’s moving vector.Introducing a two-state Markov chain to judge the availability of the distance information improves the efficiency of the cooperative navigation algorithm.Thus, aiming at the minimum cooperative unit, this paper proposes a CP method based on the follower UAV’s moving vector. The error model of the follower UAV’s INS is constructed according to the IMU error characteristic. By combining the output of the speed sensor and magnetic sensor mounted on the follower UAV, the follower UAV’s moving vector is used to construct a position observation equation of the follower UAV’s INS. The improved extended Kalman filter is utilized to estimate the state vector to obtain a follower UAV high-precision navigation solution. In addition, considering that the airborne datalink system based on radio signals may be interfered with by the UAV formation-flying environment, the follower UAV cannot obtain relative distance information with the leader UAV in real time. In this paper, a two-state Markov chain is used to judge the availability of the distance information to improve the efficiency of the CP algorithm. The innovations of this paper are as follows:The rest of the paper is organized as follows: In the x-axis pointing in the east direction and the y-axis pointing in the north direction, the z-axis is determined by right-hand rule, and the origin is located at the centroid of the carrier. The front and right directions in the body coordinate system are pointing to the x-axis, y-axis, respectively, and the z-axis is determined by the right-hand criterion.The CP scenario of the minimum cooperative unit based on relative ranging is shown in In the above CP scenario, the known position leader UAV flies in an area with available GPS signals and is equipped with a low-precision Micro-Electro-Mechanical System (MEMS) IMU, a GPS receiver in a single-point mode and a datalink communication device. The unknown position follower UAV flies in an area denied GPS signals and carries a low-precision MEMS-IMU, speed sensor, magnetic sensor, barometric altimeter and datalink communication device. The two UAVs perform time calibration by GPS system clock before cooperative flight to ensure each UAV’s time reference is synchronized. In the process of CP, the leader UAV obtains high-precision navigation information by fusing INS/GPS information. Meanwhile, the leader UAV broadcasts its position, speed and course information to the follower UAV node. According to the preset time interval period, the follower UAV receives navigation information transmitted by the leader UAV through the airborne datalink system. Under the condition that the clock of each UAV node in the minimum cooperative unit is synchronized, the relative distance between the leader and follower UAV is obtained in real time by the TOA method. Considering the positioning error of the follower UAV’s INS has accumulated and diverged for a long time, only relying on the positioning accuracy of the follower UAV’s INS is difficult for meeting the UAV cooperative flight requirement. By combining the altitude information obtained from the follower UAV’s barometric altimeter, three-dimensional navigation positioning of the follower UAV is transformed into two dimensions. The moving vector of the follower UAV at adjacent times is constructed using the information of the speed sensor and three-axis magnetic sensor. Based on the error model of the follower UAV’s INS being accurately constructed, the position observation equation of the follower UAV’s INS is constructed using the relative ranging constraint and the follower UAV’s moving vector. Meanwhile, combining the speed and heading information output from the speed and three-axis magnetic sensor, the velocity and heading observation equation of the follower UAV’s INS are constructed, respectively. In addition, considering that the datalink system based on radio signals may be interfered with by the external environment, this paper introduces a two-state Markov chain to judge the availability of the relative distance information. When the distance information among the UAVs is available, the position observation equation of follower the UAV’s INS is constructed by using the follower UAV’s moving vector. Otherwise, only the velocity and heading information obtained from the follower UAV’s airborne sensor are used as the system observation vector. Finally, the improved extended Kalman filtering is designed to estimate the state vector to improve the follower UAV’s positioning accuracy. The schematic diagram of the proposed method in this paper is shown in Considering there is only one known position leader UAV in the minimum cooperative unit, the single relative distance with the leader UAV cannot determine the follower UAV’s spatial position. The moving vector of the follower UAV has to play an important role in constructing the position observation equation of the follower UAV’s INS. The follower UAV’s moving vector represents the relative displacement vector that the follower UAV removed from time It can be seen from Formula (3) that the moving vector of the follower UAV from time Assuming that each UAV’s clock completes its time synchronization by GPS before UAV formation cooperative flight, in the process of CP, the leader UAV sends its pulse information and position broadcast through the airborne datalink system at time The circular equation at time At time The circular equation at time The first-order linearization Taylor expansion of Equation (8) is made and ignores the higher-order term above the second order, and by combining the altitude information output from the barometric altimeter, the position observation equation of the follower UAV’s INS at time The follower UAV’s onboard speed sensor can acquire the UAV’s forward velocity. The horizontal velocity can be obtained by decomposing the follower UAV’s forward velocity into the horizontal direction. The follower UAV’s horizontal velocity can be expressed as:In the above formula, At the same time, the follower UAV’s onboard three-axis magnetic sensor can provide heading information for the UAV through a sensitive geomagnetic field, which can be used as the heading observation to correct the error of the follower UAV’s INS. After temperature and magnetic compensation, the heading information output from three-axis magnetic sensor can be expressed as:According to the follower UAV’s INS state recursive equation, more details about the follower UAV’s INS state recursive equation can be found in . The staThe system state vector The airborne datalink system based on radio data transmitting and receiving is susceptible to radio signal interference. It is difficult for the follower UAV to receive communication data packets containing relative distance and the leader UAV’s position information at each sampling period. The position observation equation of the follower UAV’s INS has the following form:If the communication data packet from the leader UAV is successfully received at time Under the condition of the position observation of the follower UAV’s INS being available, the covariance estimation equation of the traditional extended Kalman filtering can be expressed as:However, under the condition of the datalink system being indirectly limited, the following equations are derived from the above formulas:Due to Therefore, when the airborne datalink system is indirectly limited, the improved extended Kalman filtering equations are as follows:An outdoor autonomous flight CP experiment involving two UAVs has been carried out on the campus playground. All sensors mounted on the two UAVs are shown in The autonomous flight CP experiment for the two UAVs is shown in It can be seen from In order to more visually compare the follower UAV’s positioning performance by using the proposed method and the traditional multi-leader UAV CP method based on relative ranging, the root mean square error (RMSE) value of the follower UAV’s positioning error is compared in The method proposed in this paper breaks through the limitation of the traditional CP algorithm on the number of known position leader UAV nodes, which lays a theoretical foundation for the future engineering application.The traditional multi-leader UAV CP algorithm based on relative ranging has a requirement on the number of known position leader UAV nodes. When the number of leader UAVs and relative distance measurements are limited, the traditional CP algorithm is not applicable. Aimed at the minimum cooperative unit composed of a known position leader UAV and an unknown position follower UAV, this paper proposes a cooperative localization method based on the follower UAV’s moving vector. Compared to the traditional multi-leader UAV CP method based on relative ranging, only the single relative distance information with the leader UAV is required to obtain the follower UAV’s position solution. By combining the information of the follower UAV’s airborne speed sensor and three-axis magnetic sensor, the moving vector of the follower UAV at adjacent times is constructed. The position observation equation of the follower UAV’s INS is constructed by using a relative distance constraint and the follower UAV’s moving vector. Meanwhile, the velocity and heading observation equations of the follower UAV’s INS are constructed by using the information of the speed and magnetic sensor. The improved extended Kalman filtering is designed to estimate and compensate the system state vector to improve the follower UAV’s positioning accuracy. In addition, considering that the datalink system based on radio signals may be interfered with by the external environment, this paper introduces a two-state Markov chain to judge the availability of the relative distance information. The real autonomous flight CP experiment is conducted to validate the performance of the proposed algorithm. The results show that the proposed CP algorithm can achieve better positioning accuracy compared to the traditional multi-leader UAV CP algorithm.


