In this study, to improve the processing performance of whole grain highland barley flour (whole grain HB flour), they were prepared by sand-roasting, far-infrared baking, steam explosion, and extrusion, and the effects of on functional properties and storage characteristics were measured. The results indicated that sand-roasting, far-infrared baking, and steam explosion all caused cracks and honeycomb structures in the outer layer and endosperm of the highland barley. The XRD analysis results indicated that highland barley starch treated by far-infrared baking exhibited typical A-type crystal structure, while sand-roasting, steam explosion, and extrusion presented the typical V-type. The results of DSC analysis revealed that the onset temperature (To), peak temperature (Tp), gelatinization enthalpy (ΔH), peak viscosity (PV), trough viscosity (TV), and final viscosity (FV) decreased significantly, while the swelling power, water-holding capacity and oil-holding capacity increased significantly. During the storage period, the moisture content and lipase activity of the whole grain HB flour after thermal treatment remained at a low level; the fatty acid value, peroxide value, and malondialdehyde value increased; finally, the cooked whole grain HB flour was unstable during storage. The functional properties of whole grain HB flour can be improved by steam explosion, and will then have better storage stability. Highland barley is the most distinctive food crop on the Qinghai Tibet Plateau, and it is also the primary food crop for the survival of farmers and herdsmen in Tibet. Highland barley has high protein, high dietary fiber, high vitamins, low fat and low carbohydrates . Its aleIt is an economical and feasible product preparation method to cook highland barley grains by thermal treatment, then grind them . ThermalThe application of cooked whole grain flour in food primarily depends on the thermal treatment method and its influence on the processing and storage characteristics of whole grain flour. A limited number of studies have reported that baking reduces the bulk density, emulsifying ability, and foaming ability of baked wheat flour, alters the gelatinization characteristics of flour, and reduces the peak value, valley value, breakdown viscosity, and final viscosity . Baked bTherefore, using untreated highland barley flour as the control, this paper studies the effects and differences of four thermal treatment technologies of sand-roasting, far-infrared baking, steam explosion, and extrusion on the structure, physicochemical, functional properties, and storage characteristics of whole grain HB flour, so as to provide a theoretical basis for the quality improvement of whole grain HB flour and its application in food development.Kunlun 15 (white-grain) highland barley is grown in Xining City. The highland barley seeds harvested in August were provided by the Qinghai Academy of Agriculture and Forestry Sciences, and the basic nutrients are as follows: protein is 10.56%, total starch is 49.58%, crude fiber is 2.44%, crude fat is 2.06%, ash is 1.59%, β-glucan is 6.07%), stored at −18 °C. All other chemical reagents were of analytical grade.Each method was pretested to determine the conditions of sand-roasting, far-infrared baking, steam explosion and extrusion. In each case, the grain was completely cooked. The specific treatment is described as follows:Sand-roasting: Soak the highland barley grains in water for 6 h until the moisture content reaches 40%, drain them and place them in a constant-temperature automatic stir-frying machine , stir-fry them at 110 ± 5 °C for 10 min, cool the fried highland barley grains to room temperature (20–25 °C), and place them in a polyethylene bag for standby.Far-infrared baking: Soak the highland barley grains for 6 h until the moisture content reaches 40%, spread them flat on the oven tray in a thin layer (thickness of 0.5 cm), and bake them with a CK-2 far-infrared food oven  at a bottom heating temperature of 150 ± 5 °C and upper heating temperature of 170 ± 5 °C for 20 min, then cool them to room temperature (20–25 °C) and place them in a polyethylene bag for standby.Steam explosion: Adjust the moisture content of highland barley to 10% before steam-explosion treatment. Place 1 kg highland barley grains in an air puffer  with a pressure of 1.25 MPa. After 7 min, conduct air puffing. Cool the puffed highland barley grains to room temperature (20–25 °C) and place them in a polyethylene bag for standby.Extrusion: After grinding the highland barley grains, add 34% pure water and process the highland barley grains into highland barley chips using a twin-screw extruder . The extrusion temperature should be 55 °C in zone I, 180 °C in zone II, and 160 °C in zone III; the feeding frequency should be 22 Hz, the rotary cutting frequency should be 26 Hz, and the screw speed should be 800 r/min. Cool the extruded highland barley chips to room temperature (20–25 °C) and place them in a polyethylene bag for standby.Grind the untreated and heat-treated barley with a high-speed grinder  into whole grain HB flour, then determine the quality of the whole grain HB flour.A WSC-S automatic color difference meter was used for detection. The same sample was measured 3 times, and the average value was taken to determine the color parameters of the whole grain HB flour. L* , a*  and b*  were obtained. Brightness (L*), red (a*), yellow (b*), and color difference between untreated and cooked highland barley flour (ΔE) were obtained by the equation:We removed an appropriate amount of highland barley flour sample and placed it on the sample stage . We spraAn X-ray diffractometer  was used for continuous scanning. The scanning voltage was 36 kV, the current was 20 mA, the scanning range was 5–40°, the scanning speed was 2°/min, and the increment was 0.02° (2θ). Jade 6.5 software was applied to calculate the relative crystallinity as a percentage of the diffraction peak area according to the total peak area.We accurately weighed a 3 mg sample and 6 mg of deionized water, placed them in an aluminum crucible, covered, and sealed them. We conducted differential scanning calorimetry measurements using a thermal analyzer  to measure the thermal characteristics . The test was performed under the condition of filling N2, with the heating rate 10 °C/min and the measurement range of 22–200 °C ,14. By aThe dynamic viscosity of highland barley flour was measured by a rapid viscosity analyzer RVA 4500  . The moiFor the tap density , we plac0) sample and placed it in a centrifuge tube, weighed M1, added 30 mL distilled water , heated with boiling water, and stirred for 15 min. We cooled it to room temperature, centrifuged it at 3000 r/min for 20 min, placed the test tube upside down on the test tube rack, let it stand for 10 min, drained the water (or edible oil), and wiped the sample dry with filter paper, then accurately weighed the mass M2. The WHC and OHC were calculated with the equation in the formula [We weighed a 2.5000 g (M formula .(2)WHC/1, added 10 mL distilled water, stirred evenly, let it stand at room temperature for 24 h, and read the volume of the sample as V2.The method described by Crosbie, G.B. (1992) was used . We accuFor the accelerated storage test, the whole grain HB flour after thermal treatment is packed at 500 g/share under the temperature of 50 ± 1 °C and humidity of 50 ± 1% conditions for accelerated storage. The moisture, lipase activity, fatty acid value, peroxide value, and malondialdehyde value were detected every 14 days. Each measurement was 60 g, 7 times (accurate to 0.01 g). 1 day under 50 °C was equivalent to 20 °C for 8 days.Lipase activity was determined according to Yu’s study . We weig1 (mL). Meanwhile, we replaced the sample with petroleum ether for a blank test, and recorded the volume of NaOH consumed V0 (mL) [We mixed 2 g whole grain HB flour with 50 mL petroleum ether, shook for 10 min, and filtered and collected the filtrate. We mixed 25 mL filtrate with 75 mL 50% ethanol solution, added 5 drops of phenolphthalein, and titrated with 0.01 M NaOH until the color turned light pink. We recorded the volume of NaOH consumed V V0 (mL) .(5)Ak , then took the supernatant and measured the absorbance at 500 nm with a spectrophotometer. The above solution without sample was used for the blank control. The entire measurement should be completed within 10 min [We accurately weighed 0.1000 g whole grain HB flour, mixed it into 9.8 mL chloroform methanol (7:3) solution, and shook it in a vortex mixer for 4 s. We added 50 μL ammonium thiocyanate (NHSCN) solution and shook for 4 s. Then we added 50 μL Fe+ solution and shook for 4 s. We stored it at room temperature for 5 min and centrifuged it (1000× n 10 min .(6)PeroWe Weighed 2.000 g whole grain HB flour, added 10 mL 10% trichloroacetic acid, and centrifuged it for 10 min at 4000 r/min. We removed the supernatant and diluted it to 10 mL with trichloroacetic acid. We added 2 mL 0.6% sulfurized barbituric acid. After mixing, we bathed it in boiling water for 15 min and measured the absorbance at 450, 532, and 600 nm after cooling .