To determine the main factors influencing dynamic pressure and large deformation roadways, a targeted set of support technologies was designed. The 2603 air inlet roadway of the Zhangcun coal mine in Lu'an, Shanxi Province, was taken as an example. The influence of the Wenwangshan South normal fault and in situ stress field on the dynamic pressure roadway was analyzed theoretically, and the main factors influencing this dynamic pressure and large deformation roadway under natural geological conditions were determined. The effect of the existing roadway support scheme was evaluated by field test methods such as nondestructive bolt testing. The influence of mining two working faces on the dynamic pressure and large deformation roadway was studied by the FLAC3D numerical simulation method. On this basis, a new grouting material was developed, a complete set of technical schemes of full-section integrated cooperative support of dynamic pressure and large deformation roadways was proposed, and the field application effect was verified. The results showed that under natural geological conditions, the 2603 air inlet roadway was located within the influence range of the Wenwangshan South normal fault, which was significantly affected and controlled by the fault. The included angle between the roadway extension direction and the maximum principal stress was 74°, which was not conducive to the stability of the roadway. The range of the roadway loose zone was large. Under the existing support conditions, the surrounding rock could not form a relatively stable structure, which was one of the main reasons for the large deformation of the surrounding rock in the dynamic pressure roadway. The 2603 air inlet roadway was affected by the mining of both the adjacent working face and the 2603 working face. The stresses were superimposed, and the roadway was greatly deformed and damaged. A new grouting material was developed. A crosslinking agent prepared by toluene diisocyanate and polyether polyol was added to the existing polyurethane material to form a new grouting material, and a complete supporting technical scheme was proposed. The field application results showed that the displacement and floor heave of both sides of the roadway were reduced by approximately 87%, the deformation and failure of the coal and rock mass of the roadway were effectively controlled, and the deformation of the dynamic pressure roadway was greatly reduced. The total length of coal mine roadways in China reaches 50,000 km, and most preparation roadways and recovery roadways are arranged in coal seams, of which the length of recovery roadways accounts for more than 60% of the total length of roadways2. Coal seam roadways will form dynamic pressure roadways under the influence of mining or other dynamic influences; the deformation of dynamic pressure roadways is often large and reworking work is frequent, which significantly increases the support cost, seriously affects the safe and efficient production of mines, and restricts the intensive production of coal mines. Therefore, the key to reducing the deformation of dynamic pressure roadways and the cost of support is to clarify the main factors affecting the large deformation of dynamic pressure roadways and to select and improve support measures in a targeted manner.China’s coal resources were formed in many different periods, with complex maturity and distribution conditions. More than 90% of coal mine production originates from shaft mining3 believed that the increase in roadway section area is one of the main factors of large deformation produced by dynamic pressure roadways. According to Liang4, the amount of roadway surface displacement increases faster at the early stage of roadway drivage. As the distance from the headway increases, the amount of roadway deformation gradually tends to stabilize. Zhang5 and Liu6 considered that when the coal seam retrieval roadway is located at a large burial depth, the mechanical properties of the top and bottom plates of the roadway will change, which is one of the main factors for the large deformation of the dynamic pressure roadway. Li7 considered that the main reason for the large deformation of dynamic pressure roadways is the stresses borne by the top plate of the roadway and the two gangs are released through the unsupported roadway bottom plate. Liu8 considered that the weak lithology of the top and bottom slabs of the roadway is the main factor influencing the large deformation and damage in the roadway. Sun9 considered that the control range of the anchor rod support structure is less than the damage depth of the roadway gang, and the failure of some anchor rods and anchor cables in the roadway gang is the main reason for the large deformation of the dynamic pressure roadway. Wang10 analyzed the phenomenon of damage of dynamic pressure roadways and the evolution law of surrounding rock stress and concluded that the mutual superposition of the mining-induced stress and vertical stress of coal columns is the main factor influencing large deformation of dynamic pressure roadways. Zheng11 studied the deformation and damage mechanism and surrounding rock reinforcement technology of a roadway group under strong dynamic pressure and large deformation and concluded that the stress concentration generated by dense coal pillars and workface retraction are the two main factors controlling the large deformation of the surrounding rock in the roadway group. Cai12 concluded that the main reason for the destruction of the surrounding rock in the roadway chamber is that the axial direction of the roadway is perpendicular or oblique to the direction of the maximum principal stress. Yuan13, based on the elastic‒plastic theory and field investigation and analysis, established the mechanical model of a circular roadway under a deep dynamic pressure environment, derived the implicit equation of the plastic zone boundary, and further revealed the large deformation mechanism of a deep dynamic pressure mining roadway. Kuai 14 used numerical simulation software such as FLAC3D and ANASYS and laboratory tests to optimize the parameters of support materials in accordance with the surrounding rock stress environment and roadway deformation characteristics, combined with the failure of roadway support materials in the failure section affected by dynamic pressure. Chen15 studied mechanical models of the microstructure of bolts, anchor cables and type I and anchor cables and sliding surfaces based on the deformation characteristics of dynamic pressure mining roadways in a fully mechanized caving face and the distributions of two types of sliding surfaces and proposed the support idea of “carrying the top and bottom, controlling the two sides”. Liu16, according to the stress state of the surrounding rock and geological conditions, determined that the transport crosscut roadway in the south wing of a mine should follow the principle of “rigid and flexible complementation, combination of long and short, timely initiative, coordination and control”. Wu17, under the influence of various factors, monitored the stress of the anchor cable and carried out a systematic stress analysis to give full play to the active support role of the anchor cable and provide basic data for the optimization of the support scheme. Wu18 proposed the control of the surrounding rock of the remaining roadway in a large mining height working face by using coupling and pressure equalizing support technology and achieved remarkable results.Regarding the main factors influencing the large deformation produced by dynamic pressure roadways, LiThis paper aims to study the influence of 2603 working face mining on the large deformation of a roadway, determine the factors influencing a dynamic pressure large deformation roadway in a wind tunnel, and then optimize the support parameters. On the basis of extensive research, we analyze the stress evolution and deformation of the roadway surrounding rock, select reasonable surrounding rock control technology, optimize the support mode and parameters of the back mining roadway in the Zhangcun coal mine, develop new grouting materials, and form a complete set of technologies for full-section integration and cooperative support of the dynamic pressure large deformation roadway in the Zhangcun mine. The research results will improve the safety and stability of the roadway, reduce the cost of support, and provide a reference for the roadway support of mines with similar conditions.19. The 2603 air intake roadway is a typical dynamic pressure roadway in the 26 mining area, which adopts the joint support form of “anchor rod + anchor cable + steel ladder beam + W steel belt + metal mesh”, and the support form is shown in Fig. The Zhangcun coal mine mainly mines coal seam No. 3, which is a stable and mineable