Cardiac development is characterized by the active proliferation of different cardiac cell types, in particular cardiomyocytes and endothelial cells, that eventually build the beating heart. In mammals, these cells lose their regenerative potential early after birth, representing a major obstacle to our current capacity to restore the myocardial structure and function after an injury. Increasing evidence indicates that the cardiac extracellular matrix (ECM) actively regulates and orchestrates the proliferation, differentiation, and migration of cardiac cells within the heart, and that any change in either the composition of the ECM or its mechanical properties ultimately affect the behavior of these cells throughout one’s life. Thus, understanding the role of ECMs’ proteins and related signaling pathways on cardiac cell proliferation is essential to develop effective strategies fostering the regeneration of a damaged heart. This review provides an overview of the components of the ECM and its mechanical properties, whose function in cardiac regeneration has been elucidated, with a major focus on the strengths and weaknesses of the experimental models so far exploited to demonstrate the actual pro-regenerative capacity of the components of the ECM and to translate this knowledge into new therapies. The human heart has a poor regenerative capacity and myocardial damage is invariably repaired by scarring, with the progressive loss of the contractile function . This maThe extracellular matrix (ECM) is the non-cellular component of all the tissues. Besides providing structural support to cells, it conveys multiple signals that influence different aspects of cell behavior, including proliferation and differentiation. Therefore, both ECM components and its mechanical properties may likely control the cardiac cell fate during the regeneration of the heart. Some concepts supporting this hypothesis are the massive remodeling of the ECM during the regeneration-to-repair transition in rodents ,4,5 or tHowever, the translation of this knowledge into new heart regenerative therapies is still missing. One reason may be the fact that the models used to assess the role of the ECMs’ proteins on cardiac regeneration often oversimplify the problem and display specific limitations. Furthermore, in addition to CM proliferation, cardiac regeneration requires an adequate revascularization to provide trophic support to the growing myocardium, a process that has been largely overlooked . In this review, we discuss the evidence supporting the role of the ECM in promoting the regeneration of the myocardium, including cardiac vessels. In addition, we describe and discuss the models and experimental approaches which have been used to assess how the components of the ECM control cardiac regeneration, and we conclude that the complementary use of cell culture-based (in vitro) and in vivo approaches is required to provide convincing evidence of the therapeutic potential of the ECMs’ components and thus to consider them as targets for cardiac regeneration. Although a key function of the ECM in regulating the different phases of the development of the heart is well documented, very few studies specifically assessed the role of the proteins of the ECM in controlling CM proliferation. However, sparse evidence supports this concept. Hyaluronan, the most abundant glycosaminoglycan in the developing mouse heart, is known to provide a hydrated environment that promotes cell proliferation . In addiEvidence that the loss of the regenerative potential of the mouse heart soon after birth is accompanied by profound ECM remodeling has recently supported its role in this regeneration-to-repair transition. In fact, the ECM from P1 regenerative hearts is more effective in inducing CM proliferation than the ECM isolated from P7 hearts. This has been attributed to agrin, a heparan sulfate proteoglycan particularly abundant at P1, which promotes CM proliferation in vitro and is able to reactivate the CM proliferation in adult mice and pigs after myocardial infarction (MI) ,12. ThisAnother ECM protein claimed to promote a myocardial regeneration is periostin, which is abundantly expressed in mammals by both the developing heart and the adult myocardium after MI. In neonatal mice, periostin induces CM proliferation after MI through a PI3K/GSK3β/cyclin D1 signaling-mediated mechanism . The abiParallel proteomic studies in mice have revealed a novel function for two embryonically enriched ECM proteins, Slit2 and nephronectin, in stimulating the cytokinesis of postnatal CMs both in vitro and in vivo, thus shifting from binucleation to cell cycle progression . In addition to their direct role in promoting CM proliferation, the components of the ECM can also contribute to cardiac regeneration through alternative mechanisms. For example, in the regenerating zebrafish heart, fibronectin does not stimulate the CM division, but it allows for their mobilization and integration into the injured site . Angiogenesis is the main mechanism by which new blood vessels arise in adult organisms and therefore is of outmost importance for a cardiac revascularization after MI . The ECMA series of studies indicate that the ECMs’ proteins can be exploited as novel therapies to induce angiogenesis after MI. For instance, the injection of the ECM hydrogels derived from healthy porcine myocardium improves the cardiac function and reduces adverse remodeling in both the small and large animal models of MI ,26. WhilAs mentioned above, in addition to their scaffold function, the ECMs’ proteins control the formation of new blood vessels by acting as a reservoir of the growth factors and cytokines . For ins+ endothelial cells [During the heart regeneration of zebrafish, fast angiogenic sprouting, which is highly dependent on collagen guidance , is neceal cells . Collectal cells , althougBeyond its composition, the mechanical properties of the ECM also affect cell proliferation and regeneration in the heart. The sudden loss of the CM proliferative potential after birth occurs exactly at the time when the stiffness of the ECM increases . The injAt the same time, alterations in the rigidity of the ECM also influence the vessel growth. Multiple studies show that the reduced stiffness of the ECM promotes angiogenesis and cardiac regeneration ,41,42. CAs briefly summarized in Starting from these descriptive data, a functional validation is achieved using either the whole ECM or its specific components, as described in To address the role of the specific components of the ECM, the latter can be generated using recombinant DNA technology, enabling the application of individual ECM proteins to both cultured cells and animal models ,12,14. AThe functional role of either the whole ECM or its specific components can be validated in vitro and in vivo, often entailing inter-species applications. This is possible because of the high homology among mammalian genomes  and because a complete cell and DNA removal upon decellularization may avoid most problems of immunogenicity and rejection ,41,49,57As cardiac regeneration requires the formation of both new muscle tissue and new vessels, multiple in vitro models have been generated to assess the effect of the ECMs’ proteins on both CMs and endothelial cells.One challenging objective is the induction of cell cycle progression in primary CMs. Considering the absence of the proliferative potential of adult CMs in mammals, most studies adopted neonatal CMs harvested from rodents within the first week of life, when the cardiac regenerative capacity is partially preserved . More reThe three cell types