(7)MDA The moisture content of whole grain HB flour was determined according to the Chinese standard (GB5009.3-2016). In short, the whole grain HB flour was kept at 105 °C and dried in a drying oven  until the sample weight was stable. The weight before and after heating was measured by electronic analytical balance .All the above tests were conducted in three groups . The significant difference between Duncan test and Pearson correlation was calculated by IBM SPSS 22.0. All data for this work were described using Origin 18.Next, the microstructure of the cross-section B–D. SpecThe information about the relative crystallinity and crystal type was obtained by XRD for the study of starch structure . The resIn this study, compared with the untreated samples, the XRD peak intensity and crystal structure of whole grain HB flour were significantly improved after thermal treatment. The XRD pattern after infrared baking was like that without treatment, exhibiting a typical A-type crystal structure. The whole grain HB flour treated by sand-roasting, steam explosion, and extrusion presented a typical V-shaped diffraction pattern. This pattern may be the result of complexes formed by the interaction between starch molecules and polar organic molecules during thermal treatment, such as starch-lipid complexes , which wp ˃ 0.05), yet higher than that of highland barley flour after steam explosion. This effect may have been caused by the different heating mechanisms of the selected heating methods [The color characteristics and color parameters of untreated highland barley flour and highland barley flour after different thermal treatments are portrayed in  methods ,16. The p ˃ 0.05), and the total color difference (ΔE) of whole grain HB flour after pressurized puffing was the lowest (9.94 ± 0.128). This was mainly due to the comprehensive influence of different processing methods on different color parameters  [In addition, all treatments in this test increased the a* and b* values of whole grain HB flour from 0.96 ± 0.035 and 11.87 ± 1.205 (untreated highland barley) to 4.46 ± 0.015 and 20.47 ± 0.012 (highland barley after steam explosion), respectively. These changes were attributed to the production of brown substances with different molecular weights at the later stage of the Maillard and caramel reactions, resulting in the increase of a* and b* . The totp < 0.05). The respective variation ranges were 72.50–34.50 °C, 93.40–64.90 °C, and 7.54.0–2.36 J/g, which was consistent with the results of Zhu’s study [The thermal properties of whole grain HB flour with different thermal treatments are portrayed in ’s study . In gene’s study . The dif’s study . The resp < 0.05). The peak viscosity mainly reflected the ability of binding water or the degree of granule swelling. The higher the peak viscosity was, the stronger the viscosity of the sample would be. The decrease of PV may have been the result of the decrease in starch polymerization degree or starch degradation caused by the rupture of starch chain. The PV value of whole grain HB flour after extrusion puffing was the highest, followed by the samples after sand-roasting and infrared-baking, and the PV values of the sample after steam explosion were the lowest, at 1461, 993, 670, and 425 cp, respectively. The results indicated that the whole grain HB flour after extrusion had stronger water-binding capacity than those treated by other methods, and a strong gel could be formed after water swelling. This may be related to the formation of starch polymer chain, molecular chain rearrangement, and change in crystallinity [Gelatinization characteristics represent the cooking quality and texture behavior of grain flour. allinity .The trough viscosity (TV) was related to the ability of starch to resist physical damage during cooling. Compared with the control sample, the TV value of whole grain HB flour treated by sand-roasting was the highest, followed by the samples treated by extrusion and far-infrared baking, and the TV values of the sample treated by steam explosion were the lowest, at 863, 436, 468, and 288 cp, respectively. The results indicated that the whole grain HB flour treated by sand-roasting had strong shear resistance after gelatinization and cooling. FV was related to the rearrangement and reorientation of starch granules, particularly the amylose content. The FV value of the cooked whole grain HB flour was lower than that of the untreated sample, which was attributed to the decrease in the stability of the gel formed by cooling after cooking.The breakdown viscosity (BD) indicated the thermal stability of whole grain HB flour paste. The greater the BD value was, the worse the thermal stability of whole grain HB flour paste would be. The BD also reflected the fragility of grain flour particles and the stability of paste during heating . After tp < 0.05), at 69 and 146 cp, respectively. The setback value (SB) of the whole grain HB flour treated by sand-roasting and far-infrared baking was significantly higher than that of the control (p < 0.05), at 818 and 641 cp, respectively, thus indicating that the whole grain HB flour treated by steam explosion and extrusion did not easily undergo setback and had a strong anti-aging ability. Therefore, steam explosion and extrusion were beneficial to improving the anti-aging ability of highland barley flour and could be used as an anti-aging agent. Therefore, sand-roasting and far-infrared baking are beneficial to improving the gel strength of highland barley flour and can be used as thickening methods.The setback viscosity (SB) reflected the aging or setback degree of the whole grain HB flour, along with the strength of the gel formed during cooling. The higher the SB value was, the worse the stability of the whole grain HB flour would be after gelatinization and cooling, while the stronger the gel was, the easier the aging would be. The setback value (SB) of the whole grain HB flour treated by steam explosion and extrusion was significantly lower than that of the control sample (p ˃ 0.05). There were large voids and fragments in the tissue of highland barley after extrusion and steam explosion . The density of whole grain HB flour after sand-roasting  and steam explosion  was significantly lower than that of the control. This was consistent with the result that thermal treatment reduced the bulk density of highland barley, barley, and wheat reported by Yi-peng Bai, Altan, and Subhamoy Dhua [Bulk density is an important index to reflect the filling property of flour. The bulk densities of the untreated whole grain HB flour and heat-treated whole grain HB flour are portrayed in moy Dhua ,16. The moy Dhua . TherefoWater-holding capacity and oil-holding capacity have important roles in biscuit and pastry products . The resCompared with untreated whole grain HB flour (1.24 g/g), the oil-holding capacities of whole grain HB flour after steam explosion (3.22 g/g), sand-roasting (1.75 g/g), and far-infrared baking (1.59 g/g) were significantly increased, while extrusion (1.31 g/g) had no significant effect on these values. The change in oil-holding capacity of whole grain HB flour during processing was related to the dissolution and degradation of protein in the flour and the increase or decrease of polar and nonpolar binding sites. Thermal treatment led to protein dissociation in whole grain HB flour, increased the non-polar and polar binding sites, and enhanced its oil-holding capacity . SimilarIt is thus concluded that the swelling power, water-holding capacity and oil-holding capacity of whole grain HB flour are affected by different thermal treatment methods. Extruded whole grain HB flour is more suitable for manufacturing instant flour products, while sand-roasted and far-infrared baked whole grain HB flour are more suitable for making bakery products such as biscuits and pastries, and steam exploded whole grain HB flour is more versatile and can be used as raw material for instant flour and pastry products.The moisture content of grain is related to the weight of dry matter and is a major factor affecting storage stability. p ≤ 0.05). The moisture content of extruded whole grain HB flour reached about 8% on the 14th day. With the extension of storage time, the moisture content of the control gradually decreased. After 56 days of storage, the moisture content tended to balance, and stabilized at about 7%.With the extension of storage time, the whole grain HB flour absorbed the water in the environment, and the moisture content gradually increased . After 1p < 0.05), all maintained below 5 mg g−1. With the increase of storage time, the lipase activity increased accordingly. The lipase activity of whole grain HB flour treated by extrusion and steam explosion remained high in the first 28 days of storage, then decreased. There was no significant difference among the other treatments, and the lipase activity remained at a low level the entire time. This was consistent with the change trend of moisture content during storage. The water reabsorption of whole grain HB flour reduced the inhibition and improved the lipase activity. The moisture content of whole grain HB flour was kept at a low level of 7% during storage , at 18.8 mg/100 g, 24.33 mg/100 g, and 12.38 mg/100 g, respectively. This result indicated that thermal treatment exerted little effect on the fatty acid value of the whole grain HB flour.Fatty acid value is a sign to measure the content of free fatty acids in fat, and it can be used as an indicator of the degree of fat hydrolysis during storage. A low fatty acid value signifies that the degree of fat hydrolysis is small, and that the sample is fresh and not prone to rancidity . Figure During accelerated storage, the fat in whole grain HB flour was slowly hydrolyzed to produce a certain amount of free fatty acids, resulting in the increase of fatty acid value to varying degrees . With thp > 0.05). The peroxide value of untreated whole grain HB flour was 0.0047 meq/kg. After steam explosion, extrusion, far-infrared baking, and sand-roasting, the peroxide values of the whole grain HB flour were 0.0354 meq/kg, 0.0708 meq/kg, 0.0503 meq/kg, and 0.0800 meq/kg, respectively, indicating that oxidative decomposition of lipid occurred during thermal treatment of highland barley. The reason for this may be that the thermal treatment process induced the decomposition of cell wall, and thus increased the fat-soluble components. Meanwhile, the low water activity broke the bound water on the surface of lipid molecules and increased the lipid oxidation rate [Peroxide value is an important index by which to reflect the initial oxidative rancidity of fat, mainly focusing on the deterioration of fat during storage . It can ion rate .p < 0.05). With the extension of storage time, the fat of whole grain HB flour continued to undergo oxidative rancidity, and consequently, the peroxide value of whole grain HB flour gradually