The issue of laser-induced damage of transparent dielectric optics has severely limited the development of high-power laser systems. Exploring the transient dynamic behaviors of laser damage on KDP surface by developing multi-physics coupling dynamics model is an important way to reveal the mechanism of nanosecond laser damage. In this work, KDP crystals are taken as an example to explore the mechanism of laser-induced surface damage. Based on the theories of electromagnetic field, heat conduction and fluid dynamics, a multi-physics coupling dynamics model is established for describing the evolution of nanosecond damage processes. The dynamics of laser energy transmission, thermal field distribution and damage morphology during nanosecond laser irradiation are simulated with this model. It is found that the enhancement of light intensity caused by surface defect plays an important role in the initial energy deposition and damage initiation of the laser irradiation area. The evolution of temperature field and crater morphology during subsequent laser irradiation is helpful to understand the laser damage process. The feasibility of this model is verified by the morphology information of typical defect-induced laser damage. This work provides further insights in explaining the laser-induced damage by surface defects on KDP crystals. The model can be also applied to investigate the laser damage mechanisms of other transparent dielectric optics. Potassium dihydrogen phosphate (KDP) crystals are generally used as electro-optic switches and frequency conversion elements in ICF laser facilities, due to their specific physical properties, e.g., the wide-region spectrum transparency, relatively high nonlinear conversion efficiency and reproducible growth to the large sizes needed4. However, tiny defects  are inevitably generated on the KDP surfaces during the processes of ultra-precision machining due to its weak mechanical properties. Structural defects on the surface of optical component would reduce their own laser damage resistance6. With the required increase of output laser power, the laser-induced damage (LID) of crystal components has become a major issue, limiting the development of ICF laser systems.Inertial confinement fusion (ICF) driven by high power lasers is a promising strategy for new clean energy9. At present, LID models for transparent dielectric optics can be generally classified into avalanche ionization models, electromagnetic field models, thermal models, and hydrodynamic models. Jupé et al.10 solved the laser-induced damage threshold in optical component using the ionization models combining with photo-ionization processes, avalanche ionization processes and relaxation processes from conduction band to other electronic states. The contribution of ionization phenomena was assessed during the ultra-short laser pulse and they found that the laser-induced damage threshold was dependent on the laser wavelength. Chen et al.11 simulated the light field distribution by calculating the electromagnetic field equation and found that some cracks with specific shapes and dimensions on KDP surface can produce light intensification as high as hundreds of times, which is sufficient to initiate the laser-induced damage. With modeling and experimental methods, Carr et al.12 studied the behavior of solid-state laser supported absorption fronts generated in bulk fused silica under high-power nanosecond laser pulses. They found that laser damage size was dependent on laser intensity and mainly driven by the temperature-activated optical absorption. DeMange et al.13 used the experimental and hydrodynamic modeling to investigate the early-period laser damage dynamics to explain the mechanism of bulk laser damage during nanosecond laser irradiation. The results suggested that the hydrodynamic instability at the unstable phase-changing interface between the two phases in the damage region played a major role in generating the cracks in the solid optics of high stress.In recent decades, laser-induced damage of optical components has been a hot topic around the word17. Because the duration of nanosecond laser damage is longer, multiple physical mechanisms like light modulation, heat absorption, fluid flow, etc. are included and even coupled with each other during the damage processes20. Previous work on laser damage has researched on the effect of pulse duration or wavelength on bulk damage, the mechanism of impurity-induced “explosion” inside the boules and the light modulation of surface cracks. However, the calculation of a single thermal or electromagnetic field model could not explain the laser damage mechanism well. In order to comprehensively simulate the damage process during nanosecond pulses, different physical mechanisms need to be considered. Besides, previous studies on laser damage for optical elements mainly focused more on bulk damage, which is not as complex as surface damage due to the changeable surface defects and the participation of air during damage initiation. Non-isothermal fluid action caused by the interaction between the thermal field and the flow field is very violent. Therefore, the mechanism of LID on KDP surface under nanosecond laser irradiation is still not clear. With the continuous improvement of KDP crystal growth technique and laser conditioning process, the bulk damage of KDP crystal exposed with strong laser irradiation (high electric field) has been well restrained22. However, surface damage is still a major issue, limiting the enhancement of damage threshold due to the existence of manufacturing-induced defects. In a word, it is of great theoretical and practical significance to explore the laser-induced surface damage mechanisms, which are beneficial to optimize the optical manufacturing processes and develop the laser damage resistance of KDP crystal.The main mechanisms of laser-induced damage of femtosecond pulse lasers and nanosecond pulse lasers are intrinsic ionization and defect-based heat absorption, respectivelyFortunately, the multi-physics coupling technology provides an access to study the mechanism of laser damage induced by machining defects on KDP surfaces under nanosecond laser irradiation. In this work, a multi-physics coupling model is firstly established to model the laser damage behaviors of KDP crystals under strong nanosecond lasers. Then, the evolution of damage processes such as laser propagation, heat deposition and crater formation is simulated. Further, a combination of micro-indentation and laser damage test is presented to experimentally verify the triggering effect of surface cracks on the laser damage processes of boiling and flowing. The novelty of this work is building a multi-physics model, coupling the electromagnetic field, thermodynamic and hydrodynamic fields. Using this model, the damage evolution from laser irradiation to crater formation is investigated to explore the mechanisms of damage initiation and its growth. The contribution of surface defect, energy deposition, phase transition and fluid action can be proved by the theoretical and experimental evidences. The results help us explore the generation mechanism of laser damage on KDP surface under nanosecond laser irradiation and provide new insights in understanding the effect of temperature and fluid on the damage evolution, which are essential for optimizing the surface processing technic and improving the optics laser damage resistance.23. Under the strong laser irradiation, the light intensity inside the KDP crystal is enhanced due to the special geometric structure of the defect. Then there will be a local light intensity hot spot near the defect, which induces the generation of free electrons in the insulator by ionization24. Thus, an electromagnetic field model is used to calculate the laser energy propagation characteristics in crystal during laser irradiation. Under the subsequent laser irradiation, free electrons interact with the laser and then plasma is generated, which makes the temperature of the material increase rapidly due to the inverse bremsstrahlung. The increasing temperature of the material will in turn promote the production of free electrons inside the crystal. A re-write energy equation needs to be modeled at this moment. When the material temperature rises to the melting point or boiling point of the crystal, dynamic behaviors such as melting, boiling and even material flow would occur in the local damaged area. In addition, the evolution of local mechanical properties during the phase changes25 is also an important cause of crystal surface damage, especially near the defects with low mechanical strength. Therefore, the physical equation describing the material phase change and fluid flow is indispensable in the model.The surface damage processes of KDP crystals under nanosecond laser irradiation are complicated. Figure y direction perpendicular to the front surface of the crystal.Figure The calculation flow chart of multi-physics coupling model is shown as Fig. 26. Due to the fact that the surface defect of KDP crystal in practical engineering is far smaller than the spot size of internal optical path in large laser system, we assume that the incident light is a harmonic plane electromagnetic wave and the equations can be simplified to the Helmholtz equation, as Eq.  near the lateral crack on the front KDP surface, the temperature of the hot spot solved by the electromagnetic field model is assumed to be 9000 K at a the initial time due to the breakdown effect. Then, energy deposition at different moments under laser irradiation is obtained by solving the absorption law between laser and material. The Beer-Lambert law is employed to describe the energy absorption of the incident laser by the material12. For a beam of incident light intensity with Ilaser, this law can be written as the differential form, as Eq.  is temperature-dependent heat absorption coefficient. ρ, C and κ are the density, heat capacity and thermal conductivity of KDP crystal, respectively, in different conditions28. ΔL is the latent heat during the phase change. δ(φ) represents the Dirac delta function. φ is the solution variable of phase-field equation. v is the velocity vector at each point in the solution domain. I is the unit