that mainly compose the heart  can be cultured individually or combined in either 2D co-cultures or 3D tissue-like structures . Despite their apparent simplicity and naiveness, 2D approaches present numerous advantages. First, they are relatively inexpensive and highly reproducible, suitable for imaging and high throughput screening. Second, the proliferation rate of both CMs and cardiac endothelial cells is usually higher in 2D cultures compared to 3D tissues, which require a long-term differentiation. Thus, numerous studies evaluating the role of the ECMs’ proteins on cardiac cell proliferation have used 2D models, in which the components of the ECM are available to the cells in the solution as a supplement to the cell culture media, or as a coating after the adsorption to the well surface. In these studies, specific components of the ECM were tested in the form of recombinant proteins or lyophilized/cryo-pulverized dECM ,50,57. FDifferently from the 2D assays, 3D systems preserve and reproduce spatial cues that may direct cell growth and migration. One example is represented by cardiac organoids , which hAn alternative approach consists of the use of the dECM as a 3D scaffold for a subsequent recellularization with multiple cell types, that are expected to migrate and distribute following the original spatial organization of the matrix ,65. ThisThe relevance of zebrafish as a model of cardiac regeneration stems from its capacity to regenerate new myocardium in response to damage throughout its life. This happens through the partial de-differentiation and proliferation of existing CMs, without the involvement of any stem cell population . In addiMultiple approaches can be used to study cardiac regeneration in zebrafish. The genetic manipulation of zebrafish allows for the generation of organisms either overexpressing or lacking specific ECM components, such as different VEGF isoforms that are retained in the ECM and that are essential for new vessel formation during heart regeneration . On the Rodents, and particularly mice, are frequently used in experimental research, as they show a >99% homology with the human genome , a fast The first approach to study the role of specific ECM proteins on the heart regeneration in rodents is their genetic depletion, which can be either constitutive or conditional (using the Cre-Lox technology) ,13,16. FTherapeutically, the whole ECM can be either sewed/glued onto the epicardial surface or injected into the infarcted region. The most common preparation consists of liquid hydrogels, although solid ECM microparticle formulations may increase the functionality by extending the stability and controlling the release of the ECMs’ proteins . To shedBesides stimulating an endogenous regeneration, the ECM has been used in combination with human cardiac progenitor cells (hCPCs) to create a patch for myocardial repair. While the initial aim of this approach was to promote the retention of hCPCs, subsequent studies ascribed the main therapeutic effect to the presence of the ECM, which, per se, promoted tissue remodeling and preserved the cardiac function in a rat model of right ventricular failure ,58,66.Acomys cahirinus), which shows wound healing without scarring in different organs, including the heart upon MI [It is noteworthy that there are rodent strains that show an enhanced capacity to regenerate and that could expand the option to study the role of the ECM in cardiac regeneration. One example is the MRL mouse, a strain that manifests the autoimmune disorders mainly caused by the genetic alteration of the Fas gene ,42. Nota upon MI . These mDespite the high clinical relevance of large animals, only a few studies have assessed the therapeutic activity of the ECMs’ proteins in MI pig models. For example, the administration of agrin resulted in being cardioprotective and pro-regenerative , whereasHere, we reviewed the existing evidence supporting the role of the ECMs’ proteins in promoting a cardiac regeneration. This concept arises from the demonstration that both the composition and the mechanical properties of the ECM change dramatically between regenerative and non-regenerative conditions, for example, between zebrafish and mammalian hearts or between pre-natal and post-natal hearts. To date, ‘omic’ technologies have generated a detailed description of the ECMs’ composition and its relative changes in different experimental settings. While proteomics provides a realistic description of the actual composition of the ECM, it often fails in detecting the changes in the proteins’ isoforms, for instance, those generated by alternative splicing as in the case of fibronectin . Thus, tPerhaps, the most direct and striking evidence that the ECM can be exploited for regarding heart regeneration is that the implantation of the ECM harvested from either zebrafish or fetal mammalian hearts elicits a regenerative response in an injured adult myocardium. Despite being interesting for a basic investigation, this approach presents obvious limitations in terms of the translatability into a clinical scenario. On the one hand, the use of an ECM from other species might induce a potentially dangerous immune response . On the In addition, some studies indicate that even the adult ECM in mammals retains some regenerative potential, which can be further enhanced by partial enzymatic digestion . As mentAn additional outstanding question is whether it is better to implant the whole ECM or its individual components, which can be produced and administered as recombinant proteins. While the second approach is more straightforward and can be easily standardized, the whole ECM has the unique property to interact with and possibly stimulate all the cell types needed to build a new myocardium. Indeed, while most of the approaches have so far aimed at stimulating either CM proliferation or the formation of new blood vessels, an ECM-based biotherapeutic might have the potential to simultaneously drive both processes. Finally, a fundamental issue that still needs to be clarified is the most efficient mechanism that can regenerate the heart in vivo. Many studies have tried to either implant exogenous cardiac progenitors or to activate a putative population of cardiac stem cells. These approaches have been harshly questioned and, in any case, they have failed in providing a benefit in patients . More reIn conclusion, multiple approaches have been used to claim the pro-regenerative role of ECM components. While in vitro experiments provide clearcut and straightforward readouts to elucidate the effect of the ECM proteins on cardiac cells , in vivo studies appear essential to prove a therapeutic benefit. As highlighted in