increased during storage (Under the same conditions, the storage time exerted a significant effect on the peroxide value of whole grain HB flour during storage ( storage , and incWith the oxidation of fat, the peroxide produced will degrade and the peroxide value will drop, yet the malondialdehyde value will continue to increase. Consequently, the malondialdehyde content may better reflect the oxidation degree of fat . Figure Sand-roasting, far-infrared baking, steam explosion, and extrusion could effectively alter the appearance and internal starch structure of highland barley, while the XRD of highland barley starch after steam explosion was B-shaped, and the XRD of highland barley starch after extrusion was amorphous. The gelatinization characteristics, swelling power, oil-holding capacity, and water-holding capacity of the flour were altered significantly by thermal treatment. Extruded whole grain HB flour has high water-holding capacity, swelling power, bulk density, the lowest oil-holding capacity, and maximum gelatinization viscosity, thus making it suitable for producing instant flour products. Meanwhile, sand-roasted and far-infrared baked whole grain HB flour has high oil-holding capacity, and is suitable for producing bakery products such as biscuits and pastries. Steam-exploded whole grain highland barley powder has good expansion force, water-holding capacity, and oil-holding capacity, and the bulk density is the smallest, thus it can be used as the processing raw material of high-oiliness baking products. Sand-roasting and far-infrared baking bear relatively little effect on the physicochemical properties of whole grain HB flour. Under the same storage conditions, the untreated whole grain HB flour is stable during storage, and the whole grain HB flour after different thermal treatments is unstable during storage. However, the storage time of the whole grain HB flour treated by steam explosion is the longest, followed by far-infrared baking and sand-roasting, while the storage time of the whole grain HB flour treated by extrusion is the shortest. The physicochemical properties of whole grain HB flour can be obviously improved by steam explosion, and it has better storage stability. In the future, the storage conditions and regulation technologies of cooked whole grain HB flour must be studied to prolong its shelf life, and research in this area is of great significance to the development of whole grain HB food.


Propagation of acoustic emission signals in continuous conjugated media under real-time loading was explored. The results of explored plastic deformation polymer coatings on a metal base using the acoustic emission method with synchronization of deformations and the moments of occurrence of acoustic emission signals are presented. Using the principal component method, the acoustic emission spectra, which make it possible to trace the evolution of deformation transformation processes, were analyzed. Presented the results of theoretical and experimental studies on the separate propagation of acoustic emission vibrations in a polymer coating, a metal base, and their joint combination in the form of multilayer structures. Boundary problems of propagation of acoustic emission signals in the conjugation of continuous media are considered from the standpoint of an elastic continuum and wave representations. The main variables are the force that initiates the appearance of acoustic emission signals and the displacement that determines the propagation of elastic waves. Based on the local rearrangement of the internal structure of conjugated media under conditions of development of deformation processes in the material, the verification of the main theoretical models of energy spectrum acoustic signals in continuous media at the micro-, meso-, and macro-levels was carried out. In this work, we present experimental data on a set of basic acoustic emission characteristics for four-point bending. It is shown that the principal components method reduces the dimension of data while maintaining the least amount of new information. Using the method of principal components to determine the stages of plastic deformation of polymer coatings on a metal base using the acoustic emission method. With the digitalization of acoustic emission signals and noise filtering, new possibilities for isolating a weak signal at the noise level appear even when its amplitude is significantly lower than the noise level. The study results can be used to predict the degree of destruction of two-layer materials under loading. Polymer coatings are used to protect equipment from corrosion damage and destruction. During the operation of protective coatings on a metal base, it becomes necessary to control the state of both the metal base and the coating since damage to the protective layer leads to metal corrosion. Despite a wide range of polymer composite coatings, the most common are anti-corrosion adhesives based on epoxy oligomers. The acoustic emission (AE) method makes it possible to single out the stages of plastic deformation of materials, each of which is a scale level with its deformation mechanism. To obtain an appropriate information base, experimental studies on the deformation of materials with simultaneous recording of acoustic signals in real-time are required.The relationship between the processes occurring in the structure of materials under loading and the accompanying AE effects makes it possible to predict changes in materials’ mechanical properties and structure based on acoustic measurements ,2. A litThe problem diagnostics and identification form of the structure of materials are solved by studying the effects and mechanisms of generation and propagation of AE signals that change their parameters under loading. In , the behThe study of the kinetics of deformation materials under load is based on the analysis of response to an external force.In ,12, the It should be noted that only homogeneous materials without coatings were studied. Studies of multilayer structures using the AE method have not been carried out before. This is the novelty of the review.The technology for determining the residual resource of metal products under combined load conditions by AE measurements is presented in . In 19,,19,20, cIn , the resTo reduce the data dimension, losing the least amount of information allows for the principal components method. When analyzing AE signals, the features of AE spectra are often highly dependent on each other, and their simultaneous presence is redundant. The method is based on the idea of constructing a linear feature transformation, in which the signal-to-noise ratio in the new coordinate system decreases with increasing coordinate numbers. The data are presented as the sum of the useful signal and the uncorrelated noise in this case. The principal component analysis is designed to extract uncorrelated feature combinations from correlated data. As follows from the above review of practical applications of the AE method, the novelty and relevance of this work lie in the study of deformations on coated materials and the use of effective methods for processing AE information.In , the ideIn ,26, the Cluster analysis of AE signals in combination with infrared thermography was used in  to analyThe principal component method makes it possible to visualize data, simplify calculations and interpret compressed volumes of input information. The proposed approach can be applied in the study of plastic deformation processes to diagnose the deformation behavior of materials. With regard to the analysis of the features of the study of AE signals under loading of multilayer structures, it will allow us to discover new effects that occur when they are loaded. Among all the analyzed works, our studies are new and unparalleled.The solution to the scientific problem of diagnostics and identification of stages of change in the structural states of epoxy coatings on a steel substrate under loading consists not only in the use of new samples of measuring equipment but also in the use of new forms of processing informative parameters that are sensitive to changes in the structure of materials through the use of the method of the principal component.The scientific direction of the proposed work lies in a more profound use of the principal component method in assessing the stages of deformations of multilayer structures and determining the boundaries of their changes.This work aims to study the structural features and characteristics during the deformation of epoxy coatings on steel substrate in developing an analytical apparatus for identifying the state of materials.Samples of St3sp steel used as a base and ED-20 epoxy resin used as a coating were used as research materials. The choice of epoxy resin as the research material is explained by the fact that it is characterized by high adhesion to metal, glass, and concrete . One of Acoustic emission measurements of the stress–strain state of continuous media under real-time loading were used as research methods ,37. The Modern mathematical models of the energy spectrum of AE signals take into account the presence of several scales in the medium, their coordinated interaction, and the possibility of energy transfer from one level to another at the micro-, meso-, and macro-structural levels. Interest in solving the problem of studying the plastic deformation of polymer coatings on a metal base using the AE method requires a more detailed study of the dependence of the properties of materials on their microstructure. Suppose deformation processes in materials can be described on the basis of loading diagrams. In that case, the evolution of the defective structure of metallic materials during the formation of AE signals can only be described at the atomic level ,39.The discrepancy between the coefficients of thermal expansion coating and base materials leads to the appearance stresses and their interfaces, which causes damage to the coating, the formation of cracks, and other defects. Finding the energy spectrum of AE signals in continuous conjugated media is a means of predicting the destruction of materials ,41,42.Operator beams in studying the spectral properties of AE signals in the problems of motion of structural imperfections subjected to bending forces are considered in .The model of a two-layer conjugated medium in the form of a linear chain of atoms with a simple single point defect is shown in When pairing two continuous media in each of them, it is possible to single out the boundary regions S and S*, in which acoustic signals propagate. They have dimensions depending on the mechanical parameters of the medium. Further, the signals do not propagate due to attenuation.