coal seam throughout the whole area, with an average thickness of 6.28 m. In the 26 mining area of the No. 3 coal seam, the 26 belt roadway group, 2603 air inlet lane and other lanes are seriously deformed by the repeated dynamic pressure from the working face, thus making them need to be repaired frequently. At the same time, the dynamic pressure also increases the maintenance cost of the lane and the difficulty of repairing the lane. Such roadways affected by mining or other dynamics form dynamic pressure roadwaysThe Wenwangshan South normal fault extends eastward to Zhouwangshan, intersecting the Jinhuo fault zone (north by east 70°) and intersecting the Wenwangshan North fault (south by west 80°) when it extends westward to Hongshigou village. The relative positional relationship between the Wenwangshan fault influencing area and the Zhangcun mine is shown in Fig. 20, the mine is affected by an active fracture when the linear distance between the minefield boundary and the fracture is less than the fracture influence range.According to the evaluation index of the fracture structure influence range in the evaluation index system of the geodynamic conditionsAccording to the exploration results of the geological department, the Wenwangshan South normal fault has misplaced the Quaternary sediments and is a moderately active fault with an activity coefficient k of 2. The influence range of the Wenwangshan South normal fault at the northern boundary of the Zhangcun mine is 4.6–8.0 km, and all 26 mining areas are located within the influence range of the Wenwangshan South normal fault and thus are affected and controlled by it. The presence of the Wenwangshan fault increases the stress level in the area, which is not conducive to roadway support. At the same time, there are several small faults within the Zhangcun minefield, and the coal seams and rocks near the faults are broken such that sloughing and roof fall often occur, causing the bottom plate to be uneven, which affects the recovery operation and roadway support to a certain extent.21. Yan22 applied the integrated seismic source mechanism solution method and the grid search method, using fault data to obtain the characteristics of the orientation distribution of the tension axis at the junction of Jin, Ji and Yu. From the integrated seismic source mechanism solution method, it was determined that the maximum principal stress orientation in the Changzhi region is mainly oriented in the NW-WNW direction, and the dip direction is close to horizontal23. Therefore, the ground stress test results suggest the a maximum horizontal principal stress value of 16.79 MPa, a minimum horizontal principal stress value of 9.32 MPa, a vertical stress value of 13.01 MPa, and a maximum principal stress direction of N74.0°W, and we selected these data for analysis and calculation. The included angle between the in situ stress direction and the air inlet roadway of 2603 working face is shown in Fig. In May 2021, the Mining Design Division of Tiandi Technology Co Ltd. monitored the ground stress in the Zhangcun mine using the hydraulic fracturing method at three measurement points. Academician Hongpu Kang et al. concluded that the maximum horizontal principal stress direction was concentrated between N19.1° W and N72.9° W between the Wenwangshan South normal fault and the Egangshan North Main Fault24, we use the perimeter rock structure detection method to measure the width and range of fissures in the 2603 inlet windway to determine the main deformation of the perimeter rock and the direction of the main fissures in the rock to accurately reveal the state of the underground engineering perimeter rock and the rock yield, the development of fissures, and the development of engineering perimeter rock deformation to speculate the range of the loosening circle.Before the excavation of the tunnel, the rock body bears the original rock stress and remains stable; after the excavation of the tunnel, the stress of the tunnel surrounding rock is redistributed, and a stress change zone and stress concentration appear in the surrounding rock. According to the theory of perimeter rock loosening circle supportAccording to the loosening circle test results, the roadway surrounding rock stability classification can be carried out. Table We selected three test sections in the 2603 inlet airway to perform loose circle testing: at 645 m, 670 m and 700 m. Among them, 645 m is 18 m from the triangular coal, 670 m is the outer end of the overrun maintenance section, and 700 m is 30 m from the overrun section. The loose circle detection results show that the range of the loose circle of the 2603 wind tunnel roof is 2–4 m, and the range of the loose circle of the two sides is 6–7 m. The range of the loose circle of the 2603 wind tunnel roof is 2–4 m, which corresponds to the V–VI type of surrounding rock and the category of unstable to extremely unstable surrounding rock; the range of the loosening circle of the two sides is 6–7 m, which belongs to the VI type of surrounding rock and belongs to the category of extremely unstable surrounding rock. Considering the loose circle detection results, the current anchor support parameters used in the 2603 windway and other dynamic pressure lanes are as follows: top anchor spacing 0.85 m, row spacing 0.9 m, 7 rows each; gang anchor spacing 0.85 m, row spacing 0.9 m, 5 rows each; anchor type rebar anchor, diameter Ф22 mm, length 2400 mm; anchor cable support. The top anchor cable adopts a “three–two” arrangement: three anchor cables with a spacing of 1.5 m and row spacing of 1.8 m, and two anchor cables with a spacing of 2.0 m and row spacing of 1.8 m. The top anchor cable is steel strand anchor cable with a diameter Ф17.8 mm and length of 7300 mm; the two gang anchor cables have a spacing of 2.0 m and row spacing of 1.8 m and are steel strand anchor cables, with a diameter of Ф17.8 mm and length of 4300 mm. According to the loosening circle test results, the existing support parameters cannot meet the requirements of surrounding rock control, which is one of the main factors controlling the large deformation of dynamic pressure roadways.25. Three sets of pullout tests were carried out at 645–670 m in the 2603 inlet airway, and each set was pulled out three times. These tests were conducted to understand the performance of the anchoring system of the surrounding rock in the dynamic pressure and large deformation roadways of Zhangcun coal mine. The results of the anchor pullout test in the 2603 inlet airway of the Zhangcun coal mine are shown in Table The purpose of the anchor pullout force test is to determine the anchorability of the roadway envelope and to evaluate the performance of the anchor, resin, and envelope anchoring system and the anchorage force of the anchorThe size of the anchorage force is related to the nature of the surrounding rock at the anchorage point and the anchorage effect. According to the regulations of the Lu’an Zhangcun coal mine, the anchor pullout force should meet the anchorage strength (120–190 kN) requirements. According to 3 sets of 9 pullout tests, the anchor section failed at an average anchor force of 182.2 kN when the anchor section length was 120.8 cm, which satisfied the anchor strength (120–190 kN) requirement.This indicates that the anchor quality and anchor force are not the main factors influencing the large deformation of dynamic pressure lanes such as the 2603 inlet airway.For the anchoring performance of anchor rods, nondestructive testing of anchor rods in the inlet airway of the 2603 working face was completed. Three locations were selected, in the same section as the peephole; 645 m, 670 m and 700 m.The results of the nondestructive testing of the anchor rods showed that the integrity of the anchor rod support process was good and that the performance of the anchor rods was “excellent”. The anchor rod anchorage performance is not the main factor influencing the large deformation of dynamic pressure lanes such as the 2603 air intake lane.In summary, under natural geological conditions, roadways such as the 2603 air intake roadway are seriously deformed due to the influence of ground stress, and according to the loosening circle test results, the existing support method is not sufficient to maintain roadway stability. In addition to the geological conditions, the roadway is affected by the mining of the working face, and further research is conducted on the influence of the mining of the working face on the roadway, such as the 2603 air intake roadway.Detailed analysis of the impact of workface back mining on the 2603 air inlet lane, was performed via modeling and calculation of the 2603 workface as an example. The 2603 working face of the Zhangcun coal mine is located in the middle of the 26 mining area, with the 26 mining area alley to the