The loss of resistance (LOR) method has been used exclusively to identify epidural space. It is difficult to find the epidural space without the risk of dural puncture. Various devices have been developed to improve the accuracy of the LOR method; however, no method has overcome the problems completely. Therefore, we devised a ligamentum flavum rupture method (LFRM) in which the needle tip is placed only on the ligamentum flavum during the epidural injection, and the injection pressure is used to rupture the ligamentum flavum and spread the drug into the epidural space. We confirmed the accuracy of this method using ultrasound with superb microvascular imaging (SMI) to visualize the epidural space. Here, we report two cases of 63-year-old and 90-year-old males. The 63-year-old patient presented with severe pain in his right buttock that extended to the posterior lower leg. The 90-year-old patient presented with intermittent claudication every 10 min. LFRM was performed, and SMI was used to confirm that the parenteral solution had spread into the epidural space. Our results indicate that LFRM can be used for interlaminar lumbar epidural steroid injections. The loss of resistance (LOR) technique is the most commonly used method for identifying epidural space for an epidural block . HoweverThe laminae were visible in the cross-section as sloping hyperechoic lines in a “sawtooth” pattern in a paramedian sagittal oblique view of the lumbar spine. An interlaminar foramen was identified between the laminae. Two deeper hyperechoic lines representing the posterior dura mater and the anterior dura mater, separated by the hypoechoic intrathecal space, were identified from the interlaminar foramen A,B. The A completely aseptic technique was used during the procedure. First, the skin was disinfected using a chlorhexidine solution, which remained on the skin for at least 2 min to kill bacteria causing deep tissue infections following skin puncture A. After We confirmed that the needle tip had reached the ligamentum flavum by observing the monitor and by the ligamentous resistance tactile sensation transmitted to the syringe. Once the needle tip approached the ligamentum flavum, the US was switched to SMI mode to confirm the position of the needle tip and injectant spread A. The syTo confirm the accuracy of the ligamentum flavum rupture US-guided ILEDSI, we used a contrast medium instead of dexamethasone  in 5 mL of 0.25% lidocaine. After injecting the contrast medium, the anterior-posterior and lateral epidurograms of the lumbar spine were captured A,B. The Case 1: A 63-year-old man presented with severe pain in his right buttock extending to the posterior lower leg. No obvious neurological symptoms were observed. The visual analog scale (VAS) score was 10. Diagnostic facet joint and sacroiliac joint blocks had no effect. Magnetic resonance imaging (MRI) revealed L2/3, L3/4, and L5/S1 disc herniation. A total US-guided epidural injection of 1 mL dexamethasone (4 mg), 4 mL of 0.25% xylocaine, and 5 mL of 0.9% saline were administered at L1/2 as his pain had persisted for 2 weeks. During examination, SMI was used to confirm that the parenteral solution had spread into the epidural space. The spread of contrast within the epidural space was assessed using epidurograms and CT epidurograms to confirm the accuracy of the US-guided LFRM. The axial CT epidurogram confirmed the spread of the contrast from L1 to Th9 . SubsequCase 2: A 90-year-old man presented with intermittent claudication every 10 min. No obvious neurological symptoms were observed. The VAS score was 10 and the MRI revealed lumbar canal stenosis. In the examination room, SMI was used to confirm that the parenteral solution had spread in the epidural space. Unfortunately, the SMI signals appeared in the thecal sac ; therefoAn epidural block is usually a four-step process:Guide the needle into the ligamentum flavum.Advance the needle to the depth where resistance disappears (LOR).Confirm that the site of LOR is the epidural space.Confirm that the drug solution is appropriately distributed into the epidural space.Processes two through four are difficult to assess in real-time, and it is difficult to assess whether they were done appropriately, which can lead to complications. To solve these problems, we devised a method of breaking the ligamentum flavum with injection pressure that does not involve the LOR method.The distance from the insertion point to the ligamentum flavum was measured before injection to perform LOR and avoid dural puncture complications. However, the LOR method cannot accurately identify the epidural space if there is a false lumen with the LOR outside the epidural space, as it only uses a decrease in pressure as an indicator. Efforts have been made to improve the success rate by measuring the distance from the epidermis in advance using MRI, CT, or sonography to avoid mistaking the false lumen for the epidural space ,5,6. ImaUltrasonography can be used for the preprocedural imaging of anatomical landmarks or the real-time US guidance of the procedure. Moreover, ultrasonography is more accurate than surface landmarks or palpation in identifying a specific intervertebral level. Palpation could result in inaccuracies of two or more intervertebral levels from the targeted level . US alsoThe success of the LOR method depends on the finger senses of the surgeon to detect subtle changes in pressure. Furthermore, attempts have been made to identify the epidural space using special devices to measure pressure changes without using finger senses ,8. TheseSeveral methods have been reported for evaluating whether the needle tip is in the epidural space, including multiple intraoperative CT scans , fluorosUS-guidance is difficult to be determined by the US alone, especially when the needle is deep and the trajectory has passed through several layers of soft tissues so that the edge shadow may sometimes block the needle tip view. LOR may help to confirm the epidural access but is still not accurate, and dural puncture has been reported ,26,27,28Accurate needle tip guidance into the ligamentum flavum behind the epidural fat layer;Palpation of resistance by finger sense during ligamentum flavum insertion while confirming with sonography;Confirmation of the position of the needle tip in the ligamentum flavum;Tracing the spread of the drug in the epidural space using SMI during the injection.In the present study, we developed a US-guided lumbar intervertebral epidural injection to address this problem in the lumbar region. The ligamentum flavum was bluntly ripped by applying injection pressure to the needle tip within the ligamentum flavum rather than penetrating the needle tip shown in , which iNeedle movement during injection caused by unintentional patient movement due to pain or other factors can cause a subarachnoid block; however, the risk can be minimized if interrupted by a small drug infusion. Our method can detect intrathecal injection during epidural injection and prevent subarachnoid block.Toshiba has developed an innovative Doppler US technology called SMI using the Aplio™ i-series , which enables the visualization of slow-flow vessels without the need for a contrast medium. SMI is a promising new tool for detecting injection flow . SMI imaPeri-discal blood flow is a thin, narrow flow that is continuous to the base of the hernia and presents an SMI image in the epidural space, whereas CSF flow is a wider flow than this but does not flow epidurally, resulting in flow in the dural canal even if the stenosis is strong. In addition, CSF flow is susceptible to spinal extension, and SMI in the case of strong stenosis is not affected by inflammation around the intervertebral disc, whereas the SMI signal associated with CSF flow is also lost because CSF flow is lost with lumbar extension. The CSF flow is also more susceptible to SMI signal enhancement due to the dura mater being pushed down with an epidural block, whereas the inflammatory SMI signal in the disc is not affected.We believe that SMI signaling via CSF flow or peri-discal blood flow may have a potential application in identifying the responsible vertebral body or disc level in patients with multiple lesions.Many fluoroscopic methods have been reported to guide the needle in real-time but have limitations due to the use of the bone as a landmark, and some complications have also been reported ,13. KarmSince the epidural fat layer varies in thickness from patient to patient, the placement of the needle tip in the same area cannot completely avoid the