matrix, and μ is the dynamic viscosity of liquid phase for KDP crystal. p is the local hydrodynamic pressure. The Darcy friction FDarcy on the solid-liquid interfaces represents the lost momentum of the solid and liquid phases.Firstly, the Maxwell equations are used as governing equation to solve the electromagnetic wave propagation characteristics during the laser action, as Eq. . Based o, as Eq. . And the, as Eq.  is choseω (λ = 355 nm) plane wave along the direction normal to the front KDP surface was adopted in this calculation domain. The meshing size in the FEM calculation is less than one-sixth of the laser wavelength. The incident laser is TE polarization mode with light intensity Ilaser = 10 GW/cm2 and flat-top pulse width of 4 ns. The light intensity enhancement factor (LIEF) is used to describe the local light intensification relative to perfect crystal without any defects on the surface. Other model sets of the electromagnetic field parameters can be referred to ref. 29.The 330. Since heat absorption coefficient of the crystal at room temperature is very low (0.005 cm−1), the re-write law needs to satisfy that the absorption coefficient must have sufficient response when the crystal temperature reaches 2273 K, which is the temperature of phase change under a high pressure condition19. Besides, when the temperature is high enough, the heat absorption coefficient would keep stable at a higher value.The heat absorption coefficient of KDP crystal under high temperature conditions is obtained by re-writing. Saito has introduced a method based on the vibrational band edge distortion to solve heat absorption coefficient. It is pointed out that the absorption coefficient model is widely used for crystalline solids, because deviation from perfectly ordered systems can also be generated by the thermal vibration inside crystalsSince the two-dimensional model is built in this work, the optical anisotropy of the component is not considered in the calculation process. Besides, the effect of material phase change on the calculation results of the model is sufficient to replace the effect of its parameters with temperature variation. Thus, the precise influence of temperature on material parameters can be temporarily ignored.The energy absorption module and the heat transfer module can be bidirectionally coupled through local energy deposition and iteration of local temperature values. Finally, the positive feedback of the local temperature rise to the laser damage process during the interaction of the laser and material would achieve.The setting of the fluid flow module is complex, mainly because the particles in different fluid media have various motion states. Even in the local microscopic regions of the material phase interface, there may be opposite forms of motion and huge velocity gradients. For the solid and liquid phases of KDP crystals, it is assumed that they are incompressible.28. When the temperature and pressure of the gas material change, its density will also change greatly. Thus, the Navier-Stokes equation for compressible flow is chosen as the governing equation in the gas domain.The material becomes boiling at the temperature above 3273 Kσ is the surface tension coefficient, 0.0588 N/m. n is the liquid-gas (L/G) interface unit normal vector.The velocity of the liquid in the outward direction normal to the gas phase side is higher than that of the gas. Because there are three forces that act on the liquid on the interface, the natural boundary condition near the liquid-gas interface for the liquid domain is described by Eq. , which gThe continuity equations of hydrodynamics characterize the mass conservation in this system. But some transformations are employed for governing equations on various calculation domains.31.The solid-liquid phase is incompressible in the model, And the continuity equation at the liquid-gas interface needs to be modified to represent the phase change from liquid to gas32. The temperature equation defined in porous media domains is based on the convection-diffusion theory with thermodynamic properties averaging models to describe both the solid matrix and fluid properties. The moving speed of the phase change material is dependent on the temperature of each calculation unit. When the moving speed reduces to an infinitesimal value, the porosity of the local domain is defined as zero, meaning that the material is completely solid. By solving the porous-media transport, a variable θ of solid-phase volume fraction that describes the solid-liquid state of the material would be obtained.The method of heat transfer in porous medium interface is utilized to describe the change from solid phases to liquid phases33. The gas phase domain and the solid-liquid phase domain are represented by phase-field variable ϕ = −1 and ϕ = 1, respectively. Since the phase transition process is involved in the model, it is necessary to modify the traditional phase-field model and add terms related to phase transition. The algorithm is developed from statistical physics. Based on the Ginzburg-Landau phase change theory, the phase-field variable is obtained by the combination of differential equations like reaction diffusion, ordering potential and thermodynamic driving force. Then, the state of the material and the L/G interface in the solution domain can be determined according to the phase-field variable.The L/G interface is tracked by phase-field transport methodsCoupling the physical government equations such as heat conduction, fluid flow, porous-medium transport and phase-field transport, we simulate the dynamic laser damage behavior and the evolution of typical physical parameters like temperature and phase-field variable. By establishing the laser-induced damage model initiated by KDP surface defects under laser irradiation, the dynamic behaviors of laser energy propagation, energy absorption, material change and fluid flow in the process of damage can be solved, which provides support for the exploration of damage mechanism.35. As for the lateral and radial cracks, they are mainly generated by a Vickers indenter on the substrate surface. Therefore, we choose artificial cracks prepared by Vickers hardness tester on KDP crystal surfaces to perform the laser damage test. Figure In order to verify the effect of surface defects on LID of KDP crystal and the damage processes like boiling or melting, the experiments were performed by laser damage test on typical surface defects and observing the morphology of damage sites. Defects on KDP surface are common with various morphology and structure. This is because the KDP crystals are soft-brittle and sensitive to the temperature changes. Thus, some defects are inevitably introduced on the KDP surface from accidental vibration of the machine tool during daily machining, handling for cleaning, or even slight changes in external temperature. However, surface defects are generated randomly and there are no nearly identical defects that can be applied for repetitive experiments. Through statistical analysis for large amount fracture behavior of brittle materials, the microcracks on the manufactured surface or subsurface of brittle material  are roughly divided into conical cracks, lateral cracks and radial cracksThe indentations with peripheral cracks around on the crystal surface after loading are presented in Fig. 2 was performed on the indentation pits. The output laser energy has a spatial distribution of Gaussian profile on the front surface of the crystal with the effective spot diameter of 388 μm (1/e), which is large enough to radiate the whole region of each defect. The change of surface morphology during each laser pulse irradiation is detected in situ using a CCD camera. In addition, according to our previous work, the light intensity enhancement generated by the slender radial cracks is much lower than that of the lateral cracks11. Therefore, we believe that the damage initiation is mainly caused by the lateral crack in this laser damage test. However, it can be seen from Fig. Figure Results of physical parameters correspond to the whole equations set can be obtained by the multi-physics coupling model in a single solution. This section firstly shows the calculation of light field, thermal field and crater morphology during the nanosecond laser irradiation. Then the mechanism of laser damage on KDP surface during the strong laser irradiation is discussed. Next, the experimental results of laser damage test and damage morphological are analyzed to verify the dynamics process simulated with the coupling model of multiple physical fields.E/E0|2. Parameters E and E0 are the electric field intensity inside the KDP crystals with surface defects and ideal surface, respectively. When the lateral crack is located on the front KDP surface, light diffraction will occur around the defects inside the crystal due to the disturbed light propagation. In the cross-sectional profiles of LIEF along xOy plane of the Cartesian coordinates, some areas are much brighter, indicating that there is larger light intensity enhancement in these locations. However, some weak regions of light intensity are located behind the lateral crack. Uneven distribution of light intensity would directly result in differences in subsequent energy deposition. Besides, there is an elliptical hot spot in the center position of the lateral crack whose relative intensity is more than 4 times. However, local light intensification with value more than 4 is unacceptable generally29. In addition, the heat absorption coefficient will also change greatly at that time due to the sub-band gap level structure and the photosensitive contaminant in the vicinity of the defect. Thus, the local energy deposited by the hotspot of laser light provides the energy source for the subsequent damage process. As long as the initial deposition energy reaches a certain threshold, the subsequent damage processes, such as material thermal action and phase transition, can be initiated under the action of nanosecond laser. These dynamic processes would finally affect the eventual damage morphology of the crater.The simulation result of laser light propagation is shown in Fig. T in the model) distribution simulated by the model in the damage area with time