south, the minefield boundary (Wenwangshan South Fault) to the north, the 2601 working face mining area to the east, and the unmined area to the west. The 2603 working face has a cut-hole length of 320 m, a recoverable length of 1153 m, and a recoverable reserve of 2.84 million tons. The 2603 working face uses the technique of leaving an alley along the roadway to assist in the working face mining. The working face 2603 uses the “Y + high extraction road” roadway layout. The finite difference software FLAC3D was used to establish a numerical simulation model based on the production and geological conditions of the 2601 and 2603 working faces and to analyze the surrounding rock stress distribution during working face mining through numerical calculation. The numerical model of working face mining was established as shown in Fig. Constraints along the X-axis are imposed on the boundaries at both ends of the model X-axis, i.e., the boundary displacement in the X-direction is zero.Constraints along the Z-axis are imposed on the boundary at both ends of the model Z-axis, i.e., the displacement of the boundary in the Z-direction is zero.The model Y-axis (bottom) boundary imposes a fixed constraint along the Y-axis, i.e., the displacements in the Y-direction of the bottom boundary are all zero.The top of the model is a free boundary.The mechanical parameters of each coal seam are shown in Table A stress of 16.94 MPa is applied in the X-axis direction of the model.A stress of 9.32 MPa is applied in the Z-axis direction of the model.A stress of 12.5 MPa is applied in the Y-axis direction of the model, an equivalent load of 12.5 MPa is applied to the upper part of the model, and the self-weight load is set in the Y-direction.Combining the results of ground stress measurements in the minefield, the model boundary load conditions were calculated as follows.The wind tunnel selected observation point is located in the open cutting eye at 300 m, as shown in Fig. 26, and the superposition of the stress caused by back mining is the main reason for the large deformation and damage of the surrounding rock of the 2603 air intake lane.From the above analysis, it can be seen that the 2603 inlet roadway of the Zhangcun coal mine is affected by the mining-induced stresses of both the 2601 working face and 2603 working face. Under the influence of the primary mining of the 2601 working face, the stress concentration coefficient of the bottom plate of the 2603 inlet roadway is 1.68, and the stress concentration coefficient of both gangs is 1.47–1.72. Under the influence of the secondary mining of the 2603 working face, the stress concentration coefficient of the bottom plate of the 2603 inlet roadway is 2.64, and the stress concentration coefficient of both gangs is 1.74–2.32. The stress concentration coefficient of the 2603 inlet lane is 2.64, and the stress concentration coefficient of both gangs is 1.74–2.32. Compared with that after primary mining, the stress concentration coefficient of the 2603 inlet lane bottom plate is increased by 0.96, and the stress concentration coefficient of both gangs is increased by 0.27–0.60 under the influence of secondary mining of the 2601 and 2603 working faces. The change in the stress concentration coefficient of the 2603 inlet lane under the influence of mining is shown in Table According to the analysis results of factors such as the plastic destruction of the surrounding rock of the 2603 inlet airway, under natural geological conditions, ground stress has a great impact on the 2603 working face inlet airway, which is not conducive to maintaining the stability of the roadway, and the existing support method is not sufficient to maintain the stability of the roadway through the loosening circle test. Under the influence of mining, the bottom coal body undergoes plastic deformation first, which in turn leads to the stress of the two gangs and the overlying coal rock layer transferring to the bottom rock layer through the surrounding rock in the elastic‒plastic zone, causing damage to the 2603 air-in tunnel and the two gangs. The weakness of the self-supporting capacity of the 2603 air-in tunnel roadway is the root cause of its large deformation and damage, and improving and maintaining the self-supporting capacity of the surrounding rock is a reliable way to solve this kind of problem. For this situation, three kinds of grouting reinforcement plans were designed for the surrounding rock of the tunnel, and the specific implementation plans of the three grouting plans are shown in Table The effect of the existing support and three grouting reinforcement optimization schemes are simulated and analyzed by FLAC3D numerical simulation, and the comparison of the effect of the existing support and three grouting optimization schemes is shown in Table According to the simulation results, under the full-section grouting condition, the top slab sinkage is 630 mm, which is 44% lower than the original support, the bottom slab bottom bulge is 1210 mm, which is 67% lower than the original support, and the two supports of the roadway are shifted closer by 1570 mm, which is 74% lower than the original support. This result shows that the effect of full-section grouting is the best with optimization option three. The full-section grouting support scheme has the best effect on the control of the roadway surrounding rock compared with the anchor cable grouting of the two supports and the anchor rod grouting of the bottom plate; therefore, the full-section grouting support scheme is recommended for roadway surrounding rock reinforcement.Research processAt present, the material selected for roadway grouting in the Zhangcun coal mine is polyurethane material. To meet the requirements of the accounting culture, the performance of the support material is further improved on the premise of reducing the existing cost by 5%. To this end, new grouting materials were developed.The materials and reagents used in the experiments are shown in Table The two-component polyurethane reinforcement was prepared, poured into uniform-size cylindrical plastic paper cups before the drug started to set, and demolded after it had completely set and formed. The seven groups of demolded samples were sanded with sandpaper one by one to a cylinder 30 mm in height and 50 mm in diameter and left for compression testing. The compression specimens are shown in Fig. (B)Research resultsFourteen stainless steel strip pieces with a size of 100 mm × 25 mm × 15 mm were prepared and wiped with anhydrous ethanol, and the surfaces of the samples were thoroughly cleaned. In pairs, a 25 mm × 15 mm plane butt joint was created with a 1 mm gap. Then, the 7 groups of test pieces were placed on the horizontal table. Nest, the following steps were taken: Prepare the two-component polyurethane reinforcing agent. Before it starts to solidify, use a pipette to absorb a proper amount of medicine, fully inject it into the gap reserved for the butt joint sample, and let it stand for more than 24 h to make it fully and completely solidify, as shown in Fig. Each group of specimens produces a slight difference in deformation variables, and the specimens after the compression experimentation are shown in Fig. The force-compaction curves of the seven sets of compressed specimens drawn by using origin software are shown in Fig. It can be concluded that in the raw material, the cross-linking agent content and the hardness of polyurethane reinforcement are positively correlated and that the higher the cross-linking agent content is, the higher the strength of polyurethane reinforcement. The force–elongation curves of the seven groups of bonded specimens drawn by using Origin software are shown in Fig. When the cross-linking agent combined with toluene diisocyanate and polyether polyol was added, the bond strength of sample No. 3, i.e., with 4% cross-linking agent, was the largest and 1.87 times that without the cross-linking agent; the elastic modulus of sample No. 7, i.e., with 12% cross-linking agent, was the largest and 6.33 times that without the cross-linking agent. Considered together, the elastic modulus is 3.56 times that without the cross-linking agent, and the bond strength is 1.87 times that without the cross-linking agent when 4% cross-linking agent is added to the existing support material.To study the field application effect of the new grouting material in the full-section grouting method, 510–530 m of the 2603 air-inlet roadway was selected as the test roadway, and the technology was applied in the field. To verify the reinforcement effect after grouting, two monitoring sections were set up at 520 m (grouted section) and 490 m (nongrouted section), and the crisscrossing method was used to monitor and compare the displacement of both sides of the roadway and the displacement of the top and