risk of complications. To avoid complications, the needle tip should be placed as far away from the dura mater as possible. Therefore, we devised a method in which the needle tip is placed only on the ligamentum flavum during the epidural block and the injection pressure is used to rupture the ligamentum flavum and spread the drug into the epidural space. The most important difference from the cervical epidural block is the depth to the epidural space and the volumetric measurement of the surrounding tissue. In the cervical region, the needle can be inserted tangential to the dura mater and parallel to the probe, allowing good needle visibility and the accurate location of the needle tip by echo, whereas in the lumbar region, it is difficult to insert the needle tangential to the dura mater and parallel to the probe. Therefore, the needle is inserted at an acute angle to the dura and at an angle to the probe, resulting in poor needle visibility.This method requires the application of a sufficiently high injection pressure to break the ligamentum flavum, making it difficult to evaluate whether the drug has flowed into the epidural space with the usual LOR method.To evaluate whether the epidural ligament was correctly ruptured and the drug flowed into the epidural space, the SMI method was used as shown in the cervical epidural block. The advantages of this method are the accurate assessment of the needle tip position, real-time tracking of the spread of the drug, and the ability to visualize the intrathecal injection by dural puncture, which allows early interruption of the injection.To the best of our knowledge, this is the first study to identify ligamentum flavum rupture epidural steroid injections as a possibility. The SMI method is a safe adjunct to our injection technique because it allows us to visualize the needle tip, the spread of the drug into the epidural space, and the intrathecal injection in real-time.A limitation of this study is that SMI is only available in Canon medical ultrasonic equipment but not in others, which will limit the generalization of this technique to spine intervention.The main advantage of the US-guided LFRM is its lack of radiation exposure and use of a contrast medium. Furthermore, predicting epidural space spread using the SMI method during US-guided LFRM is accurate and feasible in clinical settings. This method predicts the injectant spread into the epidural space and prevents intrathecal injection by attempting epidural steroid injection under US guidance.


Understanding neck pain is an important societal issue. Kinematic data from sensors may help to gain insight into the pathophysiological mechanisms associated with neck pain through a quantitative sensorimotor assessment of one patient. The objective of this study was to evaluate the potential usefulness of artificial intelligence with several machine learning (ML) algorithms in assessing neck sensorimotor performance. Angular velocity and acceleration measured by an inertial sensor placed on the forehead during the DidRen laser test in thirty-eight acute and subacute non-specific neck pain (ANSP) patients were compared to forty-two healthy control participants (HCP). Seven supervised ML algorithms were chosen for the predictions. The most informative kinematic features were computed using Sequential Feature Selection methods. The best performing algorithm is the Linear Support Vector Machine with an accuracy of 82% and Area Under Curve of 84%. The best discriminative kinematic feature between ANSP patients and HCP is the first quartile of head pitch angular velocity. This study has shown that supervised ML algorithms could be used to classify ANSP patients and identify discriminatory kinematic features potentially useful for clinicians in the assessment and monitoring of the neck sensorimotor performance in ANSP patients. Understanding neck pain is an important societal issue ,2. The oIdentifying kinematic features from time series and comparing them between groups, e.g., to evaluate treatments or classify neck pain motion across ageing, is a widely used method ,13,14,15Resorting to artificial intelligence (AI) techniques may lead to another type of analysis, i.e., “the machine” should find the relevant specifications of time series. The present study is devoted to the latter case. AI is defined as a field of science and engineering concerned with the computational understanding of what is commonly referred to as intelligent behavior and the creation of artefacts that exhibit such behavior . MachineThe first aim of this work was to evaluate the discriminative ability of AI and SML methods in sensorimotor assessment of yaw angular displacement of the head in patients with ANSP compared with healthy control participants (HCP) with data from a previous study  obtainedhttps://www.a-e-c.eu, (accessed on 30 January 2019) Brussels, B200-2018-103) and conducted in accordance with the Declaration of Helsinki. The authors confirm that all ongoing and related trials for this drug/intervention are registered .This study included 80 subjects (38 ANSP patients and 42 HCP) from a previous study . Data weThe protocol was described in a previous study . It esseDuring the DidRen laser test, head angular displacement kinematics were recorded in 3D  using the DYSKIMOT inertial sensor . The detIn our previous papers ,15, we aIt is generally difficult to determine a priori which ML algorithm performs best on a given dataset . TherefoThe comparison between selected algorithms was based on metrics such as accuracy and the Area Under Curve (AUC) score, computed from the Receiver Operating Characteristic (ROC) curve. These metrics are only meaningful if the predictions are based on data that the ML algorithms have never learned. Therefore, the dataset was randomly split into two parts. The first part is the “training set”, which consists of 80% of the dataset used to train the ML algorithms. The second part (remaining 20%) is the “test set” used to make the predictions with the trained ML algorithms. The validation of the ML algorithms is performed by n-fold cross-validation . To miniFor KNN, the optimized parameters were the following: the number of neighbors , the weighting function  and the algorithms used to compute the nearest neighbors , kd_tree, auto, ball_tree). For Linear SVM, different values for the regularization parameter or C-parameter  were used in the evaluation to test the dependence of the approach on the C-parameter. For SVM RBF, the C-parameter  and the kernel coefficient Gamma  parameter were optimized. For DT, the optimized parameters were the maximum depth of the tree , the function to measure the quality of the splits , and the strategy to select the split nodes . For RF, the optimized parameters were the maximum depth of the tree , the number of trees in the forest , and the number of features considered in the search for the best split . For Adaboost, the optimized parameters were the maximum number of estimators at which boosting stops  and the weight applied to each classifier at each boosting iteration . For GaussianNB, the optimized parameter was the ratio of the largest variance of all features added to the variances for computational stability .All the computations related to the determination of the best performer were made in Python 3.8 and SciKit-Learn 1.0.2 software.The most informative kinematic features, i.e., the features that trigger the most predictions, were computed by using the Sequential Feature Selector (SFS) forward and backward . The bacAll the computations related to the determination of the most informative features and ML