ρ-defect zone material density, υ-the speed of its particles, f–density of mass forces acting on an elementary volume V, xσ, yσ, zσ—normal stress tensor components, xτ, yτ, zτ—shear stress tensor components.The equation of motion of the defective zone has the form:By the local properties of functions, one can judge the global properties of the object’s materials. The properties of beams are determined by the properties of tensor fields of local manifolds . Under dSρ and S*ρ material density of both media, sq and s*q—interaction forces, Φ—elastic energy operatorThe equations of motion of particles in the regions S and S*  have thek—integral equation kernel, λ—characteristic number, a, b—integration limits, f(x)—free member.For a defect-free structure of the material, when the elastic bonds between the atoms of both media are stable, we have a static problem that can be reduced to an integral Fredholm equation of the second kind:S and S*, limited on the one hand by the damping of oscillations, on the other hand by the mechanical properties of the structure of materials H and H*, which are determined by the boundary conditions for the existence of signals at ≤ t ≤ bt and geometric dimensions of the medium xa ≤ x ≤ xb  characterizes the receiving signal, and y(x)-triggered signal.Aggregate G–Green’s function.The solution of the boundary value problem of the structure of the energy spectrum of the AE signal is given by the formulaThe rationale for using Green’s function to determine the energy spectrum of AE signals in continuous conjugated media lies in its physical meaning-this is a displacement field created by a single force that causes the formation of structural defects and AE signals acting on one atom of the cell.Green’s function is the kernel of the operator inverse to the elastic energy operator Φ. The construction of Green’s function in the theory of defect-free structures was carried out in . With soTo obtain a solution to the integral equation of motion of particles in conjugate media, we reduce it to a boundary value problem of a linear operator using the Fourier transform.Each linear operator corresponds to a linear equation, on the basis of which its eigenvalues are found.Thus, the methodological basis for determining the energy spectrum of AE signals in conjugated media is the use of Green’s function and the Fourier transform. It follows that the better the function is concentrated in time, the more it is blurred in frequency. With an increase in the applied voltage, high-amplitude acoustic signals are formed, which correlates with deformation jumps.The value λ included in the Fredholm equation denotes the variety of energy spectrum components that can be recorded by various AE measurement methods.The initialization of AE signals under the loading of a material is considered using the evolutionary concepts of the theory of dislocations. The presented solution of the equation of motion of a system of conjugate media during the development of internal structural defects allows us to perform a spectral analysis of differential operators of elastic energy and their distribution over eigenvalues.For polymer coatings based on a metal-based epoxy matrix, the situation is complicated by generating AE signals from materials of different physical natures. In addition, the application of the AE phenomenon, which accompanies the processes of various types of loading and control of technological processes associated with a change in the structure of materials, reveals great technical difficulties associated with the variety of recommended information parameters and their representations for further processing and use.The test specimens were cut from sheet metal 200 × 20 × 3 mm in size. ED-20 resin with polyethylenepolyamine (PEPA) hardener was used as a protective coating applied on one side of the sample. The coating thickness was 1 mm.In the experiment, the coating thickness was fixed. As follows from numerous literature sources, there is a relationship between the plasticity of the metal substrate and damage to the coating under loading, due to the thickness of the coating. The consequence of this is cracking on the coating, interfacial delamination, microcracks, etc. This is an important scientific area of research in the field of materials science, structural mechanics, and the theory of strength of conjugated media. Its consideration goes beyond the scope of more than one similar scientific article and will undoubtedly be the basis for further research.Epoxy resin ED-20 was used to form the epoxy matrix. For crosslinking the epoxy binder, cold curing hardener PEPA was used, the content of which was q = 10 mass.h. (indicated per 100 mass parts of epoxy resin ED-20).The formation of the epoxy matrix was used in the following sequence: heating the resin to a temperature T = 353 ± 2 K and holding at a given temperature for a period of time τ = 20 ± 0.1 min; ultrasonic treatment of the composition over time τ = 1.5 ± 0.1 min; cooling the composition to room temperature over time τ = 60 ± 5 min; and the introduction of the hardener and mixing the composition over time τ = 5 ± 0.1 min.t = 12.0 ± 0.1 h at a temperature T = 293 ± 2 K, heating at a rate v = 3 K/min up to temperature T = 393 ± 2 K, exposure of samples at a given temperature for a period of time t = 2.0 ± 0.05 h, free cooling to temperature T = 293 ± 2 K for a time t = 24 h on air.The materials were cured according to the experimentally established regime: the formation of samples and their exposure for an hour Four-point bending tests were used to evaluate bending stresses.The experimental setup used for measurements is shown in The functional diagram of the experimental setup is shown in The measurement process was carried out in combination with mechanical tests and acoustic emission measurements. At the same time, the process of registering loading, deflection and time changes, as well as fixing AE signals, was fully automated by means of synchronous processing of the received data from the moment the machine drive was activated. A general view of the setup for AE measurements for four-point bending is shown in Measurement of the deformation of the samples under uniaxial loading was determined by fixing the elongation using a Micron digital indicator DT-7011 micrometric electronic displacement indicator. The micrometric electronic indicator of displacement, in contrast to the mechanical one, is adjusted to zero at any point of the scale, so that you can observe the deviation from the dimensions of the test sample in the range of 0–12.7 mm with an inaccuracy of 0.001 mm. According to , bendingFor acoustic measurements, broadband sensors to the AE of the AF-15 device with a bandwidth of 0.2 … 0.5 and 0.2 … 2.0 MHz were used. The information-measuring system used in the experiment provided the indication and registration of AE signals with their subsequent storage in the computer memory using a RIGOL DS1052E digital oscilloscope.To improve the accuracy of measurements during dynamic bending tests, the installation is supplemented with a loading synchronization system with the registration of the AE signal coupled with a personal computer. The computer simultaneously receives information from the parameters of the loading device, deflection, and moments of the occurrence of AE signals as a function of time. During the tests, information about the deformation of the sample and the amplitude of the AE signals was recorded in a file with a given periodicity. The tests were carried out with registration of the load and the corresponding deformation with simultaneous fixation of the moments of occurrence of AE signals in compliance with standards . AE sensTo clarify the question that the recorded AE signals refer specifically to the coated samples, and not to the metal substrate, it is necessary to compare the results of measurements performed separately on the metal substrate, on the epoxy coating, and on their conjugation under identical measurement conditions. The results of AE measurements synchronized with mechanical tests at four-point bending, performed for a polymer matrix used in the form of coatings, are shown in Similar complex AE measurements and mechanical tests performed for the metal base of ST3sp steel are shown in Visualization of the measurement results of coated samples at different loads is shown in The results of comparative AE measurements and mechanical tests shown in The location of the signals corresponds to the order in which they occur under loading. The peculiarity and originality of such a presentation of AE signals in Relationship between the processes of defect formation and the occurrence of AE signals makes it possible to determine the degree of change in the structure of materials under load. The most difficult moment in studying the behavior of materials under load is the identification of AE signals that characterize the state and mechanical properties of materials directly at the source of initiation of AE signals. Information about the source of AE signals can be obtained not only by measurements but also by integrating theoretical models of AE occurrence.According to the definition, plastic deformation is an irreversible deformation in which, after the end of the applied forces, an irreversible