bottom plates. The comparison of the deformations and bottom bulges of the nongrouted section and grouted section are shown in Figs. Through comparative analysis, during the 30-day monitoring period, the bottom drum volume of the nongrouted section reached 1198 mm, and the displacement of both gangs reached 1043 mm. The bottom drum volume of the roadway changed considerably at the beginning, but the increase in the bottom drum volume decreased at the later stage, and the displacement of both gangs increased almost linearly. After grouting, the bottom drum volume and the displacement of both gangs were controlled, the maximum bottom drum volume was 130 mm, the maximum displacement of both gangs was 153 mm, and the displacement and bottom drum volume of both gangs were reduced by approximately 87%. These findings show that the original broken coal rock body was solidified into a complete whole under the action of slurry after the roadway grouting reinforcement, so the anchor rods and anchor cables were fairly effective. After adding the new material, the deformation volume was further reduced by 13% compared with the optimized results of the numerical simulation, and the effect of the new grouting material was more significant, which effectively controlled the deformation and damage of the coal rock body of the roadway, indicating that the stability of the roadway was improved after grouting reinforcement.Zhangcun coal mine 2603 wind tunnel is located near the Wenwangshan Mountain South normal fault and is influenced by it; the tunnel is arranged along the north‒south direction, and the maximum principal stress orientation is 74°. The ground stress has a great impact on the 2603 working face in the wind tunnel, which is not conducive to maintaining the stability of the tunnel.Anchor quality, anchor force and anchor performance are not the main factors influencing the large deformation of dynamic pressure roadways such as the 2603 air intake roadway; the large loosening circle and the inability of the surrounding rock to form a relatively stable structure under the existing support conditions are some of the main reasons for the large deformation of the surrounding rock in the studied dynamic pressure roadway.The 2603 wind tunnel is affected by the mining-induced stresses of the 2601 working face mining and 2603 working face mining, the stress concentration coefficient of the 2603 wind tunnel bottom plate is 2.64, and the two support stress concentration coefficients are 1.74–2.32. The superposition of stress caused by back mining is the main reason for the large deformation and damage of the 2603 wind tunnel surrounding rock.According to the main factors influencing the large deformation and damage of the dynamic pressure lane, such as the 2603 air intake lane, a new support method of full-section grouting was determined. The specific parameters are as follows: top and bottom plates adopt φ22 × 2400 mm rebar anchor rods, with interrow spacing of 850 × 1000 mm and 7 sets in a row; top anchor rods adopt φ17.8 × 7300 mm grouted anchor rods, with a spacing of 1500 × 2000 mm and 2 sets in each row; the left and right gangs adopt φ22 × 2400 mm threaded steel anchor rods, and the distance between rows of anchor rods is 800 × 1000 mm, with 5 sets in a row; the anchor cables adopt φ17.8 × 4300 mm grouted anchor cables, and the distance between anchor cables is 1200 × 2000 mm, with 2 sets in each row.A new grouting material was developed with the addition of a cross-linking agent formulated from toluene diisocyanate and polyether polyol to the existing coagulation force polyurethane. The bond strength was the highest at 4% cross-linking agent, which was 1.87 times that without cross-linking agent, and the elastic modulus was the highest at 12% cross-linking agent. A field test was carried out at 520 m in the 2603 wind tunnel, and the result was that the deformation of the tunnel surrounding rock was significantly reduced and the effect was remarkable.


The representation of cement–augmented bone in finite element (FE) models of vertebrae following vertebroplasty remains a challenge, and the methods of the model validation are limited. The aim of this study was to create specimen-specific FE models of cement–augmented synthetic bone at the microscopic level, and to develop a new methodology to validate these models. An open cell polyurethane foam was used reduce drying effects and because of its similar structure to osteoporotic trabecular bone. Cylindrical specimens of the foam were augmented with PMMA cement. Each specimen was loaded to three levels of compression inside a micro-computed tomography (μCT) scanner and imaged both before compression and in each of the loaded states. Micro-FE models were generated from the unloaded μCT images and displacements applied to match measurements taken from the images. A morphological comparison between the FE-predicted trabecular deformations and the corresponding experimental measurements was developed to validate the accuracy of the FE model. The predicted deformation was found to be accurate (less than 12% error) in the elastic region. This method can now be used to evaluate real bone and different types of bone cements for different clinical situations. Percutaneous vertebroplasty is a minimally invasive treatment for osteoporotic vertebral fractures. During the treatment, polymethylmethacrylate (PMMA) bone cement is injected into the fracture site to augment the fracture and relieve pain. The success of the treatment is still under debate, with clinical trials reporting conflicting results in terms of pain relief.The behavior of the cement–bone interface is likely to be an important factor in determining the performance of the procedure in the longer term.et al.et al.In order to investigate these possible mechanisms, higher resolution models are necessary. A number of authors have previously developed micro finite element (μFE) models of trabecular structures based on μCT images , with porosity over 95%, cell size between 1.5 and 2.5 mm and wall thickness between 0.15 and 0.3 mm, was chosen since its structure is similar to that of human osteoporotic trabecular bone.In order to replicate the experimental test conditions in the FE model, the displacements of both ends of the specimens were calculated from the μCT data. From the pre-loaded images, the coordinates of a set of points from both the top and bottom surface of each specimen were recorded according to their positions relative to the tube edge. The coordinates of the points in images from each of the subsequent loading increments were measured using the same method and the relative displacement calculated. More than five points were compared at each end of each specimen and the average difference between the coordinates was determined. The calculated displacements were subsequently applied to the FE models.All the μCT scans were converted to grayscale images and down-sampled from 25 μm to 50 μm using image processing software . This resolution was able to capture the detailed morphology and maintain the connectivity of the synthetic bone trabeculae while reducing the size of the final FE models. Threshold values were chosen from the pre-loaded images by visual observation to segment the cement and synthetic bone regions. For one of the specimens (Specimen 1), a manual method was used to further refine the segmentation. Here, local modifications were implemented by visually comparing the regions with the underlying images on each individual slice to provide a more representative segmentation of the two regions.For each specimen, a μFE model with element size 50 × 50 × 50 μm was generated from the down-sampled pre-loaded μCT images using commercial software . The cement and synthetic bone materials were meshed as separate parts and all surfaces of the model were smoothed using tetrahedral elements. The total number of elements for each model was approximately 3.2–3.6 million. For Specimen 1, two models were generated, one from the standard “automated” segmentation method and a second from the manual segmentation method.The material properties of both the synthetic bone and cement were considered to be homogenous and linearly elastic, with elastic moduli of 280 and 2280 MPa® Xeon® CPU X5472 @ 3.00 GHz 2.99 GHz, 32 GB memory) was used for the analysis.All of the models were processed using ABAQUS 6.81 . A high specification computer  using the method described in “The difference between the predicted deformations seen on the FE slices and the μCT images for the manual segmentation model is shown in Fig. Similar results were found for the automated segmentation models, as shown in Fig. The predicted deformations near the interface between the cement and synthetic bone for the FE models are shown in Fig. For Specimen 1, the difference in stiffness, maximum