during nanosecond laser irradiation. With the continuous irradiation of the strong laser, the temperature in the damage site increases. The cross-section area of high-temperature region (HTR) gradually expands. Especially in the gas phase domain, the expansion rate of the HTR is particularly severe. At the irradiation time of 3 ns, the local temperature of the damage exceeds 10000 K, which is in good agreement with previously reported experimental results in ref. 36. The HTR is mainly composed of gaseous KDP, which forms plasma during the interaction between KDP and strong laser. Under the subsequent laser irradiation, it will absorb a large amount of laser energy and aggravate the damage behavior. Besides, it is generally accepted that physical quantities  with tremendous changes would produce shock waves on the step surface  of the corresponding physical parameters. In the temperature simulations, the step surface of high temperature in the damage site is represented by white lines, whose changes are consistent with that of plasma interface previously reported in ref. 18. When KDP crystal is exposed with high power nanosecond lasers, the interaction between laser and matter produces a large amount of energy deposition. Then the vapor produced in the initial stage rapidly transforms into plasma under the action of high temperature environment and strong electromagnetic field. The deposition energy in the damage area provides necessary conditions for subsequent plasma expansion.Figure ϕ calculated in the multi-physics coupling model could represent the laser damage crater morphology. Figure 38. As the material properties of high-temperature phase transition region are affected by multiple physical parameters such as temperature, pressure, ionization and so on, a small parameter change would incur a huge impact on the morphology of laser damage crater. Thus, there are some slight fluctuations on the bottom of the crater because of the instability of the damage system.The phase-field variable t = 2.8 ns, a substance with different refractive indexes from the surrounding medium appears in the center of the damage, which can be seen inside the yellow curve in Fig. Based on the time resolved pump and probe method, the early kinetics of laser damage on KDP surface is captured. Figure 39, the temperature indirectly dependent hydrodynamic pressure, the expansion pressure produced by phase change, and the local mechanical properties of materials which are not dependent on the temperature. Therefore, if the laser energy deposition during the initiation of the damage is defined as the pre-damage process, the fracture may occur at any stage in the middle and late stages of the damage. When the fracture occurs in the melting process, the local damage region is still in a significant high temperature environment, and traces of melting can be found on the fracture surface at the final damage morphology. When the fracture occurs after the melting process, the damaged surface with the molten material will break away from the substrate as the material fracture, leaving a new smooth fracture surface. However, due to the relatively slow deposition process of gas phase materials, a large amount of vapor deposition can still be seen on some newly generated fracture surfaces. Under certain special conditions, the local defect even produces secondary fractures, which are mainly related to the local mechanical properties of the material. For example, assuming that the original site in Fig. The SEM of laser damage morphology after 355 nm-wavelength single-shot laser irradiation is shown in Fig. Combined with the above simulation analysis, the original damage process can be understood as a sharp light absorption point on the surface or subsurface of the KDP crystal induced by manufacturing-induced defects. Then, the surrounding material interacts with the high power laser. The temperature rise of the material is accompanied with the melting, boiling, flowing, and even ejecting processes. The uneven distribution of the thermal field would cause a large thermal stress. Besides, fluid flow and phase change expansion also produce enormous recoil pressure. Once there is a weak point inside the crystal, the material will be broken and an obvious damage pit would be produced.Based on the theories of electromagnetic field, thermodynamics and hydrodynamics, a multi-physics coupling dynamics model is established to describe the behavior of laser damage processes. The propagation characteristics of laser energy, the evolution of temperature distribution and crater morphology in local damage area were simulated. Light intensifications modulated by lateral cracks lead to energy hotspots, which are sufficient to launch avalanche ionization and trigger laser damage on KDP surface. The high-temperature region formed by energy deposition plays an important role in the damage evolution process. It provides a power source for materials phase change, fluid flow and crater morphology evolution. Besides, plasma generated by high-temperature vapor interacts with the subsequent laser irradiation, which accelerates the laser energy deposition. The crater of laser damage presents a bowl-shaped morphology during the laser irradiation. As the increase of laser action time, there would be liquid ejecting around crater, which is mainly due to the uneven distribution of fluid temperature in the damaged area. The temperature of local damage area and the surface morphology of the shock wave obtained by simulation are consistent with the experimental results reported in the literature. By conducting laser damage test and observing laser damage morphology on KDP surface, it is found that lateral cracks are the dominant source to trigger the laser damage on KDP crystal. The experimental evidence of material boiling and melting on the damage sites is consistent with the simulation results. The detection of fracture surface also provides a new idea for the subsequent study of damage formation process by analyzing the evolution of stress and pressure. This work proves that the laser damage involves physical law of light, heat, fluid and fracture. Only when the multiple physics are considered at the same time can the laser damage mechanism be comprehensively explored. The dynamic model of LID initiated by surface defects under nanosecond laser irradiation can be expected to provide new insights into understanding the mechanisms of LID on manufactured KDP surface and optimizing the processing technic of high-quality KDP surface for improving its laser damage resistance.


Movement covariates, such as electromyographic or kinematic activity, have been proposed as candidates for the neural representation of hand control. However, it remains unclear how these movement covariates are reflected in electroencephalographic (EEG) activity during different stages of grasping movements. In this exploratory study, we simultaneously acquired EEG, kinematic and electromyographic recordings of human subjects performing 33 types of grasps, yielding the largest such dataset to date. We observed that EEG activity reflected different movement covariates in different stages of grasping. During the pre-shaping stage, centro-parietal EEG in the lower beta frequency band reflected the object’s shape and size, whereas during the finalization and holding stages, contralateral parietal EEG in the mu frequency band reflected muscle activity. These findings contribute to the understanding of the temporal organization of neural grasping patterns, and could inform the design of noninvasive neuroprosthetics and brain-computer interfaces with more natural control. So far, most neural decoders of grasping movements have been developed to control neuroprosthetic devices or robotic limbs. These decoders have been evaluated invasively in non-human primates9 and in humans with sensorimotor disabilities14, but also noninvasively in humans24. Typically, such neural decoders rely on optimizing the level of discriminability between the (grasping) movements. However, knowledge is still lacking about how the neural mechanisms behind the neural decoders of distinct grasping movements are represented in electroencephalography (EEG), and how these EEG representations are related to the behavioral response described by covariates of movements such as those that result from muscle or kinematic activity.The pathway between the brain and the hand, which ultimately enables the motor control of reaching and grasping movements, has been of interest to scientists for many decades25 that can capture differences between movements by comparing behavioral movement features with neural patterns29. Such models can be used to address not only the relation between the movement patterns encoded in specific brain regions, but also the extent to which the neural representation of the movement is reflected in the patterns of different movement covariates.To gain a better understanding of the mechanisms that the brain uses to conduct goal-directed movements, researchers seek and evaluate representational models31. For example, the findings of several studies have shown that the role of primary motor cortex is to generate movement but not represent it33. It is well established in movement neuroscience that the primary motor cortex is one of the main sources of cortical output to the spinal cord during reach-to-grasp movements36. However, other regions like dorsal and ventral premotor cortices, as well as the posterior parietal cortex have also been associated with reach-to-grasp movements40. Furthermore, a recent study that attempted to characterize the representation of sequences of finger movements using functional magnetic resonance imaging (fMRI) recordings29 showed that premotor and parietal areas encode sequences of finger movements. Such behavior can be observed in dexterous movements such as grasping movements. Moreover, the findings of these studies have supported the existence of a temporal relation between different stages of grasping movements that involve similar brain areas but at different time points.We believe that gaining an understanding of the underlying neural functions used by the brain to perform grasping movements can augment the knowledge revealed by neural