displacement of interatomic bonds occurs.The mechanisms of plastic deformation can be considered depending on the scale levels on the basis of mesoconcepts about the dislocation structure of materials ,21.The mechanism of plastic flow at the mesoscale level is based on energy dissipation, which leads to discontinuity with the appearance of cracks in the surface layer during the development of mesobands of localized deformation in the metal substrate. Mesoconcentrators of stresses in coated materials arise at their interface, developing towards the surface of the sample due to inconsistent shear deformation of mating media.The mechanism of plastic deformation stages requires the use of continuum mechanics and dislocation theory approaches. Plastic deformation in continuum mechanics takes into account the translational motion of defects under the action of an applied stress. The plastic flow curve is obtained by calculating the strain hardening above the yield strength of the material. The theory of dislocations describes the microscopic behavior of a deformable body on the basis of the mechanisms of generation of elementary acts of plastic shear and their dislocation ensembles.The translational nature of plastic deformation as a multilevel system underlies a new scientific direction in strength physics and materials science—the physical mesomechanics of a deformable solid ,45.The mechanisms of plastic flow and the corresponding stages of the hardening curve obey the principle of scale invariance. The hierarchy of structural levels of plastic deformation of solids can vary from three stages, including elastic deformation, elastic–plastic and fracture, to five or more, depending on the structure of the material.For St3sp steel coated with epoxy resin ED-20, plastic deformation at the initial stage occurs during the propagation of the Lueders band front. At the same time, the coating prevents the fronts of the Lueders bands from propagating at a constant speed and the movement occurs abruptly at distances equal to the cracking period. The velocity of the front of the Luders strip is maximum in the initial period of crack formation and is equal to zero at the moment before the formation of the next transverse crack in the coating.The frontal nature of the Luders band propagation is characterized by the formation of an extended yield plateau. The accumulation of the bending moment during the propagation of the Lueders band in the metal substrate leads to the formation of elastoplastic fracture precursors in the coating. The development and accumulation of damage in contiguous media caused by deformation processes are fixed by a change in the surface structure. According to the state of the surface, it is possible to assess the degree of deformation, moments, places of its localization, and degradation ,47.In industry, technological tests are used, the task of which is to evaluate the plasticity of deformed semi-finished products. The criterion for the suitability of products can be a given bending angle and the appearance of the first crack after bending at an angle equal to or greater than the specified one, as well as the possibility of bending the plate to a parallel state.Flexural tests are aimed at evaluating the transition from brittle to ductile. For a coated metal material, the bending diagram allows you to determine the magnitude of the loads corresponding to the limits of proportionality, elasticity, yield, and bending strength. When testing for bending medium-carbon steels, the diagram σ, ε does not have a pronounced yield point. In this case, the yield strength is determined by a certain tolerance through the elastic modulus of the material.The resistance to plastic deformation is determined from the deformation diagram in coordinates σ, ε. The stress required to create plastic deformation determines the yield strength. The strain hardening intensity is expressed in terms of the strain hardening coefficient K = dσ/dε.During plastic deformation of epoxy coatings on metal substrates using the acoustic emission method, a successive change in the stages of plastic deformation associated with the features of plastic flow is observed. To determine the boundaries of the stages of plastic deformation, the values of the strain hardening coefficient were calculated from the measured values of the load and deflection. From the inflections of the dependences of the values of this coefficient on strain, it is possible to more correctly determine the boundaries of the stages than directly from the stress–strain curve . AccordiDuring the experiments, five identical coated samples were tested. In this case, AE signals arose in certain zones of the loading diagram with a particular spread. Considering this scatter and instrumental errors in measuring mechanical stress and deflection, the total absolute errors in determining mechanical stress and deflection were calculated for a confidence level of 0.98. The maximum standard deviation for mechanical stress ±9.529 Mpa, for deflection ±0.215 mm.The measurement results are shown in Acoustic emission is an energy indicator of the processes occurring during the restructuring of the structure caused by plastic deformation under loading.A joint analysis of the strain hardening curve, the evolution of the deformation structure under loading, and the established patterns of changes in AE signals can serve as better estimates of the transition from one stage of hardening to another.L as a dependency K = f(σ) are also presented in The results of constructing the deformation curve according to data of the force-measuring device when changing the deflection ΔK, stage II—the beginning of plastic deformation, the observed decrease in the slope of the curve σ = f(ΔL), and transition coefficient K to the horizontal zoom area ΔL, stage III—continuing decrease in the slope of the curve σ = f(ΔL) and weak dependence of the coefficient K from ΔL, stage IV—pre-fracture and a sharp decrease in the coefficient of strain hardening, at which the coefficient K changes sign.Stage I represents an almost linear section of purely elastic deformation with a nonlinear decrease in the coefficient The nature of the stages of plastic deformation is explained by the internal structure of the material. The appearance of stage I is due to the onset of the formation of dislocation structures. This stage is associated with uniform plastic deformation. Stage II is characterized by the formation of individual spatially distributed mesobands along the surface of plastic deformation, associated with the emergence of deformations at the interfaces between the media in contact. In the polymer matrix, the processes of rearrangement of its intramolecular structure take place, while the strain hardening coefficient behaves unstable. In stage III, segments of polymer molecules acquire a certain mobility, which results in their orientation along the direction of deformation. Stage IV is characterized by the appearance of microcracks.The shape of the AE curve reflects the division into stages and qualitative changes during transitions to the hardening stages. At small strains, dislocation glide bands and recrystallization twins are observed. In the elastic state, there are no stress concentrators capable of generating plastic shear and acoustic emission. A further increase in the load leads to powerful plastic effects, which manifest themselves in the form of slip lines. AE emission occurs between active deformation centers, which leads to the birth of a new hardening stage. Jumps of individual microcracks are detected in the form of high-amplitude AE pulses. The development of microcracks together with ongoing dislocation processes ensures the existence of the pre-fracture stage.The mechanisms of plastic deformation can also be considered depending on the scale levels of macrorepresentations.AE signals in the time domain demonstrate a tendency to increase in impulsivity . FeatureA powerful tool for predicting the state of samples in the frequency domain is spectral kurtosis. Visualization of the spectral kurtosis of AE signals at different loads in metal-based polymer coatings is shown in Therefore, statistical characteristics of AE signals in the time domain were chosen for analysis and processing, such as the mean value (Mean), standard deviation (Std), skewness (Skewness), kurtosis (Kurtosis), full swing (Peak2Peak), root mean square value (RMS), crest factor (CrestFactor), form factor (ShapeFactor), impulse factor (ImpulseFactor), marginal factor (MarginFactor), and energy (Energy), as well as statistical characteristics of the spectral kurtosis, such as mean value (SKMean), standard deviation (SKStd), asymmetry (SKSkewness), and kurtosis (SKKurtosis).The choice of the analyzed characteristics was due to the fulfillment of the monotonicity requirement. The fulfillment of the monotonicity conditions required that the values of these characteristics exceed the level of 0.4. In addition to these characteristics, features of spectral kurtosis in the frequency domain can be calculated, such as peak and centroid frequency, which are commonly used to characterize various damage modes ,50. HoweThe values of these characteristics for experimental AE signals are given in digital form in To reduce the dimension and combine the features, the principal component analysis (PCA) was applied in the work. Principal component analysis is one of the most common factor analysis methods. It uses an orthogonal transformation of a set of observations with associated characteristics, each taking different numerical values, into a set of variables without linear correlation.Using the Matlab 2018b computer mathematics system, when processing the data in The numerical values of the first two principal components with a successive increase in the deflection of the sample during testing are presented in The graph in The numerical characteristics of the first two principal components with a successive increase in deflection at the