stress and deformed morphology between the manual segmentation model and the automated segmentation model are shown in Table For the manual segmentation model, the effects of using different interaction properties  at the interface between the cement and the synthetic trabeculae in terms of the stiffness and the maximum von Mises stress are shown in Fig. The difference in the predicted deformed morphology between the tied and frictionless models in the registration areas at different load increments was found to be very small; with the maximum difference after the final compression step less than 0.7% Table .Table 3DA comparison of the localized deformation between the tied and frictionless contact models in the cement–trabecular interface region is shown in Fig. In this study, specimen-specific μFE models of cement–augmented synthetic bone were generated to represent the structure at the trabecular level. Previous continuum level models of similar structures have been relatively successful in capturing the overall specimen behavior when a reduced modulus is applied to the cement–composite region.In the current study, the specimen size was also limited by the dimensions of the loading stage in the μCT. This led to difficulties in clamping the ends of the specimens, and some slipping and twisting occurred during the compression which could not be fully replicated in the FE models, accounting for some of the error seen in the validation. In order to generate a boundary region between the cement and synthetic bone in these specimens, rather than injecting cement into the center of the specimen, the ends were embedded into cement. This approach was used because of the size of the specimen and also to generate flat, parallel surfaces necessary for fixation into the loading stage. The limitation of this approach was that the cement boundary was perpendicular to the loading axis, so was only loaded in compression. In a vertebroplasty procedure, the cement is injected into the vertebral body forming a bolus surrounded by trabecular bone, so around the boundary of the cement there are different relative loading directions. The methodology presented here could now be applied to other configurations of cement to examine the boundary behavior under alternative modes of loading.In order to generate the FE models, it was necessary to segment the μCT images into the synthetic bone and cement regions. However, there was some overlap in the grayscale distributions of the two materials. Therefore, further local manual modifications were implemented on one of the specimens using visual comparisons with the underlying images on each slice to provide a more representative segmentation of the two regions. The manual modifications preserved better connectivity of the synthetic bone trabeculae within the composite region and visually looked more accurate. However, from the FE modeling results Table , the difIn this study, the effect of the friction and interactions at the interface were examined using the manual segmentation model, by varying the contact interaction properties from frictionless, to a frictional coefficient of 0.3, and to a tied contact. Some differences between the tied and frictionless contacts were observed in the local deformations Fig.  at the cA new validation method was developed in this study by examining the difference in the deformed morphology between the FE models and the experimental images. The FE models and the μCT images were compared at the initial unloaded position as a calibration Fig. a to gaugAt the region of the interface between the cement and Sawbone, a localized comparison between the FE model and the μCT images at each loading step Fig.  showed gin vitro cement–bone interface under load. A method of validating the models against μCT images of the same specimen under the same loading conditions by comparison of the deformed morphology was also developed. The focus of this study was on compressive loading, with the longer term aim of improving the understanding of the mechanics of cement augmented vertebra after percutaneous vertebroplasty. The effect of interaction properties at cement–bone interface was found to be minimal in compression, where the interlocks of cement and bone dominate the micro-mechanics at the cement boundary. This method will now be applied to real bone augmented with different types of bone cements used for vertebroplasty. Although this study focussed on vertebral augmentation, the modeling and validation methods developed could be used in other loading cases, such as shear or tension, to evaluate other applications such as total joint replacement.This study developed a method of generating specimen-specific μFE models of cement augmented synthetic bone at the microscopic level, to represent the


This is known as the peaking phenomenon, a common situation in the analysis of gene expression data. Highly predictive bivariate gene interactions whose marginals are useless for discrimination are also affected by such phenomenon, so they are commonly discarded by state of the art sequential search algorithms. Such patterns are known as weak/marginal strong bivariate interactions. This paper addresses the problem of uncovering them in high dimensional settings.One of the drawbacks we face up when analyzing gene to phenotype associations in genomic data is the ugly performance of the designed classifier due to the small sample-high dimensional data structures  as a search engine in order to detect such signals. The choice of QDA is justified by a simulation study for a benchmark of classifiers which reveals its appealing properties. The procedure rests on an exhaustive search which explores the feature space in a blockwise manner by dividing it in blocks and by assessing the accuracy of the QDA for the predictors within each pair of blocks; the block size is determined by the resistance of the QDA to peaking. This search highlights chunks of features which are expected to contain the type of subtle interactions we are concerned with; a closer look at this smaller subset of features by means of an exhaustive search guided by the QDA error rate for all the pairwise input combinations within this subset will enable their final detection. The proposed method is applied both to synthetic data and to a public domain microarray data. When applied to gene expression data, it leads to pairs of genes which are not univariate differentially expressed but exhibit subtle patterns of bivariate differential expression.We have proposed a novel approach for identifying weak marginal/strong bivariate interactions. Unlike standard approaches as the top scoring pair (TSP) and the CorScor, our procedure does not assume a specified shape of phenotype separation and may enrich the type of bivariate differential expression patterns that can be uncovered in high dimensional data. A challenging problem within this domain is the identification of inputs or interactions of them highly correlated to the outcome. The low sample-high dimensional (n ≪ p) structure of the data we handle makes this challenge a difficult task, in particular when we are concerned with the detection of bivariate interactions. Some papers that tackle this problem using indexes of pairwise feature association are [The development of high-throughput technologies, such as gene or proteinn microarrays, has provided the scenario of the state of cells by monitoring the expression levels of hundreds or thousands of biological inputs  in accordance with the following scheme: the conditional distribution of Z|Y = 0 —black labels— is bivariate normal with mean vector µ0 = ; meanwhile, the other class conditional distribution for Z|Y = 1 —red labels— is bivariate normal with mean vector µ1 = . We assume both distributions have the same covariance matrix given byThe observations are drawn from bivariate random variable X =  in accordance with the following scheme: the conditional distribution of the random variable X|Y = 0 —black labels— is uniform over the quadrants X|Y = 1 —red labels— has a uniform distribution over The observations for the XOR pair are drawn from a bivariate random variable R =  with vector means µ =  and covariance matrix the indentity I. The labels are assigned in accordance to the following rules: if Y = 0 —black labels— and if Y = 1 —red labels.Cases are simultated from a bivariate normal distribution V =  and the outcome variable Y is given by the following rules: V|Y = 0 —black labels— has a uniform distribution over V|Y = 1 —red labels— has a uniform distribution over Observations in this situation are drawn from uniform distributions confined to the domain n0 = n1 = 40. Note that if the points are projected on each one of the axes, both categories of the outcome do overlap; however, if both variables of the pair are considered together