decoding performance. Some studies have addressed the difference between the brain patterns that led to high decoding performance and the underlying brain processes that are necessary to accomplish a task41. The generation and representation of reach-to-grasp movements involve distinct brain regions. Acquiring neural data using EEG benefits from a high temporal resolution and allows us to record from broad brain areas, capturing the interactions between the different regions involved in the prehension network47. The findings of previous studies have revealed differences in the EEG neural correlates of different movements of the same arm/hand 48, as well as among three grasp types: power, pincer and intermediate grasps49. However, it is still unclear whether different brain areas and frequency bands are involved in different stages of the grasping movement, and which covariates of the grasping movement are encoded in these brain patterns.Grasping is a complex, skilled behavior that consists of several temporal movement stages, beginning with the planning of the movement and ending with the finalization of the grasping execution. The hand pre-shaping stage depends on the object’s intrinsic properties, such as its size and shape. The hand pre-shapes during its journey to the final destination 51. Hence, in this exploratory study, we chose to investigate the similarity in human grasping movements between EEG representations and their associated movement covariates, in three stages of the grasping movement: hand pre-shaping, reach of the final grasping position and holding. Having in mind this exploratory goal for our investigation, we recorded a rich dataset containing simultaneous EEG, electromyographic (EMG) and kinematic activity, while 31 human subjects performed 33 different types of grasping movements, yielding the largest such dataset to date. We categorized the grasps based on the shape and size of the object, position of the thumb relative to the palm, in addition to the standard grasp type categorization in power, pincer and intermediate. We conducted this study at a group level, and applied representational similarity analysis (RSA)54 to investigate the similarities among the effects of the neural, behavioral (muscle and kinematic) representations and categorical models at different stages of grasping movements.We believe that exploratory approaches in the case of broad research questions are as relevant as the confirmatory approaches for specific, narrowed down questions55, which is used to evaluate the hand preference for several grasping types. We have included the exact items of the questionnaire in the Supplementary Materials (Appendix A). This experiment conformed with the statements of the Declaration of Helsinki (DoH) regarding ethical principles for medical research involving human participants. In addition, the protocol of this study was approved by the ethical committee of Medical University of Graz . After being briefed regarding the protocol of the study, participants signed the informed consent. They were paid 7.5 euros per hour for their participation.We recruited 31 healthy human participants . All participants had normal or corrected-to-normal vision and had no reported neurological or musculoskeletal disorders. All subjects were right-handed. In addition, we also investigated their handedness through an adapted version of the Edinburgh Handedness Inventory56 that contains the most thoroughly investigated collection of static and stable grasps performed with one hand. We categorized the grasps based on three criteria: type of grasp, position of the thumb relative to the palm and object’s shape and size.The experimental task required the execution of 33 different grasp types, which are described in more detail in the Supplementary Materials (Appendix B). We chose this set of grasps because they are part of a taxonomy of graspsFirst, participants attended a practice session at which they became familiar with each of the 33 grasps that they would have to perform later in the study. To this purpose, we presented one example of each of the 33 pictures of the grasps and instructed the participants to explore the position of the fingers, as well as the shape and size of the object, shown in an image on the computer screen located in front of them. Next, the participants were asked to replicate as closely as possible the observed grasp using their right hand, but without using any object. After attending the practice session, subjects took a short break and then took part in the actual experimental task. Each of the 33 grasps was presented in blocks of eight sequential repetitions. Each repetition  was fifteen seconds long. The structure of a trial as a part of a block is depicted in Fig. First, as part of a trial, participants were instructed to focus their gaze on a cross located in the middle of the screen and avoid eye movements for three seconds. Next, during the observation phase which lasted four seconds, participants were presented with a static image showing a hand in a final grasping position together with the grasped object. During this observation phase, participants could move their eyes and observe the shape and size of the object, as well as the position of the fingers and the overall shape of the hand. During the fixation and observation phases, as well as during the break, participants rested their hand on a transparent, custom-made plexiglass hand support, shown on the right side in Fig. https://github.com/sccn/labstreaminglayer). For the recording of the EEG and EOG activity, we used a 64-channel ActiCap system connected to two 32-channel BrainAmp amplifiers . The data was sampled at 1 kHz. The amplifiers have a hardware first-order, high-pass filter operating at 0.01 Hz and a low-pass filter operating at 250 Hz. EEG activity was recorded through 61 channels covering all the brain regions according to the 10-10 international system. The remaining three channels were used to record EOG activity from the outer canthi of the left and right eyes and from the above of the nasion. The ground sensor was placed on AFz and the reference sensor on the right mastoid. To record the muscle activity, we used a Myo armband . This device has eight equidistant EMG sensors and a nine-axis inertial measurement unit (IMU) which provides accelerometer, gyroscope and magnetometer data. The data was acquired via the Bluetooth Low Energy protocol. The Myo armband requires calibration every time it is put on the arm. We only calibrated the armband at the beginning of the experiment, since none of the participants removed the armband during the study. The armband was located on the right arm close to the elbow, above the extrinsic hand muscles. It has been found that the reconstruction of the grasps of different-sized objects can be obtained using only extrinsic muscles58. Hence, we targeted the extrinsic muscles of the hand such as the palmaris longus, flexor carpi radialis, brachioradialis, and flexor carpi ulnaris muscles on the anterior forearm, and the extensor carpi ulnaris, extensor digitorum, extensor carpi radialis brevis, extensor carpi radialis longus muscles on the posterior forearm. EMG activity was recorded at a sampling rate of 200 Hz. A hardware filter was applied to remove powerline interference and then, the EMG activity was streamed through 8 channels of 8-bit data. The other signals from the Myo armband were recorded at 50 Hz.For the simultaneous acquisition of the data, we used the Lab Streaming Layer (LSL) framework . Using a customized application for the LSL, we recorded kinematic data using the Leap Motion controller on the finger segments length, position and joint angles, as well as the palm position and velocity. These were recorded at a variable sampling rate between 80 and 120 Hz. Later in the analysis, we interpolated the data using a cubic spline interpolation, to achieve a fixed sampling rate of 100 Hz. The timestamps of the grasp’s presentation were synchronized offline with the other recorded signals by means of a photodiode, which captured an impulse on the screen at the start of each observation period.findchanges, which minimizes the sum of the residual (squared) error from the local mean.For all data preprocessing and analyses, we used Matlab R2016b . EEG data was first filtered using a Butterworth fourth-order, zero-phase, band-pass filter between 0.1–40 Hz and then downsampled to 100 Hz. EEG, EMG and joint angles data were epoched in fifteen-second-long segments relative to the beginning of the trial. All the trials were reordered according to a common order of grasping conditions among subjects. We rejected, from all types of data, the trials in which the task had been incorrectly executed  and those in which the hand had been incorrectly tracked by the Leap Motion Controller . On average, we rejected thirty trials per subject from the total of 264. After rejection, each grasp type had a median of 7 trials in a 25% to 75% quartile range of 6.38 to 8 trials among all subjects. The movement onset was computed based on the accelerometer signal. Specifically, during the first second following the movement execution cue, we detected the first abrupt change in the signal’s mean and slope by using the Matlab function 59 implementation of Semi-Automatic Selection of Independent Component Analysis (SASICA)60, which performs the correction of EEG data using several methods. For this analysis, we used ADJUST61 and the three EOG channels. After data cleaning, we projected the components into the channel space, maintaining the original frequency range between 0.1–40 Hz. We also used the extracted weights to clean the fixation period . Next, we computed the time-frequency representation (TFR) using Morlet wavelets62 with a resolution of 0.5 Hz in the range 0.1–40 Hz for both the fixation period and the movement execution period. Finally, we calculated the event-related desynchronization (ERD/S) with respect to the baseline period, determined by the average of the two-second long fixation period of all the trials per subject. We calculated the ERD/S using the following formula from63:Next, and only as a preliminary step to clean the EEG data of artifactual eye movements, sensor pops and electrocardiographic (ECG) contamination, we high-pass filtered the data above 1 Hz, using a Butterworth fourth-order, zero-phase filter. After aligning all the trials according to the movement onset, we extracted the first three seconds of the movement execution after the onset. We used the EEGLABz-score and, finally, the envelope (power) of the data was computed. From the signals recorded using the Leap Motion controller, we used the nineteen joint angles for the rest of the analysis. These joint angles correspond to the five proximal , five intermediate and five distal joints of each finger, as well as the four in-between fingers joints. Given the high degree of correlation between some of the explored joints, we applied principal component analysis (PCA) to reduce the dimensionality of the kinematic data. We retained for each subject the first five components, which accounted on average for more than 95% of the data variance.The eight EMG data channels were processed using Hilbert transform, standardized using 64. We found a small within condition and within subject variability at a repetition level and a slightly larger inter-subject variability for all the recording modalities. We include the results of these analyses in the Supplementary Materials Figs We assessed the within grasping condition variability between the grasping patterns of the three acquisition modalities, both at a repetition level and at a subject level, as described in65.Henceforth, for each of the three acquisition modalities , we averaged single repetitions of the same grasp condition both within subject and between subjects leading to one group-level representation per grasp condition. For the averaging of the joint angles we used the circular mean, as implemented in the CircStat toolbox66. The first window was associated with the reaching and pre-shaping of the hand, and it started from the movement onset. The second window was associated with the finalization of the grasping movement. The third window contained information about the holding position of the grasping. From the three windows we extracted the patterns of interest from the three data acquisition modalities: EEG, EMG and joint angles.For the extraction of the features, we defined three temporal windows of interest in the movement execution segment. The windows were consecutive and each window was 500 ms long, which is in line with the latencies of the grasping phases previously reported in the literature67 to extract ERD/S patterns simultaneously at different spatial locations and frequency bands. We present the searchlight approach in more detail in the Supplementary Materials Fig. For the EEG pattern extraction, we implemented a searchlight techniqueWe applied the searchlight technique on each of the three windows of 500 ms from the movement execution segment. All the information within a two-dimensional window was concatenated into a vector. This vector defined the pattern of activity for the region with given centroid in space and in frequency. For the EMG envelope and for the kinematic joint angles, the behavioral patterns resulted from the concatenation of all channels (components) of data over each of the three inspected temporal windows.r (where r is the Pearson correlation) as the distance metric between the patterns of different conditions. Next, we ranked and scaled the distances between 0 and 1, and computed the representational dissimilarity matrix (RDM)52 between pairs of grasping conditions. We present a conceptual description for the RDM calculation based on the grasp patterns extracted from our three acquisition modalities  in the Supplementary Materials Fig. For each of the three temporal windows and acquisition modalities , we compared the patterns of activity of the different grasping conditions, extracted previously. We used 1-56, and on the shape and size of the object.In addition to the brain and behavioral representations, we also implemented categorical models, as shown in Fig. The RDMs of these categorical models were binary representations, which contained a 0 for each pair of stimuli falling into the same category and a 1 for each pair of stimuli falling into different categories. We chose three categorical models: Grasp type, Thumb position and Object shape, which describe the relation between grasps based on intrinsic characteristics of groups of grasps . The categorical model Grasp type described the relation between grasps based on a categorization in three types: power, precision and intermediate. The categorical model Thumb position showed the relation between grasps based on the position of the thumb: abducted or adducted. The categorical model Object shape depicted the relation between grasps based on the shape and size of the grasped object: large bar, small bar, large sphere, small sphere, disk, card and scissors. In an RDM, the representation of each grasp condition in the brain region of interest  was compared to the representation of all the other conditions. Thus, each RDM leads to a representation of the overall differences between conditions that are encoded in that region of interest. Statistical inference determines which candidate  model best resembles the reference (EEG) RDM in a specific brain region of interest.52. We used RSA in order to explore the similarities at a representational level between three types of data: EEG data (in green), behavioral data (in orange) and categorical data (in blue). From the preprocessed EEG data, we extracted the patterns of interest, by performing a searchlight analysis as presented previously and in more detail in Supplementary Materials Fig. In Fig. 68.In the center of Fig. To evaluate the consistency of our observed RSA effects we conducted a bootstrap analysis with 500 iterations. We performed the bootstrap analysis on a pool of 31 different samples corresponding to our subject number, and in each iteration we replaced the 31 samples with other randomly pulled 31 samples. In this manner, through bootstrapping we could estimate the confidence interval, as the variance of the mean (described by the distance between the reference and candidate RDMs) in our population. We report the 95% confidence interval (CI) of the procedure together with the observed mean effect. Hence, the population mean would be included within the ranges of 95% of the CIs of the mean calculated from repeatedly sampled data with a 95% probability.69. MDS is a general dimensionality reduction method that projects entities in a low-dimensional space, such that their distances reflect their similarities. Specifically, similar entries will be located closer to one another, while dissimilar ones will be farther apart. For MDS visualization as a 2D plot, we used the Matlab function mdscale, which performs nonmetric MDS for two dimensions with the squared stress criterion.To visualize the distances between the representations of different grasping movements, we used multidimensional scaling (MDS)Next, we performed a second-level analysis between all the representational models, in each of the three time windows. More precisely, we explored the similarities between RDMs in specific regions of interest , behavioral RDMs and categorical RDMs. We again used MDS as an exploratory visualization technique to simultaneously relate all RDMs  to each other. The conciseness of the MDS visualization comes at a cost: the distances between entities are distorted (depending on the number of representations included); however, these distortions are accounted for by the thickness of the line connecting two entities. In a similar way to a rubber band, the connecting line becomes thinner when stretched beyond the length that would reflect the dissimilarity value that it represents, and thicker when compressed. Hence, the dissimilarity is a combination between the distance and the thickness of the connecting line. Nevertheless, this exploratory visualization technique provides a useful overall picture. It can alert us to relationships we had not previously considered and prompt confirmatory follow-up analyses.Based on the assessment of the Edinburgh Handedness Inventory included in the Supplementary Materials (Appendix A), we found that all the subjects were dominantly right-handed.We computed the reference representations based on the searchlight analysis of the time-frequency representation of the EEG data in the three time windows of interest: hand pre-shaping, reaching of the final grasping posture and holding. The searchlight analysis yielded a total of 806 (31 space centroids × 26 frequency centroids) reference RDMs for each window. The candidate representations are based on the behavioral patterns (envelope of the EMG activations and joint angles kinematics). In addition, we also used as candidate representations three categorical models, based on the type of grasp, the position of the thumb relative to the palm and the shape and size of the object. We present in the Supplementary Materials Fig. 70. We observed clusters of grasp conditions involving elongated or spherical objects.For the behavioral representations, we observed that the differences between the grasps were preserved over the course of the three windows, with some small changes. The first window, corresponding to the hand-preshaping phase was slightly more different than the other two windows. Specifically, for the EMG RDMs the distance between the first window and the second was 0.1, and 0.16 relative to the third. For the kinematic RDMs the distance between the first window and the second was 0.24, and 0.33 relative to the third. The second and the third windows were highly similar for both muscle and kinematic modalities, with a distance of 0.04. Furthermore, we also found high similarities between the two behavioral models, which are in line with previous findingsNext, we present the exploratory results of the representational similarity (RSA) analysis between the EEG representations extracted through the searchlight analysis, and the behavioral and categorical representations, for the three time windows. Specifically, we investigated the relationship between the candidate RDMs and the reference EEG RDMs. A complete overview of the exploratory results for all the comparisons between the reference RDMs and the candidate RDMs can