moments of successive fixation of AE signals revealed a linear trend of increase with increasing loading with a stable prospect of using the first principal component.K = f(ΔL).As follows from the consideration of The boundaries of stages III and IV are quite clearly traced when observing this section of the curve a for theA comparison of Based on this, it can be noted that when the scale of structural changes in the materials under loading occurs at the macroscopic level, its only display, determined using the principal component method, can be used as a processed information characteristic of the acoustic spectrum.The AE method has been quite actively used in studies of the plastic flow of metals and alloys under load; however, this method has not been previously used for continuous conjugated media in the form of metal-based polymer coatings. Performed on the basis of theoretical models and experimental measurements of four-point bending for samples coated on a metal base with synchronous measurements of the strain curve and AE, a multiscale accumulation of strains and their stages were established.The AE energy indicator of the different staging of plastic deformation of polymer coatings on a metal base is the hardening diagram constructed according to the data of a force-measuring device with a change in deflection with the synchronous implementation of AE measurements and their statistical characteristics in the space of principal components.It has been established that the linear dependence of the first principal component with a successive increase in deflection at the moments of fixation of AE signals can serve as an indicator of the state of the material of a polymer coating on a metal base under loading. The first main component makes it possible to fairly clearly separate stages III and IV of plastic deformation of metal-based polymer coatings using the AE method, while the second component allows one to quite clearly separate stages II and III.The plastic deformation of conjugated media proceeds inhomogeneously, the process involves in turn different areas of the deformable material at several structural levels, each of which is characterized by a scale determined by the nature of structural defects. The structural state of the coated material determines the nature of plastic deformation and affects the production of AE signals to the same extent. The AE of the material with coating in bending is structurally sensitive.


UBE3A gene in neurons. Antisense oligonucleotide therapies are under development to reinstate UBE3A protein production. Non-invasive biomarkers to detect target engagement and treatment response are needed to support clinical trials. Delta power measured in the scalp EEG is a reliable biomarker for Angelman syndrome but varies widely across individuals and throughout development, making detection of a treatment effect using single measurements challenging.Angelman syndrome is a neurodevelopmental disorder caused by deficiency of the maternally inherited n = 41) to detect antisense oligonucleotide-mediated treatment effects on absolute delta activity and Ube3a expression. In humans, delta power at a second time point can be reliably predicted using the natural history model. In mice, a treatment effect can be detected after antisense oligonucleotide treatment targeting the Ube3a-antisense transcript through at least 8 weeks post-treatment (P < 1e-15). Deviations in delta power from the expected natural history correlated with Ube3a expression in the mouse model (P < 0.001). Deviations in delta power from a human natural history model in Angelman syndrome can detect antisense oligonucleotide-mediated improvement in Ube3a expression in Angelman syndrome mice and may be relevant for human clinical trials.We utilized a longitudinal dataset of 204 EEG recordings from 56 subjects with Angelman syndrome to develop a natural history model of delta (2–4 Hz) power, with predictors of age, elapsed time, and relative delta power at an initial recording. Using this model, we computed the sample and effect sizes needed to detect a treatment effect in a human clinical trial with 80% power. We applied the same model structure to a mouse model of Angelman syndrome ( Ube3a expression in Angelman syndrome mice and may be relevant for human clinical trials.Deviations in delta power from a human natural history model in Angelman syndrome can detect antisense oligonucleotide-mediated improvement in   Therefore, delta power may present a useful biomarker for severity of disease and may provide a simple, non-invasive metric to track improvement in clinical trials. However, although delta power is reliably increased in AS compared with healthy control subjects, in cross-sectional studies, delta power measurements vary widely between individuals and throughout development. Longitudinal measurements of delta power, accounting for each subject’s age and elapsed time between measurements, are required to develop a more sensitive measure of target engagement in clinical trials.Many studies indicate that abnormal delta power (2–4 Hz) measured in the scalp EEG is a reliable and sensitive biomarker for AS. Delta power is highly elevated in AS subjects compared with typically developing individuals,Ube3a expression in Ube3a-ATS ASO-treated and control ASO-treated mice. This work provides a non-invasive method to detect potential treatment effects with confidence in AS and validates that increased Ube3a expression corresponds to deviations from the natural history of delta power in a mouse model of this disorder.Here, we first analyze a small database of prolonged continuous EEG recordings in AS subjects to show that delta power estimates remain stable over the course of a 24 h sample. Then, utilizing a large longitudinal data set of EEG recordings from subjects with AS, we develop a natural history model to predict delta power at a subsequent visit from delta power at an initial visit, age, and elapsed time between visits. We utilize this model to compute the sample and effect sizes needed to detect a treatment effect in a human clinical trial with 80% power. We then fit the model on a longitudinal AS mouse data set and measure for a treatment effect after ASO treatment. Finally, we compare deviations from the natural history model with Human subject data were obtained from (i) a database of EEG recordings from subjects with AS seen at Massachusetts General Hospital (MGH); and (ii) a database of EEG recordings from the multicenter AS Natural History Study  conducted as part of the Rare Diseases Clinical Research Network, Angelman, Rett and Prader-Willi syndrome consortium.In (i), all AS subjects with longitudinal EEG recordings obtained between 2005 and 2019 were included. To prevent a disproportionate impact of subjects with multiple visits and to represent EEG recordings obtained across varying intervals of elapsed time between visits , pairings of longitudinal EEG recordings separated by hourly, daily, weekly, monthly, and yearly IVIs were included with an approximately equal distribution, as available for each subject. In total, 116 EEG recordings from 26 subjects  were included. Recordings in this data set were separated by a median of 8.2 months (range: 2 days–4.4 years).In (ii), subjects were recruited at six sites between 2006 and 2017 and EEG recordings were collected from the sites at Rady Children’s Hospital/University of California San Diego and Boston Children’s Hospital. Consent was obtained according to the Declaration of Helsinki and was approved by the institutional review boards of the participating sites. In total, 88 EEG recordings from 30 subjects  were included. Recordings in this data set were separated by a median of 1.1 years (range: 8.4 months–7 years).The final combined data set included 56 subjects with longitudinal EEG data from 204 total visits.16 For the MGH data, five recordings lasting ∼24 h were available. For the remainder of the data, recordings were of ∼50 min duration . The data were sampled at either 256 or 512 Hz, using a C2 spinous process reference. For the NHS data, 30 min of wake recording and 30 min of sleep recording were attempted at each session . The data were sampled at 200–512 Hz, using a linked-ear reference. Some of the NHS subjects contributed EEG recordings that were obtained for clinical purposes.All EEG recordings were collected using the international 10–20 montage on either BioLogic or Xltek systems.14 We focused on wake data because it was more widely available and more reliably identified. The final data set included wake recordings of mean duration 37.4 min (range: 1 min–6.5 hrs).All EEG data were manually staged for wake and sleep states by an experienced clinical neurophysiologist (CJC) and wake data selected for model development. We note that delta rhythms are abnormal during wake and sleep in AS.17 Following the procedure in Ostrowski et al.,14 we analyzed only occipital and parietal electrodes, O1, O2, P3, Pz, and P4 referenced to a group average across those electrodes. There, it was shown that delta power estimates from the uncleaned posterior electrodes provided the best predictor of cognitive function as these electrodes are free of muscle artifacts and provide the largest amount of data from which to estimate delta power. For each channel, we computed the power spectrum on non-overlapping 1 s interval . Within each interval, we estimated the relative delta power as the average 2–4 Hz summed power over channels divided by the 1–50 Hz total power over channels. We then averaged the delta power over all intervals to yield a single relative delta power value for each subject.Power spectra were calculated using the Chronux toolbox.n = 2 deletion, n = 2 UBE3A mutation, n = 1 uniparental disomy). For this, we implemented a resampling procedure to estimate the relative delta power from 1 to 3600 randomly sampled (without replacement) 1 s epochs from the 24 h data set, reflecting data durations ranging from 1 s to 60 min. For each sample