the classes are neatly separated. Therefore, the discrimination comes from the bivariate interaction between them. This is the reason why we call this type of interactions weak marginal/strong bivariate interactions.Figure n0 = n1 = 40. For each scenario, we add j independent noisy features, j = 1, 2,…, 100, with standard normal distribution and estimate the error rate for the following four classification rules: Adaboost [We consider the previous synthetic scenarios and generate samples of sizes Adaboost , Random Adaboost , a suppoAdaboost  . The erZ1, Z2) are used as predictors. This ugly performance is related to the type of polynomial kernel we used, a second order polynomial kernel, which is well suited for tracing nonlinear quadratic patterns but poor for identifying linear decision boundaries as in scenario 1; see the improvement of SVM classifier in scenarios 2, 3 and 4 where it makes a better job with the non linear interaction patterns ,  and  tracing the separation between the classes.Note that the error rate of the polynomial kernel in scenario 1 is high, around 0.5, when only the variables of the pair  as in [In this section we revisit the effect of the peaking phenomenon for a selection of classifiers from the CMA package: k-nearest neighbors (knn) and neural networks (nnet) , diagonaf) as in , PAM claf) as in , random f) as in , the comf) as in , the Elaf) as in  and two compare gives a picture of how these classifiers compare one with each other. For each one, it displays the boxplot of the error rate over the 10 validation sets.The function n0 = n1 = 40 samples from scenarios 1, 2, 3 and 4. The boxplots in Figures p = 2 , p = 10  and p = 20  features. We can see that QDA outperforms the remaining classification rules in almost all the scenarios. It is of special interest the XOR interaction pattern as pointed out in [p = 20. It is worth noting that for p under 10  and N, where µ1 and µ2 are the mean vectors and Σ1 and Σ2 are the covariance matrices. The decision boundary corresponding to the QDA classification rule is given byRecall that binary QDA is concerned with the discrimination between two π1, π2 the a priori class probabilities. When we are dealt with balanced classes π1 = π2 = 0.5.with When the sample estimates The previous decision boundary defines an hyperquadric whose shape depends on the elements involved in the difference of inverses ies; see  for detan0 = n1 = 40) according to patterns in scenarios 1, 2, 3 and 4, along with 80 cases from p – 2 independent standard normal variables, which are uninformative features for class prediction. On the order hand, we have generated n0 + n1 = 80 samples from p independent standard normal variables and obtain a data set with only noisy features. The error rate of the QDA classifier was estimated by 10-fold cross validation for each data set. We repeated the experiment B = 100 times in order to get both populations of error rates: with the signal and with only noisy features. We have considered feature spaces with p = 2, 5, 10, 15, 20, 30 predictors.We have drawn 80 observations , with Φ the distribution function of the standard normal variable and ∆ the Mahalanobis distance. This measure has an appealing theoretical flavor since it provides the overall error rate of the linear discriminant classifier when the multivariate normality within the classes and the equality of class covariance matrices assumptions are met; see [p increases, the amount of overlap becomes larger; therefore the QDA would be unable to catch the signal and might confuse it with the noise.The boxplots of Figures met; see . Note thp = 10 (or at most p = 15), when we are concerned with the detection of weak marginal/strong bivariate interactions in high dimensional data sets. This finding is crucial and puts the basis of the search strategy we will design to uncover this type of interaction patterns. The rationale behind this strategy is as follows. The naive solution would explore the feature space in an exhaustive way by fitting a QDA classifier to each pair of variables; a high accurate classification would be highlighting the presence of a signal. Obviously, this alternative is time consuming prohibitive since it would require a total of p(p – 1)/2 QDA fits; for example, if p = 2000 then 1999000 fits are needed.The results of the simulations have shown that QDA resistance threshold to peaking can be set at bsize and by fitting the QDA for all pairs of blocks. As we know that QDA is resistant to peaking while the number of features ranges between p* = 10 and p* = 15, we propose to take bsize such that 2 ∗ bsize ≤ p*; in this way we protect ourselves against the danger of peaking when the QDA classifier is fit with all the features belonging to the union of both blocks. Once the QDA classifiers are obtained for all the possible matchings of blocks, we know that for a matching containing a bivariate interaction pattern, the classifier will give a very low error rate; meanwhile, for a block matching with only noisy features we will obtain a high error rate. Thus, we can construct a ranking of block matchings, where the top ranked matchings will contain the informative bivariate interaction patterns, and the matchings at the bottom of the ranking carrying on only noisy features. Now, at a second stage we can restrict the search to the subset of features belonging to the top ranked matchings of blocks. For example if we confine the search to the 2 ∗ bsize features of the first block matching, we would need to explore bsize × bsize interactions in order to find out which one of them is responsible for the observation of such a low error rate in the QDA; usually this search is very low time consuming since bsize is smaller than 7.Our search strategy proceeds in a nearly exhaustive way by dividing the feature space in small blocks of features of a specified size p = 2000 and we take bsize = 5, we would obtain 400 blocks; so the search would need only 79800 QDA fits, much less than the 1999000 fits of the naive solution.Searching in the feature space in a blockwise manner has an enormous advantage with respect to the exhaustive search; for example, if This procedure has been implemented using the R platform for statistical computing downloaded from . The folIt is recommended to carry out a first screening step in order to filter the strong marginal features highly correlated with the outcome before applying the search procedure. Recall that our search strategy was designed to uncover the weak marginal/strong bivariate interactions which are usually rejected by traditional sequential search procedures or pre-screening filtering tools , ,  and  corresponding to scenarios 1, 2, 3 and 4, with E =  a vector of independent noisy standard normal variables added to the signal. For p = 200 the signal represents 1% of a 200-dimensional feature space.Let bsize = 5 to the previous synthetic scenarios and have obtained the ranking of block matchings. As we have discussed, this ranking is a useful tool that allows to restrict the search for the hidden interaction patterns by exploring its top ranked positions. Figure We have applied the QDA interaction detector procedure with Z1, Z2),  and . The red hot squares of scenarios 1, 2, 3 and 4 in Figure V2 in the V-shaped pattern. On the other hand, the isolated red hot spot in scenario 2, surrounded by light yellow and orange spots, might be explaining the weak predictive power of the components in the XOR interaction, where both variables behave as noisy features.Note that the procedure has found interaction patterns (The colon cancer data set is a publicly available experiment which can be obtained from the package colonCA in . Gene exRandom Forests (RF) outlier detector utility identified cases 18, 20, 52, 55 and 58 as outliers. These were previously identified in  as aberrntree = 5000 for the number of trees in the forest and the default for mtry, the number of eligible splitters. Figure The table of variable importance of RF identifies the most influential genes for class prediction. We took as a measure of importance the mean decrease Gini score; we utilized the values We pick up the first one hundred genes of RF table of variable importance. The list has a great agreement with other previous selections in the literature, in particular with that one in . Table 1After putting aside the biomarkers identified in the screening step and eliminating a few duplicated columns, we end up with a data set containing 1891 features along with the binary outcome.bsize = 5. Figure Before applying the procedure, we set G1334, G1573), ,  and  which come from the first, third, fourth and fifth positions of the ranking of block matchings. These associations correspond to the following gene to gene interactions: , ,  and . The scatter plots in Figure The heat matrix plots reveal interesting