be found in the Supplementary Materials Fig. The regions with the smallest distance between RDMs are the left centro-parietal and parietal in the mu and lower beta frequency bands. In the first time window, the observed effects of dissimilarities noted between the reference EEG RDMs and the Object shape model in the lower beta band were lower in the contralateral centro-parietal areas as well as in the ipsilateral parietal areas. We observed a dissimilarity effect of 0.8 with a 95% CI: . In the second time window, we found dissimilarities between the reference EEG RDMs and the EMG RDM in the mu band, which were lower in the contralateral centro-parietal areas. We observed a dissimilarity effect of 0.68 with a 95% CI: . In the third time window, we observed dissimilarities between the reference EEG RDMs and the EMG RDM in the mu band, which were lower in the contralateral parietal areas. We observed a dissimilarity effect of 0.68 with a 95% CI: . In panel B, we show the observed effect of similarity over all the centroids, as depicted in panel A, together with the 95% confidence interval of the procedure computed after 500 bootstrapping iterations.For an intuitive visualization of the relationship between the different grasping conditions, we used multidimensional scaling (MDS). Panel A of Fig. On closer inspection, we found that the grasps that involved objects with a thinner shape were clustered together (see the lower left part of the MDS representation). Surprisingly, we found that the categorization into grasp types—power, pincer and intermediate—depicted by the three colors in the MDS plot, was not congruent with the reference EEG RDM representation. Panel B shows the relation between grasp conditions based on the shape categorization. Specifically, the categorical Object shape RDM contained a 0 for each pair of grasps that fell into the same category and a 1 for each pair of grasps that fell into different categories. We found a correlation of 0.2 between the neural RDM and the categorical Object shape model during the first movement phase.In Fig. In panel A, we present the RDM and the MDS of the relation between the grasp conditions as covered by the left centro-parietal region of the brain in the mu frequency band. Panel B depicts, through the RDM and MDS, the relation between the grasp conditions as encoded by the EMG patterns.We used MDS to visualize the similarity structure of each RDM. This exploratory visualization technique Fig.  right alIn Fig. In this phase of the grasping movement, we observed that the EEG pairwise representation between grasps changed relative to those seen in the previous window, in which the grasping movement was still ongoing. On the other hand, the EMG representation remained stable compared to the one observed in the previous window. However, using the MDS visualization, we found that several grasps maintained their relative distances between representational types. As we had previously observed, the grasps that involved elongated objects clustered together also in the holding phase. We also found that some grasps, such as 9, 22, and 29, have relatively large distances relative to the majority of grasps. This relation between groups of grasps can be observed both in the EEG and in the EMG representational modalities.Next, we conducted a second-level analysis to explore all the pairwise relations between the reference and candidate representations. Fig.In Fig. r = 0.64) between the EMG and the kinematic representation based on the joint angles.Panel A shows a smaller distance between the EEG representation and the Object shape model in the hand pre-shaping phase. In the next two grasping phases, the EEG representation encoded the EMG representation to a higher extent with a distance of 0.68 (which is a moderate correlation of 0.32), as shown in Panel B. Moreover, we also observe in Panel B a small distance of 0.36 , behavioral patterns and categorical models of the largest repertoire of unique grasping movements provided in literature30. This dictum states that “if information can be decoded from patterns of neural activity, then this provides strong evidence about what information those patterns represent”. A good argument for the reasons of why the dictum is false has been given by Ritchie and colleagues in30. We believe that, complementary to the state-of-the art decoding findings, we should try to clarify our understanding of the decoding results by involving inferences about neural functions and their representations regarding their behavioral resemblances71. One way to make better inferences is by leveraging the benefits of exploratory analysis, which has the potential to address broader scientific questions and inform about promising effects observed in the data51. New BCIs could be developed based on the unitary understanding of neural functions from different brain areas and the associated behavior. For instance, Aflalo and colleagues73 have recently suggested that signals from parietal cortex rather than motor cortex can be used to control the reach-and-grasp movement of a neuroprosthetic arm in a patient with spinal cord injury.In the brain-computer interface (BCI) research, there has been a strong endeavor to decode reliable control signals from the brain, with the aim to control computer cursors, neuroprosthetics, or robotic limbs. Given the engineering and translational goals of BCI research, we often disregard the neural plausibility of the decoding results. Consequently, the decoding results should not be interpreted as a neural representation of the way in which the brain processes a certain task. This incorrect interpretation of decoding findings has been widely disseminated, and it is also known as the “Decoder’s Dictum”53.In this study, we addressed three questions: (1) Can EEG signals capture the differences between multiple types of grasps; (2) Which grasping covariate best explains how grasps are represented at the EEG level; (3) To what extent do grasping representations based on movement covariates and on EEG patterns resemble each other. To address these questions, we designed a paradigm that incorporates the execution of a large number of distinct grasping movements while simultaneously recording neural, muscle and kinematic correlates of the grasps. To explore the relations among the neural, behavioral and categorical patterns of different grasping movements, we chose to conduct a representational similarity analysis (RSA). Because it is a multivariate pattern analysis method, the use of RSA allowed us to study both the representational geometries and informational content of the grasp conditions in multidimensional space spanned by EEG sensors, different frequency bands and time points. This characteristic makes RSA particularly amenable for searchlight analysis. Moreover, RSA is especially suitable for use with condition-rich designs such as ours (33 different grasp movements). As with classifier decoding, RSA is a technique that is sensitive to information encoded in patterns of activity. However, rather than attempting to determine what information can be (linearly) read from the patterns of activity, the use of RSA allowed us to characterize the representational geometry of a rich set of conditions and compare it to various representations or models. Moreover, rather than allowing us to compare, for instance, brain and muscle or kinematic patterns, which requires defining correspondence mapping between pattern units and channels of activity), the use of RSA allowed us to compare the representations at the level of dissimilarity matrices (between conditions) of each model26, or to characterize the relation between behavioral and neural information based on the comparison of dissimilarity matrices in the case of single or multi-finger movements28. In these studies the description of the behavioral models was based either on the movement synergies or on the information extracted from the activity of the whole postural vector. Recently, Leo et al.26 conducted a study combining kinematic, electromyographic and fMRI brain activity and found that the hand postural information encoded through kinematic synergies during grasping is represented in cortical areas related to hand movement control. In our exploratory study, we found the activation of the same brain areas. However, we observed larger similarities between the EEG and the muscle representations than relative to the kinematic representation. A comparison between the performance of the behavioral models (muscle and kinematic) in our study and the ones presented in28 is not straightforward because we recorded the muscle activity from eight extrinsic (located on the forearm) hand muscles, while the previous studies recorded from both intrinsic (located on the hand) and extrinsic hand muscles, with a larger number of sensors on the intrinsic muscles. The extrinsic muscles of the hand are larger than the intrinsic ones, thus, the recorded signals are often collinear leading to a higher amplitude and a better signal-to-noise ratio when compared to the intrinsic muscles of the hand. The good performance of our muscle model could be attributed to the quality of the signals recorded from the extrinsic muscles. Also, the kinematic models are differently obtained in the current study than in previous ones , making a direct comparison more difficult. Furthermore, we believe that one advantage in our study is the simultaneous acquisition of all three recording modalities . In previous studies each modality was acquired separately, this could lead to differences in the recordings due to the nonstationarity of the signals or the state of the subjects across the sessions. The synchronous acquisition of all three modalities can allow a potentially better characterization of the grasping movements from different perspectives.In two recent studies, RSA has been applied either to study the encoding properties of models based on muscle and kinematic synergies in different cortical areas during grasping movementset al.27 explored the relation between grasp and object properties, such as shape, size and elongation, in terms of their representation in fMRI activity. They observed that object elongation is the most strongly encoded object feature during