algorithms were made in Python 3.8 and SciKit Learn 1.0.2 software.Optimal hyperparameters are presented in The ROC curve plots the False Positive Rate , which ranked first 813 times in 1400. The second most discriminative feature was the median of head pitch angular velocity (ranked first 444 times in 1400). Thus, the pitch angular velocity appears to be the best discriminating feature to differentiate ANSP patients and HCP assessed with the DidRen laser test.A logistic regression based on the median of head pitch angular velocity led to an accuracy of 77%. A logistic regression based on total duration of the DidRen test led to an accuracy of 63%.Our findings showed the effectiveness of the kernel linear SVM classifier in distinguishing ANSP patients from HCP. The accuracy of the linear SVM was 82% and the AUC score was 84%. The interpretation of the AUC score should be evaluated in terms of the importance given to its accuracy. We can assume that the medical community in the field of oncology prefers an AUC score close to 100%. Considering, on the one hand, the musculoskeletal field and, on the other hand, in relation to the non-specific pathology, the comparison between ANSP patients and HCP, which shows a great variability of the results , an AUC Seven time series (time and kinematic data) related to yaw, pitch, and roll angular displacement and velocity of the head, which can be easily acquired with a single inertial sensor, were used to train the selected ML algorithms. However, regardless of the ML algorithm and SFS, not all axes of head motion have good discriminative information, as the two best discriminating kinematic features were related to head pitch. The accuracy was best with the linear SVM and lowest with all other selected ML algorithms, such as the non-linear SVM (RBF). The same finding regarding the superiority of linear SVM over RBF has already been observed in a study with limited sample size (17 young and 17 old subjects) aimed at detecting age-related changes in running kinematics . For usep = 0.10) [Like other studies using ML algorithms to detect kinematic changes in healthy or pathological subjects ,43,44,45 = 0.10) . The linThe main discriminatory information used by the linear SVM algorithm to distinguish ANSP patients from HCP are the first quartile and the median of head pitch angular velocity. The two best kinematic discriminating features differed from those obtained by inferential statistical analysis, suggesting that ML approaches are complementary and clinically useful to detect kinematic changes in patients with ANSP.Y-axis a highly discriminatory direction that should be prioritized for future clinical trials with the DidRen laser test. Our results may seem counterintuitive at first, because the DidRen laser test consists of a sensorimotor assessment organized around the Z-axis, i.e., during the execution of yaw rotations of the head. Thus, it would stand to reason that the GyrX time series should contain most of the discriminative information. Nevertheless, it is interesting to note that the sensorimotor disturbances in ANSP patients may be highlighted by the stronger secondary coupled motion during yaw rotations. There seems to be a reason for this, because biomechanically, coupled bending rotations in the cervical spine lead to a compensatory roll rotation, which compensates for the yaw rotation of the head, and the associated coupled movements observed during pitch head movements [HCP have larger medians and quartiles for head pitch angular velocity (computed from GyrY time series) than ANSP patients, making the ovements . Indeed,ovements . If we aovements .The present discussion suggests that the ML algorithms can provide relevant functional variables and thus optimize the prediction of ANSP status during the DidRen laser test. To further illustrate this point, we mention that total test duration was the only parameter measured in the original version of the DidRen laser test . LogistiIn experimental studies, control and experimental groups are usually formed in such a way that no significant difference is observed in parameters such as age, ethnicity, gender, and degeneration/maturation stage, except for the variable of interest. In our case, this means that ANSP patients and HCP groups should differ only in terms of NDI and NPRS. Age is also significantly different in our groups, but we do not believe this is problematic for our purpose. Indeed, ML algorithms are designed to distinguish between HCP and ANSP patients. To find out the characteristics of ANSP patients, it is logical to compare them with the “healthiest” subjects, i.e., our HCP group. On the other hand, a control group with too young subjects would also have led to bias, since we have shown in a previous study that the kinematic behaviors recorded with the DidRen laser test have a U-shaped or inverted U-shaped age profile, making the differences between young and old particularly clear . BecauseIt has already been shown by authors of the present study that several kinematic features of head rotation movements were significantly different in HCP and ANSP patients in terms of statistical tests comparing means . The novWe reach the same conclusion as  regardinIn summary, we have shown that AI can help identify patients suffering from neck pain using the DidRen laser test augmented by an inertial sensor. In our approach, the accuracy and AUC scores are computed from inertial sensor’s kinematic data. The obtained ML algorithm can be implemented in any tablet or smartphone and lead to an “augmented DidRen laser test”; hence, our results may be transferred to daily clinical practice. In our opinion, the best way to merge the DidRen laser test and an inertial sensor is to develop a VR version of the test: it will improve the standardization of the test through the standardization of the environment, and any VR device has at least one inertial sensor able to collect the needed data. Such a work is in progress, see e.g., . Using A


This study assessed whether a simple technology-aided program  could be set up to enable people with motor, sensory and intellectual disabilities to control preferred environmental stimulation through two different response movements.Ten participants were involved in the study. Each of them was exposed to an ABAB design, in which A represented baseline phases without the program and B intervention phases with the use of the program. The study assessed whether the participants (a) had significant increases of each of the two response movements available and/or showed response variability across sessions and over time and (b) had signs of satisfaction/happiness during the study sessions, in connection with their stimulation access and control.The program was effective in increasing the participants' responding and consequently their self-regulated stimulation input. Half of the participants showed a significant increase of both responses available from the first intervention phase. Other participants seemed to focus more on one of the two responses. Even so, they tended to have occasionally high performance frequencies also with regard to their non-dominant (not significantly increased) response. Finally, all participants showed clear signs of satisfaction/happiness during the intervention sessions.The program represents a potentially useful approach for enabling people with extensive multiple disabilities to self-regulate their access to preferred environmental stimulation and improve their mood. People with extensive motor or motor and sensory impairment and severe/profound intellectual disability may be unable to