interactions among features which were considered useless by RF ranking of variable importance at the initial screening step. Four bivariate interactions are standing out; they correspond to the interaction of the genes at columns:  as a high scored one. The scatter plots in Figures R88740, H05899),  and  where an almost linear pattern of class separation can be traced, although not so neatly as with the pair . Unlike them, the pair , with moderate to low values of the TSP and CorScor, exhibit a non linear pattern of class separation and is an example of the distinguishing feature between these methods and our approach.Table This paper has explored the peaking phenomenon in the context of detecting marginal/strong bivariate interactions in high dimensional settings. The appealing properties of the QDA classifier and its resistance to peaking has justified its use as a search engine of a procedure that explores the feature space in order to look for this type of signals in high dimensional data.The method was applied both to artificial data and to a real microarray gene expression experiment, the colon cancer data set. The application to real data has led to promising results providing gene interactions that exhibit bivariate differential expression but are not differentially expressed when considered marginally. The results show the usefulness of QDA interaction detector procedure, which is expected to become an efficient tool for biologists and bioinformaticians for the discovery of new gene to gene interactions.The proposed method has been developed for binary classification; the analysis for multi-class problems is a natural extension for conducting future research efforts. Some research regarding the computational cost involved in the QDA interaction detector search strategy is also an issue for further improvements.The authors declare that they have no competing interests.The authors JMA and HN have equally contributed to the work. Both authors have read, reviewed and approved the final version of the manuscript.


The purpose was to test the reliability of short samples of parent/child interaction for use in single-subject research. Four variable pairs of mother/child behaviour were coded for seven mother/child play sessions. Each session lasted 20 min and 18 min of the session was behaviourally coded using frame-by-frame analysis. The co-occurrence of the mother/child behaviours within a given time window was computed and an odds ratio was calculated for the co-occurrence of the targeted behaviours. The play session was divided into shorter segments  and odds ratios of the variable pairs from the shorter segments were compared to the odds ratios from the entire session. Segments of 3 and 6 min did not yield the same pattern of results as the entire session. In single-subject research, evidence of the reliability of the time segment for behavioural coding should be reported in the methods section of original research manuscripts. Behavioural coding of live or recorded observations is often used as a tool to capture the intricacies of human interaction in a variety of fields for experimental and clinical purposes. It is an accepted practice to code a proportion of the observations or ‘thin-slices’ of interaction as a representation of the whole interaction. The term ‘thin slicing’ was coined by Ambady and Rosenthal , 1993. TThin-slicing can be analogues to brief functional assessments that are often used in psychiatry. Brief assessments are known to be reliable, but the results they provide can be limited to behaviours that occur more frequently , one time slice that was above 5 min duration (6 min—referred to as medium duration) and one time slice that represented half of the entire play session (9 min—referred to as long duration). The main experimental hypothesis of the study is that short slices of behavioural data (less than 5 min in duration) taken from naturalistic free play between mothers and children is not as reliable as longer slices of behavioural data (medium duration and long duration). A secondary experimental hypothesis of the study is that the frequency of behaviour, based on a count from the population of the entire free-play session, interacts with the reliability of data from the differing time samples. Low frequency contingency pairs will be less reliable in all the samples, but particularly in the short samples compared to higher frequency contingency pairs. A final experimental hypothesis of the study is that results based on the samples taken from the beginning of the entire play session will be more reliable than samples taken at the end of the play session. This pattern will be observed for all the sample durations .In the larger study for which we were defining our methodology, our intention was to test an experimental hypothesis which stated that the parent intervention in the clinical trial would enhance parental responsiveness. This hypothesis drove the need to develop a robust measure of parental contingency which examined the sequential occurrence of the parents’ behaviour in response to the child’s. The dependent variable was for use in a phase 1 clinical trial with single-subject design and there was a need to test the reliability of the measurement for use with single cases. It was not enough to adopt methods that had been derived from pooled data from experimental research. So there remained a question as to whether the coding of a thin slice (5 min or less) of behaviour would yield results similar to that provided from a complete play session of 20 min duration. The practical question of how much data we needed to code to get a reliable result meant that we compared three partial segments that differed in duration, one time slice that was below 5 min duration  and two girls . All mothers were hearing and all children were congenitally profoundly deaf. Two children had bilateral cochlear implants and were pre-lingual. One child  had bilateral cochlear implants, and had some level of speech. One child had a unilateral cochlear implant and was pre-lingual with severe learning difficulties .For the two girls, their father and sibling were also present in the room to keep the sessions as representative of the family as possible. However, the presence of additional interactive partners made the behavioural coding more complex than traditional face-to-face microanalytic studies. For coding purposes only interaction between the mother and her deaf child was coded. Two families had one pre-intervention visit each and two families had two visits each (pre and post intervention baseline) following the same procedures . Since the focus of this study is the methodology of choosing time segments for behavioural analysis, the intervention status of the families was not considered as part of the analysis. This gave a total of seven video cases for analyses in this paper.Informed, signed consent was obtained from the parent/caregiver prior to starting the study. The study has been reviewed and approved by the Derbyshire Research Ethics Committee and Nottingham University Hospitals NHS Trust Research and Development department. All families were reported to be in good health at the time of filming.Families were video recorded during an unstructured Video recordings were coded as a continuous variable in INTERACT software Mangold  to extraTo account for the time taken by the participants to settle in the activity the first and last 1 min was discounted from the 20 min free play video while coding, thus leaving 18 min of free play to code. In the first instance the whole 18 min was coded for each of the seven videos. Each 18 min code file was then divided into six slices that were 3 min in duration . In addition the 18 min of coding was divided into two segments of 9 min duration and three segment of 6 min duration. Each coded segment is referred to as a dataset in the analysis and results section.The coding software INTERACT stores data sets as tab-delimited text files (.ACT files). The .ACT files were extracted in ActSds using 1 s time units  for each of the seven video cases in GSEQ.In order to analyse whether the mother’s looking and verbal behaviours (Target behaviours) were contingent within 3 s of the child’s looking and vocalisations (Given behaviours), the WINDOW command in GSEQ was used to define four new codes: One coded the onset (first unit) second of the Given behaviour and the following 2 s as a Given window for the child’s looking and vocalisations separately, while the other two coded just the onset of the mother’s looking and verbal behaviours separately . The data from the single case analysis is inconclusive in this regard. There is no evident difference in the degree of discrepancy when the segments were sampled from the beginning, middle or end of the play session from the data in Table