grasping. Moreover, they found that the number of fingers used during grasping is represented both within ventral-stream and parietal regions. In our study, we found activations in the parietal and centro-parietal areas during the hand pre-shaping phase that resemble the categorization of grasps based on the shape property of the objects. Moreover, we also found that the elongation of the objects is a distinctive feature that structures different grasping movements into clusters. Yokoi et al.29 investigated the representation of sequences of finger movements in the motor cortex. Although it is well-known that the human primary cortex (M1) is the main region involved in single finger movements, it is debatable if sequences of finger movements also originate in the M1 or involve other areas. The reliable differences between different sequences of finger movements seem to be encoded in premotor and parietal regions29. Our results are in line with these findings, supporting the activation of parietal and centro-parietal areas during grasping, as a meaningful sequence of finger movements.From a behavioral perspective, we can grasp an object in many different ways. The goal of the movement and the visual properties of the object play important roles in the pre-shaping of the hand into an appropriate configuration. For instance, grasping a knife to cut bread is different than grasping a knife to perform surgery. Fabbri 76, the first few components, after dimensionality reduction methods had been applied, exhibited high degrees of similarity between the two types of grasping. Furthermore, in the current setup, real objects could occlude the fingers and lead to errors in the tracking signals. In terms of ecological validity, we aimed to increase the consistency in the execution of each movement for each subject. Given the small number of repetitions per grasping movement, we instructed each subject to perform all the repetitions of the same movement in a consist manner. This movement constraint can hinder the ecological validity of the task; however, we did not constrain the inter-subject variability. Moreover, we found that although the subjects showed similar behavioral patterns among the repetitions of the same grasping movement, their neural correlates were more variable. Potential reasons for this variability observed in the neural patterns can be attributed to the lack of consistency in the mental strategy or to a decrease in the level of engagement of some subjects while performing repeated movements of the same grasp. The movements were performed on a natural pace and none of them was unfamiliar or difficult to perform for the subjects. From an experimental design perspective, we made a trade-off between each condition’s specificity (which would require the acquisition of more repetitions of the same grasp type from each subject) and among-conditions sensitivity . Thus, this design is not suitable for decoding studies, which do not require so many different conditions, but a better characterization of each condition.One potential limitation of the current study is the absence of real objects during grasping. We chose to use imaginary objects in order to remove potential confounds driven by force or feedback differences between the grasped objects, which could contaminate the recorded signals. In studies that have explored the differences between grasping movements towards real and imaginary objectsIn summary, these findings allow us to frame hypotheses regarding the representation of distinct grasping movements based on the relation between their EEG representations and the associated behavioral (muscle or joint angles) representations, as well as relative to categorical models, describing the object’s size and shape, type of grasp, or position of the thumb relative to the palm. On a group-level, we found that the EEG representation of grasping finalization and holding the final grasping position is encoded to a higher extent in the muscle representations than in the kinematic representations. However, the two behavioral representations were highly correlated. By conducting a follow-up confirmatory analysis in a future study, we will be able to evaluate the encoding of the mixed behavioral representation in the neural patterns. Furthermore, we plan to test the proposed categorical Object shape model and confirm whether it is a suitable model for the representation of grasps during the hand pre-shaping phase. We encourage other researchers in the BCI field to explore and evaluate also other behavioral and categorical models than the ones presented here, or a combination of those.We strongly believe that a good understanding of neural mechanisms can be inferred only by incorporating the behavioral covariates. Such inferences, once collected, could allow us to gain more natural control of robotic devices or neuroprostheses in the near future.Supplementary Materials


An abdominal aortic aneurysm (AAA) is a focal dilation of the abdominal aorta, that if not treated, tends to grow and may rupture. The most common treatment for AAAs is the endovascular aneurysm repair (EVAR), which requires that patients undergo Computed Tomography Angiography (CTA)-based post-operative lifelong surveillance due to the possible appearance of complications. These complications may again lead to AAA dilation and rupture. However, there is a lack of advanced quantitative image-analysis tools to support the clinicians in the follow-up. Currently, the approach is to evaluate AAA diameter changes along time to infer the progress of the patient and the post-operative risk of AAA rupture. An increased AAA diameter is usually associated with a higher rupture risk, but there are some small AAAs that rupture, whereas other larger aneurysms remain stable. This means that the diameter-based rupture risk assessment is not suitable for all the cases, and there is increasing evidence that the biomechanical behavior of the AAA may provide additional valuable information regarding the progression of the disease and the risk of rupture. Hence, we propose a promising methodology for post-operative CTA time-series registration and subsequent aneurysm biomechanical strain analysis. From these strains, quantitative image-based descriptors are extracted using a principal component analysis of the tensile and compressive strain fields. Evaluated on 22 patients, our approach yields a mean area under the curve of 88.6% when correlating the strain-based quantitative descriptors with the long-term patient prognosis. This suggests that the strain information directly extracted from the CTA images is able to capture the biomechanical behavior of the aneurysm without relying on finite element modeling and simulation. Furthermore, the extracted descriptors set the basis for possible future imaging biomarkers that may be used in clinical practice. Apart from the diameter, these biomarkers may be used to assess patient prognosis and to enable informed decision making after an EVAR intervention, especially in difficult uncertain cases. An abdominal aortic aneurysm (AAA) is a pathological weakening and ballooning of the abdominal aorta. The abdominal aorta is considered aneurismatic when its diameter is larger than 3.0 cm or when it exceeds its normal diameter by more than 50% . EVAR involves the deployment and fixation of an endograft using a catheter, introduced through the femoral arteries. This procedure excludes the damaged aneurysm wall from blood circulation, creating an intraluminal thrombus that shrinks if the intervention is successful. Even if EVAR has shown great benefits with respect to open surgery, the long-term survival rates in both approaches are almost equivalent , typically performed 1 and 6 months after the intervention, and then at least yearly  along the aortic centerline to remove displacements of the aorta.Straightened CPR-based deformable registration to evaluate changes intrinsic to the thrombus or aneurysm.Displacement field-based strain analysis.This section describes the employed datasets and the proposed approach to extract the post-operative mechanical strains, to correlate them with the patient prognosis. In summary, our method has the following steps:Comité Ético de Investigación Clínica del Área Sanitaria de Gipuzkoa.”Our experiments are run on 44 post-operative CTA scans of 22 patients treated with the same standard EVAR technique at Donostia University Hospital (Spain). The age of the patients ranged from 63 to 87 years, and 21 of them were male. Ethical approval was obtained for the current study by the “Protocols for EVAR surveillance usually establish the need of a CTA scan at 1, 6, and 12 months after initial repair, but the 6-month scan can be eliminated from surveillance if the 1-month scan shows no concerning endoleak or sac enlargement  a landmark-based rigid registration of the vertebrae and hips to eliminate patient position and orientation changes, (2) straightened curved planar reformation of the aorta to remove aortic displacements, since blood vessels are not rigid structures, and (3) deformable registration of the thrombus to capture changes intrinsic to the aneurysm. These steps are further explained in the following subsections.The proposed registration methodology starts from the rigid alignment of the segmented vertebrae and hip, since they are the most rigid structures that appear in abdominal CTA datasets. The registration of the two post-operative datasets of each patient is initialized with a landmark-based translation that roughly brings the second CTA closer to the first post-operative scan. The lowest renal artery position, previously employed for the aneurysm segmentation, is employed as landmark, allowing optimization of registration time and ensuring convergence. Then, a rigid 3D registration procedure is performed  to the lumen and thrombus of each dataset.In vascular image analysis, one way to display vessels is to generate longitudinal cross-sections at each centerline point in order to show their lumen, aneurysm, and surrounding tissues  at each aneurysm voxel can then be computed from the displacement gradient field as follows:where U.where Assuming a finite strain regime, the Lagrangian deformations of the aneurysms can be described by