profitably interact with objects, to engage in functional communication with others, and to control environmental stimuli –5. This via simple responses such as hand, head or finger movements  the possibility of implementing the last approach (with stimulation self-regulation) successfully and (b) the seemingly greater impact of such an approach on the persons' mood compared to the impact of approaches using externally regulated stimulation , 18. TypThis study was aimed at determining whether a fairly simple technology-aided program  could be set up to enable persons with motor and sensory impairments combined with intellectual disabilities to control stimulation through two different response movements and thus manage stimulation access efficiently/comfortably. The study was also focused on (a) determining how the persons used the response movements over time  and (b) verifying whether the persons showed signs of satisfaction/happiness during the study sessions, that is, in connection with their opportunities to control stimulation through their response movements . Ten pervia the second edition of the Vineland Adaptive Behavior Scales  in relation to a number of environmental stimuli. Those environmental stimuli included music and songs, family voices, and vibratory inputs. Third, they possessed response schemes  that could be adequate for activating the micoswitches used during the study (see Technology system) and thus could be instrumental to independently trigger brief stimulation events. Fourth, staff (a) supported an intervention program aimed at helping the participants increase their stimulation input through a self-regulated process , and (b) had approved the study and the technology used for it, which had been described and shown to them in advance.Given the participants' level of intellectual disability and their consequent inability to get information about and provide consent for the study, their legal representatives were called to deputize for them. That is, the legal representatives, who had received detailed information about the study, were asked to read and sign a consent form on behalf of the participants. The study complied with the 1964 Helsinki declaration and its later amendments and was approved (including the aforementioned consent process) by an institutional Ethics Committee.Quiet areas/rooms of the care and rehabilitation facilities that the participants attended served as setting for the baseline and intervention sessions. The participants' usual areas within those facilities  served as setting for the control sessions. Three research assistants were in charge of the study . All three were familiar with the use of technology-aided interventions with people with intellectual and multiple disabilities as well as with data collection procedures. Baseline, intervention and control sessions lasted 10 min and were implemented on an individual basis, typically two to four times a day, 3–6 days a week (in line with participants' availability).The stimuli used during the intervention sessions included a variety of songs and other musical pieces as well as staff and family members' voices or vibratory inputs in different parts of the body. The stimuli, which had been recommended by staff, were selected for the study after a preference screening procedure. The screening procedure involved the presentation of two or three segments of each of the song, music, voice stimuli assessed for the participant for about 10 non-consecutive times over several assessment instances , 38. Theleonardoausili.com), which was linked to two microswitches  and delivering stimulation (during the intervention phases) in line with the intervention conditions. The smartphone was also supplied with a variety of audio files representing the preferred stimulation events  for all participants except Dustin who received vibratory stimulation.The technology system used during the intervention sessions involved a Samsung Galaxy smartphone with Android operating system combined with a Bluetooth Encore Plus interface (leonardoausili.com), (b) touch devices , and (c) proximity devices . Nine participants had two microswitches on their desk, on their body, or on their wheelchair (see via a thin plastic sheet to avoid that they could be inappropriately used or damaged.The microswitches included (a) pressure devices . A response on either microswitch was ignored if emitted while the participant was receiving stimulation following a previous response. Thus, a new response was recorded only if it occurred after an interval of 10 s or more from a previous response . For conThe measures involved the participants' (a) response frequencies  during the different phases of the study and (b) indices of satisfaction/happiness during 20–38 intervention sessions and as many control sessions, which were paired to the intervention sessions (see below). The response frequencies were recorded separately for the first response  and the second response  through the MacroDroid system log available in the smartphone. This log provided an objective and permanent data record that the research assistants used at the end of the single sessions. The indices of participants' satisfaction/happiness (a) included smiles, vocalizations, and excited body movements , anFor each participant, baseline and intervention conditions were implemented according to an ABAB design . The firDuring the sessions of each baseline phase, the participants sat in their wheelchair and had a desk in front of them. The only exceptions  were Dorine and William. The microswitches were arranged on the participant's body, on the wheelchair, on the desk, or on the desk and under the desk see . The smavia two vibratory devices placed on those parts. Data recording concerned (a) the frequency of responses throughout all intervention sessions and (b) indices of participants' satisfaction/happiness during 20–38 sessions spread over the second intervention phase.During the sessions of each intervention phase, conditions differed from those used in baseline in that the technology system delivered 10 s of preferred stimulation contingent on each response occurrence (see Technology system). The stimulation consisted of 10 s of preferred music/songs with or without the superimposition of preferred familiar voices except for Dustin. Dustin, who had hearing loss, received 10 s of vibratory stimulation provided alternatively in two separate parts of the body  Each control session (a) was paired to one of the intervention sessions in which indices of satisfaction/happiness were recorded, and (b) was carried out closely before that intervention session. During the control sessions, the participants were in their regular contexts , did not have the technology system, and did not receive any specific stimulation except for possible environmental sounds and voices occurring in the contexts.t-tests were used for the single participants to assess the differences between their indices of satisfaction/happiness during the intervention sessions and the paired control sessions  for the different phases of the study. The range and mean percentages of intervals with indices of satisfaction/happiness across the intervention sessions and the paired control sessions are reported in table form. The differences between the response frequencies of each baseline phase and those of the following intervention phase of every participant were assessed through the Kolmogorov-Smirnov test . Paired sessions .p < 0.05 and 0.01, respectively, at the Kolmogorov-Smirnov test) from the corresponding values of the previous baseline phase. The numerals within