size (1 to 3600 s), and for each subject, we repeated this procedure 1000 times to compute the standard error of the mean (SEM) relative delta power estimate. For a given estimate of relative delta power, δ, we empirically estimate the 95% confidence interval from the resampling procedure. We repeated this same procedure using contiguous epochs of durations 1–60 min, choosing 1000 random start times in the resampling procedure.To examine the stability of relative delta power estimates across full day recordings, we analyzed EEG recordings from five subjects, each with at least 24 h of continuous recording and different genotypes (10(age) and IVIs, and a random intercept for subject. We declared a variable significant when the P-value of the t-test was <0.05. We also tested the significance of including genotype in the model by evaluating the Akaike information criterion. To validate our model, we employed a cross-validation procedure. For each iteration, the visits from one subject were left out for a test set and the model was trained on the remaining data. We compute the average root mean square error (RMSE) for the test set across all iterations.For our natural history model, we fit a linear mixed effect model with dependent variable relative delta power at a subsequent time point, and fixed predictors of relative delta power at an initial time point, the interaction of logt-test with P-value < 0.05 .To simulate treatment and control groups for power calculations, we sampled (with replacement) 25, 50, 100, or 150 subject EEG recording pairs for each group from the longitudinal data set. Then, from each subject in the simulated treatment group, we subtracted a fixed offset from the subject’s observed relative delta power at subsequent visit to represent a treatment effect under the hypothesis that treatment reduces delta power. We considered relative delta power offsets ranging from 0 to 0.1. For each fixed delta power offset, we repeated this simulation 2000 times and computed the proportion of times a difference between simulated treatment and simulated control groups was detected using a one-sided m+/p−Ube3a  (JAX Stock No: 016590) × male m+/p+Ube3a  (JAX Stock No: 000664) breeders to generate offspring, including experimental m−/p+Ube3a  (AS) mice and littermate WT m+/p+Ube3a  controls. WT and AS littermates were housed in the same cage whenever possible.All experiments were conducted in compliance with the rules set forth by the Biogen Institutional Animal Use and Care Committee in accordance with the guidelines established in the National Institutes of Health Guide for the Care and Use of Laboratory Animals. Mice were group housed on a 12 h light/dark cycle with ad libitum access to food and water. Both male and female offspring were used for experiments. Breeding was performed internally at Biogen by crossing female 18 The 2′-MOE gapmer ASOs are 20 nucleotides in length, wherein the central gap segment comprising 10 2′-deoxynucleotides is flanked on the 5′ and 3′ wings by 5 2′-MOE modified nucleotides. The sequences of the ASOs are as follows: non-targeting control ASO, 5′-CTATAGGACTATCCAGGAA-3′ and mouse-specific Ube3a-ATS ASO, 5′-CCAGCCTTGTTGGATATCAT-3′.Synthesis and purification of all chemically modified oligonucleotides was performed as previously described.Ube3a-ATS ASO (500 μg) at a rate of ∼1 μl per 30 s into the cerebral ventricle. The needle was left in place for 5 min, slowly withdrawn and the incision was sutured.Lyophilized ASOs were dissolved in sterile PBS without calcium or magnesium and quantified by ultraviolet spectrometry. The ASOs were then diluted to the desired concentration required for dosing mice and sterilized through a 0.2 μm filter. Surgeries were performed +/− 3 days of postnatal Day 35 (P35). Mice were anaesthetized with 2% isoflurane and placed in a stereotaxic frame (David Kopf Instruments). After exposing the skull, a needle  was used to penetrate the skull at 0.3 mm posterior and 1.0 mm lateral to the bregma and lowered to a depth of 2.25–3.0 mm (based on weight), to deliver a non-targeting control ASO or ×g for 20 min at 4°C to clear the lysate. Protein concentrations were determined using the Pierce BCA Protein Assay Kit  and 10 μg of each sample was denatured in 6X SDS sample buffer  by boiling for 8 min at 90°C. Proteins were loaded into a Criterion 7.5% tris–glycine gel  and separated by SDS-PAGE at 120 V for 120 min. Gels were transferred to an IBlot2 nitrocellulose membrane , blocked with TBST blocking buffer  for 1 h and washed three times with TBST. The membrane was probed with primary antibodies (1:1000 dilution) in antibody dilution buffer (1:1 TBST blocking buffer and 1X TBST) overnight at 4°C. The following antibodies were used for immunoblotting: UBE3A  and GAPDH . After primary antibody staining, the blot was washed in triplicate with TBST and incubated for 1 h with secondary antibody  in antibody dilution buffer. After a final triplicate wash with TBST, the blot was visualized using the Odyssey CLx imaging system .Mice were euthanized 8 weeks after intracerebroventricular (ICV) injection and the brains were rapidly harvested and cortical pinches of grey matter (200–300 mg) were flash-frozen. The tissues were homogenized and lysed in Pierce RIPA lysis and extraction buffer  supplemented with 1% Halt protease and phosphatase inhibitor cocktail  and centrifuged at 14 000Ube3a (Cat# Mm00839910_m1), Ube3a-ATS (Cat# Mm02580988_m1) and housekeeping gene GAPDH (Cat# Mm99999915); all primers are from Applied Biosystems. Real-time PCR reactions were performed on the Via7 real-time PCR system  using the following thermocycling conditions: 2 min at 50°C, 10 min at 95°C, followed by 50 cycles of 15 s at 95°C and 1 min at 60°C. Relative gene expression levels of Ube3a and Ube3a-ATS were calculated using the ddCt algorithm.Samples for polymerase chain reaction (PCR) were lysed in RLT buffer (Qiagen) + 0.1% β-mercaptoethanol and total RNA was extracted using the RNeasy mini kit (Qiagen) and RNase-free DNase set (Qiagen) following the manufacturers protocol. Total RNA concentration was determined using the Nanodrop 8000 spectrophotometer  and reverse transcription was performed using the High Capacity cDNA Reverse Transcription kit (Applied Biosystems) using up to 2 µg of RNA as a template. About 50 ng of the resulting cDNA product was subjected to duplex PCR reactions using Gene Expression Master Mix  containing Taqman primers for et al. Mice were anaesthetized with 2% isoflurane and placed in a stereotaxic frame (David Kopf Instruments). A steel headpost was affixed to the skull anterior to bregma using cyanoacrylate glue. Burr holes (< 0.5 mm) were then drilled in the skull over binocular V1 . Tungsten electrodes , 75 μm in diameter at their widest point, were implanted in each hemisphere, 450 μm below cortical surface. Reference electrodes consisted of 000–120 CS screws inserted into the skull touching dura located over prefrontal cortex. Wires extending from the electrodes were connected to female gold pins and inserted into a plastic pedestal connector . Finally, dental cement  was applied to form a stable, protective head cap. Recordings were performed using a Tucker-Davis Technologies R25D system at ∼3K sampling rate. Mice were head-fixed for all recording sessions viewing a full-field grey screen in an enclosed dark, quiet environment. Two weeks post-ICV infusion and 1 week post-surgery, the mice were habituated to this environment for two consecutive days, at 15 min per session. Recordings were then acquired during three consecutive daily 15 min sessions and results averaged for the ‘Week 2’ time point. A portion of mice were then recorded weekly thereafter.Mice were surgically implanted with depth electrodes targeting layer IV of primary visual cortex 4–7 days after ASO administration (∼P42). Primary visual cortex was chosen to replicate and extend the delta phenotype observed previously in Sidorov 17 in MATLAB (Mathworks) for the last 10 min of the ∼15 min recording session and averaged across hemispheres . A custom algorithm was used to remove recordings from channels with noisy LFPs, in some cases due to damage to the electrode. Absolute delta activity was measured as the peak activity between 1 and 5 Hz.Local field potential (LFP) analyses were performed with the experimenter blinded to treatment and genotype. Power spectra were calculated for each hemisphere using the Chronux software packagen = 26), pairs of longitudinal recordings were defined using all possible combinations of subsequent recordings, resulting in 6–21 longitudinal pairs per mouse and 401 total longitudinal pairs.To examine model performance in the AS mouse model, we applied the same natural history model structure developed with the human data to the absolute delta power measurements from the longitudinal mouse LFP recordings. To estimate the model parameters for the mouse data, for each control ASO-treated mouse , we did not have pre-treatment absolute delta power values in the Ube3a-ATS ASO-treated mice. Therefore, to compute the model residual for an ASO-treated mouse, we randomly selected the absolute delta power value from a mouse in the youngest control ASO-treated group and used the ASO-treated mouse’s subject-specific variance to predict the absolute delta power value of the ASO-treated mouse at all subsequent ages. We repeated this procedure to compute the model residuals for each Ube3a-ATS ASO-treated mouse at all subsequent visits. We applied the same procedure to compute the model residuals for the control ASO-treated mice, while excluding pairing of the same mouse at both visits. To compute a treatment effect size for each postnatal week, we computed the difference in the median residuals of the Ube3a-ATS ASO-treated mice and the control ASO-treated mice. We repeated this entire procedure 10 000 times to generate a distribution of treatment effect sizes for each postnatal week. We used this distribution to compute the 95% confidence bounds, extending from the 