means of the right Cauchy-Green strain tensor, calculated at each voxel  as:The principal components of the right Cauchy-Green strain tensor are the squares of the principal stretches. More specifically, the largest eigenvalue of The final step of our method consists in quantitatively analyzing the extracted tensile and compressive strain fields to associate these descriptors with patient prognosis. Hence, it is necessary to define image metrics that summarize the global appearance of the tensile and compressive strain vectors. We hypothesize that the principal component analysis (PCA) of the fields can capture whether each field is globally tangential or normal to the wall, so as to achieve quantitative image-based descriptors that are able to differentiate between favorable and unfavorable evolution patients. PCA is an essential tool in shape modeling, which allows to sharply reduce the dimensionality of the strain data, maintaining the most relevant information, and eliminating noise. This property is essential to discard the information from deformation vectors produced due to small errors in the segmentation or registration process. PCA identifies directions  along which the variation in the data is maximal. This property allows us gain physical insight into dominant deformation patterns.Hence, we compute the PCA for each tensile and compressive strain field, and we obtain 3 principal components per field. These components define the principal directions of each field and can be used to perform a Receiver Operating Characteristic-Area Under the Curve (ROC-AUC) analysis. To test that in fact these principal components capture the global pattern of the strain fields and for analytic purposes, we train a linear Support Vector Machine (SVM) classifier to separate between favorable and unfavorable evolution cases. An SVM is a supervised machine learning method capable of deciphering subtle patterns in noisy and complex datasets , allows to evaluate the biomechanical behavior of the aneurysm quantitatively, and to correlate it with the long-term prognosis of the patient.On the one hand, our proposed registration pipeline is able to generate displacement fields that provide a meaningful representation of the aneurysm's intrinsic changes along time. To date, the comparison between time-points is mostly done by synchronizing two CTA series and concurrently visualizing them, without considering further information that could assist in detecting local changes difficult to see just by looking at the original gray-scale images. The visualization of the displacement fields, including color coded information about the magnitude and direction of the aneurysm surface deformation at each point, such as in Regarding the interpretation of these displacement fields, different patterns are observed for favorable and unfavorable evolution patients. Patients with a good evolution present fields that characterize the remodeling of the aneurysm after the intervention, in which many vectors point toward the inside of the aneurysm surface due to the shrinkage of the aneurysm. On the other hand, patients with an unfavorable evolution come out with fields where many vectors point outwards, representing the global enlargement of the aneurysm. With the available data, it is difficult to establish different deformation patterns for each endoleak type, but with a larger image database local deformations could be correlated with the location of the leaks.On the other hand, the displacement fields and the analysis thereof through the continuum mechanics theory allow to biomechanically interpret the information extracted from CTA time-series, providing the basis for the definition of image-based biomarkers for EVAR follow-up. The eigenvectors of the right Cauchy-Green matrix represent the aneurysm tensile and compressive strain at each voxel, which again can be visualized to understand the global strains suffered by the aneurysm post-operatively. We have observed that for patients with unfavorable evolution the tensile strain fields are tangential to the surface of the aneurysm, whereas for patients with a favorable evolution these fields have a direction closer to the normal of the surface at each point. Compressive strain fields are, however, more difficult to interpret. It seems that for patients with an unfavorable evolution compressive strain fields show a more hedgehog shape, where the minimum principal strains, i.e., maximum compressive strain, within the wall have an outward direction.To gain insight into the validity of the strain patterns that we obtain for the evolution of real aneurysms, we resort to the similarity of our mechanical study with that of cylinder stress theory. To do so, we have built a dummy finite element model that simulated a soft cylinder with characteristics roughly similar to an abdominal aorta . For simulating an aneurysm-like inflation, an internal pressure of 0.013 MPa was applied locally to a centered segment of the tubular structure with height of 1/3 of the total cylinder length with direction normal to the cylinder face. The obtained principal Lagrangian strains (eigenvalues of the Green-Lagrange strain tensor defined as Besides, there is also the need to evaluate the strains more objectively and globally to correlate them with the long-term evolution of the patient. For that purpose, we have computed the PCA for each patient tensile and compressive strain fields, obtaining 3 principal components per field that define the principal directions of the strains and that are used to perform a ROC-AUC analysis. Applying PCA to extract the global deformation pattern allows discarding noise from the deformation fields that may come from small errors in the segmentation or registration processes. When using tensile features alone to perform the ROC-AUC analysis, a mean AUC of 72.8% is obtained, which reflects that tensile strains are able to capture the differences between favorable and unfavorable evolution aneurysms. Regarding the compressive strain features, even through visual inspection the relation between compressive strain directions and patient evolution is less clear than the corresponding relation with tensile strain directions. This is confirmed by the mild performance of the classification based on the compressive features alone. Nevertheless, the ROC-AUC analysis using tensile and compressive features together yields an AUC of 88.6%, which confirms that these compressive strains contain important physical information about the wall mechanics and the evolution of the aneurysm, according to the aforementioned analogy with the cylinder stress theory.in-vivo. With our proposed approach no assumption is required, and the proposed methodology could be easily translated into an intuitive semi-automatic workflow to assist the clinicians during the follow-up of patients.Overall, a good correlation has been observed between the principal components of tensile and compressive strain fields together and long-term patient prognosis. This suggests that the strain information directly extracted from the CTA images is able to capture the biomechanical behavior of the aneurysm and it opens up the opportunity to further investigate a new way to evaluate aneurysm biomechanics directly from the image, instead of using finite element modeling and simulation. These models are sometimes difficult to calculate, which limits their applicability in the clinical routine, and require the assumption of some mechanical properties that are not precisely measurable Furthermore, the proposed principal components, treated as features, set the basis for possible future imaging biomarkers that may be used in clinical practice to assess patient prognosis and to enable informed decision making after an EVAR intervention, especially in difficult uncertain cases. These may include endotension cases or patients with visible endoleaks that do not shrink after the intervention. Besides, finding specific strain patterns depending on the endoleak type may also be valuable in order to better characterize the prognosis of the patient, which we consider an interesting future line of research.The results are encouraging, but some limitations need to be addressed in order to make our approach translatable to the clinical practice. Firstly, errors in the segmentation of the different CTA structures, as well as in the registration pipeline, may subsequently produce errors in the computed final deformation fields. The influence of these errors in the analysis of the strain fields is partly overcome by using global principal component analysis, but a detailed evaluation of its potential impact should be assessed and minimized in a future stage. Similarly, the differences in the image spatial resolution may also influence the output strain fields, since during the registration process some information may be lost or interpolated when registering an image with a reference scan with a different image spatial resolution. The extent to which these variations alter the final strain fields should also be studied. On the other hand, our dataset is mostly composed of men, and thus the strain patterns may be different for women. Even if AAAs are about four times less common in women than in men, those who develop an AAA seem to have a worse prognosis than men (van de Luijtgaarden et al., The raw data supporting the conclusions of this manuscript will be made available by the authors, without undue reservation, to any qualified researcher.The studies involving human participants were reviewed and approved by Comité Ético de Investigación Clínica del Área Sanitaria de Gipuzkoa. According to the laws of our committee, since it is an anonymized image-based retrospective study, no informed consent is required.KL-L developed the methodology, run some experiments, and wrote the manuscript. IG run some of the experiments. AG supervised the work from a clinical perspective. CC and JN provided their knowledge on the biomechanics domain. IM gave support with his knowledge on medical image analysis of abdominal aortic aneurysms. GP and MG provided methodological guidance and reviewed and revised the manuscript.KL-L, IG, CC, and IM are employed by Vicomtech. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.