the ovals indicate the number of sessions available for the different phases of the study.As shown in the figures, the number of sessions the participants received varied between 6 and 10 (first baseline), 19 and 40 (first intervention phase), 6 and 12 (second baseline), and 49 and 132 (second intervention phase). During the first baseline, the mean frequencies for the single responses ranged between below 1 (Dustin's first response) and about 6.5 (Richard's first response). During the first intervention phase, the mean frequencies increased to between about four (Dustin's first response) and 17.5 (William's second response). The intervention frequencies were significantly higher than the baseline frequencies on both the first and second response for five participants , and on one of the two responses for the other five participants. The mean response totals  varied between about 2.5 (Dustin) and 9 (Richard) during the baseline and between about 13 (Lilian) and 25 (Alec) during the intervention phase. The intervention totals were significantly higher than the baseline totals for all participants.The participants' mean frequency values for the second baseline were similar to those observed during the first baseline . Their mean frequency values for the second intervention phase varied between about 3.5 and 32 on the single responses and between about 24.5 and 35.5 on the response totals. The intervention values were significantly higher than the baseline values (a) on both responses for five participants  and one of the two responses for the other five participants, and (b) on the response totals for all participants See , 2.t-tests used to compare the intervention and control data indicate that the difference between the two sets of data was significant for each participant, with t values ranging between 3.51 and 33.59, and p values < 0.01.The results suggest that a relatively simple technology-aided program, which allowed participants with motor, sensory and intellectual disabilities to control environmental stimulation through two different response movements, was effective in increasing the participants' responding and consequently their self-regulated stimulation input. Several participants seemed to consistently use each of the two responses available  from the first intervention phase. Other participants seemed to focus more on one of the two responses, but even so, they tended to have occasionally high performance frequencies also with regard to the non-dominant (not significantly increased) response. Finally, all participants showed clear signs of satisfaction/happiness during the intervention sessions suggesting that the program may have a positive impact on mood and quality of life , 44–46. First, the program used in this study relies on commercial, easily accessible technology and that makes it a reasonably usable tool for daily contexts such as care and rehabilitation facilities –50. IndeSecond, the fact that a number of participants showed a significant increase of each of the two responses available is noteworthy from a technical and practical standpoint. Technically, such an increase could be considered a clear indication that having two microswitches (as opposed to one) can help strengthening different response schemes and facilitating access to environmental stimulation . PracticThird, the fact that participants who had significant increases of only one of the two responses tended to display occasionally high frequencies also for the non-dominant response  may be a relevant sign. Indeed, these occasionally high frequencies may suggest that the non-dominant response played a critical role for the participant's access to stimulation during specific sessions and/or days. It may be reasonable to assume that, due to positioning or other neurophysiological conditions, the participants found such response more comfortable and convenient than the dominant response during those sessions/days and thus resorted to its use to access stimulation , 35.Fourth, an intervention program that allows participants to access stimulation through the two target responses or the more convenient/comfortable response at any time may be viewed as user-friendly and have a positive impact on response performance, mood and eventually quality of life –28, 30. Fifth, the presence of significantly higher indices of satisfaction/happiness during the intervention sessions compared to the control sessions underlines the importance of the program for improving the participants' mood and quality of life while increasing and strengthening their responding and stimulation control , 53–56. Two limitations of the study may be pointed out. The first limitation concerns the fact that no direct comparison was made of the present program allowing the participants to use two responses and a conventional program relying on a single response. While it seems reasonable to believe that the present program has clear advantages over a program using a single microswitch/response, a direct comparison between the two may still be required. To carry out such a comparison, one might try to (a) expose the participants to the two programs according to a cross-over design  or (b) contrast the performance of a group of participants using two microswitches with the performance of a group of participants using one microswitch , 58.The second limitation concerns the absence of a social validation of the program used. Such validation could be carried out through interviews of staff personnel with experience in this area . The interview would be preceded by a description of the program followed by the presentation of video clips showing intervention sessions, in which the program is being used with people with extensive multiple disabilities. The staff involved in the interview would be asked to rate the program in terms of its suitability to participants with extensive multiple disabilities, its impact on the participants' overall responding, physical involvement and mood, and its applicability and acceptability in daily contexts , 60.In conclusion, the results suggest that a technology-aided program allowing the use of two different responses to access preferred environmental stimulation was effective in helping people with extensive multiple disabilities to (a) increase their responding, thus increasing their self-determined/regulated stimulation input, and (b) boost their level of satisfaction/happiness with a consequent enhancement of their quality of life. While the results are encouraging, one cannot make general statements about the program's positive impact, advantages, and usability in daily contexts until new research has addressed the limitations of this study. New research may also seek to upgrade the program to foster its effectiveness and promote its use with participants with different characteristics.https://osf.io/qj3z4/.The original contributions presented in the study are publicly available. This data can be found here: The study was reviewed and approved by the Ethics Committee of the Lega del Filo D'Oro, Osimo, Italy. Written informed consent to participate in this study was provided by the participants' legal guardian/next of kin.GL was responsible for setting up the study, acquiring and analyzing the data, and writing the manuscript. NS, MO'R, and JS collaborated in setting up the study, analyzing the data, and writing/editing the manuscript. GA, VC, and LD contributed in evaluating and arranging the technological aspects of the study, acquiring and analyzing the data, and editing the manuscript. All authors contributed to the article and approved the submitted version.