2.5% to 97.5% quantile of the distribution. We note that inter-subject variability is taken into account by utilizing all mouse data from each week.We then applied the natural history model to estimate a treatment effect in Ube3a-ATS ASO-treated and control ASO-treated mice, we implemented a resampling procedure. Under the null hypothesis of no difference between groups, we first created a combined group including both the control ASO-treated (n = 26) mice and Ube3a-ATS ASO-treated (n = 15) mice at post-treatment Week 2 . Then, from this list, we selected randomly (without replacement) two pseudo-groups of mice to represent pseudo-control ASO-treated (n = 26) and pseudo-ASO-treated (n = 15). We repeated this entire procedure 10,000 times to create distributions of treatment effect size for each week, assuming no difference between groups. To test our hypothesis that Ube3a-ATS ASO-treated mice would have larger positive residuals compared to control ASO-treated mice, we compared the observed and resampled distributions of treatment effect size at each week using a one-sided t-test with significance at P < 0.05.To test the null hypothesis of no difference in median residuals between Ube3a mRNA upregulation and the model residuals, we utilized the natural history model to compute residuals for mice at Week 7 and compare them to measured Ube3a mRNA levels obtained in the same mice at Week 8, in both control ASO-treated (n = 8) and Ube3a-ATS ASO-treated (n = 4) mice. Only a portion of the mice were sacrificed at the Week 8 time point for mRNA analysis as other experiments were run using the remaining mice. No mice were lost prematurely. To compute model residuals, for each Week 7 mouse, we compared the predicted and observed absolute delta values using a randomly selected control ASO-treated mouse at Week 2. We then matched this residual with the Ube3a mRNA measurements from the same mouse. We repeated this procedure for all 12 mice with Ube3a mRNA measurements at Week 8. We then performed linear regression to estimate the slope from a data set of 12 samples. We repeated this entire procedure 1000 times (each using randomly selected control ASO-treated mouse at Week 2) to create a distribution of slope estimates.To assess the correlation between the relative Derived human subject data obtained from MGH are available upon reasonable request from the corresponding author. Human subject data from the NHS are available at ClinicalTrials.gov (NCT00296764). Derived mouse data are available upon reasonable request from corresponding author.14 To assess the stability of relative delta power estimates over shorter time intervals, we compared relative delta power estimates using increasing data sample sizes, randomly selected from 1 s interval in five AS subjects with 24 h continuous recordings . As the amount of data increases, the standard error decreases at a rate of ∼Spectral estimates from scalp EEG are highly variable within individuals over the course of years. of ∼1/x . When th of ∼1/x  and foun10(age) at the initial visit,19 and elapsed time between the visits (IVI). Because the data consist of multiple longitudinal observations from repeat subjects, we include a random intercept to allow inter-subject variability in baseline delta power, for example due to genotype.12 The final natural history model is  and IVI negatively correlates with relative delta power at the subsequent visit . On a visual inspection, absolute delta power in AS control-treated ASO mouse models decrease with age, consistent with prior reports11 . When evaluating each week directly, we did not detect a significant difference between AS Ube3a-ATS ASO mice and AS control ASO mice for any post-treatment week  except at Week 7  and IVI .To assess the ability of the natural history model to detect treatment effects in the mouse data, we first estimated model parameters on all available longitudinal data from the AS mice treated with control ASO. As described in the Methods, since no pre-treatment observations of delta power were available for the mice, randomly selected Week 2 visits from the control group were used instead. Doing so, we found trends in all three predictors consistent with analysis of the human data; absolute delta power at a subsequent recording increased with delta power at an initial recording , all fitted slopes are positive with P < 0.001, . By including the prior delta power estimates and a random intercept, the longitudinal model controls for specific variations in baseline delta power due to genotype and disease severity and reduces noise due to inter-subject variability. Noise is further reduced in our longitudinal model by accounting for the known impact of IVI and interaction of age:genotype on delta power. This model then can be used to identify deviations in delta power outside of the expected natural history with confidence and thereby identify a significant treatment effect.Abnormally increased delta power is a consistent electrophysiologic phenotype of AS across species that shows promise to provide a meaningful biomarker for treatment efficacy. One challenge in employing this biomarker in clinical trials is that delta power varies dramatically across subjects and with age.11 and consistent with an increase in the raw score of the cognitive domain of the Bayley Scales of Infant and Toddler Development, 3rd edition14 of only 0.6 points. We conclude that small deviations in relative delta power, potentially signalling a treatment effect, can be detected by the model, even when below the threshold of detection on a performance-based test. We note that we could have used absolute or relative delta power for our analysis; however, we chose relative delta power motivated by previous work14 and to relate these changes to cognitive function. We note that changes in relative delta power can occur due to changes in absolute power at higher frequencies. However, we expect the impact of such changes to be small due to the rapid decrease in power with frequency.Using the natural history model, we performed power calculations to characterize the effect sizes and sample sizes needed to identify a treatment effect. We showed by simulation that in a sample of 50 treated and 50 untreated AS subjects, a decrease in relative delta power of 0.046 could be detected with 80% confidence, smaller than the reported 0.2 difference in relative delta power observed between controls and AS childrenUbe3a expression by unsilencing the paternal allele using an ASO treatment in mouse models of AS.10 Similar to these reports, we found that Ube3a-ATS ASO treatment correlated with increased Ube3a expression. Using our natural history model of absolute delta power, we were able to both detect a persistent treatment effect following Ube3a-ATS ASO treatment and found that the changes in absolute delta power correlated with Ube3a expression. These differences were not reliably detected using direct comparisons, but by controlling for variations expected with age, IVI, and inter-subject variability, the longitudinal natural history model had the power to detect a significant treatment effect between the treated and control groups, beyond changes expected with the natural history. The mice data analyzed here were limited by requiring us to implement model predictions between different individual mice, as in a cross-sectional data set. If longitudinal data were available, we would expect the model to be even more sensitive to detect a treatment effect between groups. The mice data were also limited by a small sample size for those with both neurophysiological measurements and Ube3a mRNA expression estimates. Additional data would facilitate a more direct correlation between deviations from the natural history model and mRNA expression within the Ube3a-ATS ASO treatment group. Finally, we did not test a vehicle control AS group in our data, though we note that prior studies have already demonstrated a non-targeting ASO has similar mRNA to AS.21 In addition, Ube3a-ATS ASO treatment has been shown to result in a sustained increase in Ube3a expression up to 4 months after treatment, corresponding to improved synaptic plasticity and cognitive functions.9 The longitudinal model developed herein enables testing for and detection of a treatment effect at any IVI post-treatment, thus enabling detection of peak effects and duration. Future work evaluating the natural history of delta power across the entire lifespan in AS mouse models, including early development, may be helpful to elucidate the impact and duration of Ube3a-ATS ASO treatment at different ages.Several groups have reported promising approaches to reinstate Ube3a expression in mouse models can be done by directly assaying neuronal tissue. Estimates of UBE3A neuronal levels in humans may be performed indirectly through cerebrospinal fluid (CSF) sampling using lumbar puncture. A reliable EEG biomarker to complement CSF data would reduce the need for invasive procedures and would enable multiple repeated measures for longitudinal observations. We find that delta power provides a simple, non-invasive alternative to invasive UBE3A measurements. Further, as enrolment of subjects with rare neurological diseases like AS in clinical trials can be challenging, our natural history model allows enrolment of subjects at different ages and follow-up intervals, and may obviate the need to enrol a control group. Future work to validate the relationship between delta power and UBE3A expression after effective treatment in humans with AS would secure delta power as a mechanistic biomarker to gauge both target engagement and therapeutic response in clinical trials.With many potentially disease-modifying treatments for AS in development, we introduce a natural history model and statistical procedure to utilize deviations from expected measurements of delta power as a sensitive indicator of target engagement and possible treatment efficacy. Measures of fcac106_Supplementary_DataClick here for additional data file.