Z-scores were computed for the Logg odds derived for each variable pair from each of the short segments. The z-score is an indication of the probability of obtaining a score within a standard population. In this study, the standard population is the entire play session. The degree of variability within the standard population affects z-scores. In statistical terms, the distribution of the standard normal population is characterised by the mean and standard deviation. In a normal distribution 95% of the population lie within ±1.96 SDs from the mean. A z-score of 2 or more (either plus or minus) can be considered to lie outside of the variance of the standard population since only 5% of the scores from the standard population would have fallen at that observed score. Therefore, for our analysis, z-scores of 2 or more were categorised as falling outside the normal distribution of the standard population.We set out to test the primary research question with the grouped data from the seven dyads. This was done by comparing the mean of the Logg odds ratios from the short segments with the mean and standard deviation of the entire play session. Z-scores for each of the shorter segments were derived for each of the contingency pairs. This data are in Fig. z-scores (standard scores) for each of the shorter segments across all four contingency pairs. Lines that are closer to zero deviate less from the Logg odds computed from the entire play session. The contingency pairs in the 9 min segments are within one z-score of the entire play session. Some of the z-scores of the contingency pairs from the 6 min and 3 min segments fall outside one standard deviation of the mean of the entire play session. Some of the z-scores from the shorter segments (6 min and 3 min) fall well below two standard deviations  thus indicating wide variation from the findings of the entire play session.These data suggest that for some contingency pairs  there was particularly wide variability when data from the short segments are compared to each other. In three of the seven cases, this contingency pair was the pair that occurred least frequently in the entire play session. With regard to the question about the position in the play session that data is sampled from, there is an indication, from observing the data in Fig. The findings from the single subject and group analysis presented here show that in single subject research, short time slices (3 min and 6 min) produced discrepant findings compared to the findings from the whole population (18 min). The results suggest that coding based on half the entire play session yielded results that were neither discrepant nor widely varying when compared to the findings derived from the entire play session. Given the centrality of contingency to the hypothesis in the larger study for which our methods were being defined, the discrepancy, and the direction of that discrepancy derived from the short time slices provided significant methodological justification for the design of our analysis of a larger study. If we had used 3 min segments to code data then our conclusions would have differed considerably from the findings based on an entire play session. For example, we would have often concluded that a mother was unlikely to show verbally contingent behaviour on her child’s vocal behaviour where, in fact, this was not the case. Therefore, the experimental hypothesis is supported.For the wider study for which we were developing our methodology the findings from this small set of cases is enough to generate a well rationalised approach to the sample selection in our single subject design. Clearly, the sample size to be selected is 9 min in duration and the beginning 9 min will be used since this was the only sample that yielded consistently non discrepant results from that of the population. If we were inclined to make a judgement about the parenting style of the parent according to level of responsiveness to the child, based on the shorter 3 min or 6 min observations, we would have classified her differently from the classification that we would have made based on a longer observation. Thus, from these data, in this context, the applicability of Ambady and Rosenthal’s thesis, which provides a rationale for thin-slice sampling, was not supported.A limitation of this study is the small sample size. Whilst this does not impact on the applicability of the findings from this study to our own single case study research or to others who might be using micro-analytic behavioural coding in single subject research, these findings do not have any implications for research adopting group designs. The findings presented here cannot be used by other research groups to provide a rationale for the specific window duration for sample selection of behavioural data. Participant numbers, the number of variable pairs coded, and the frequency of the measured behaviours will all have an impact on the power to detect the significant patterns within behavioural data. The value of this research report lies in the attention that it draws to the need for researchers to develop and test their methodology for window duration decisions for clinical and experimental research using behavioural coding.In the review of recent research in the field we were surprised to find how often no rationale on the sampling choices was provided in the study methodology. Our response to this has been to make explicit our own steps to producing robust micro-analytic methods for single-case studies. We think this study provides new knowledge which is relevant to those involved in the design or use of video footage in the applied contexts of pediatric family assessment and diagnosis. Given the constraints on resources in clinic and research, clinical scientists designing new applications using micro-analysis might be a) inclined towards thin-slice coding due resource considerations and b) draw the conclusion that thin slices of behavioural coding gives reliable indicator of a state or trait in single cases based on the group findings in experimental research. Given the potential use of clinical applications using video, such as in assessment and diagnoses and design of therapeutic interventions we urge caution in the application of thin-slice methodology and underline what Bornstein suggests, that every researcher should choose the acceptable limits of unreliability for their study. For our laboratory, making a choice based on previous research was not possible given the way in which we judged the applicability of the prior gold standard evidence on thin-slice coding to our research. Our aim in articulating our choice making process, including the results of our test is to model what Bornstein  advocate


Deterministic equations have been suggested to predict the accuracy of genomic breeding values in a given design which are based on training set size, reliability of phenotypes, and the number of independent chromosome segments ( In dairy cattle, prediction of genomic breeding values (GBV) has become a basis for selecting young bulls which are not yet progeny tested. Often, conventional estimated breeding values, daughter yield deviations or deregressed proofs are used as quasi-phenotypes when training genomic prediction models . The empFor determining e.g. the required size of the training set or SNP density to achieve a predefined level of accuracy, it would be desirable to be able to assess the expected uggested . The appuggested  and simuuggested . In thesDerivations of all these deterministic approaches imply that there are no relationship structures between the individuals. Wientjes et al. The number of independently segregating chromosome segments formulas  on how tdata set .By using empirical accuracies obtained via cross-validation in a genomic prediction with real or simulated data, it is possible to determine In our study, we suggest determining To establish and test the methodology, we used a sample of 5′698 Holstein bulls, which were genotyped with the Illumina BovineSNP50 BeadChip. Single nucleotide polymorphisms (SNPs) with a minor allele frequency lower than 1%, with missing or non-autosomal position or a call rate lower than 95% were excluded. After filtering, there were 42′551 SNPs remaining for further analyses. Missing genotypes at these SNP positions were imputed using Beagle 3.2 . To studAll bulls used for this study had estimated breeding values based on progeny testing for somatic cell score and milk yield with an accuracy >0.84, which were used as quasi-phenotypes for the following analyses.x-th marker where x was 1, 2, …, 8.To test the proposed approach in a further data set and with different SNP marker density, we used a set of 1′332 Brown Swiss bulls which was partly genotyped with the Illumina BovineSNP50 BeadChip and partly with the Illumina BovineHD BeadChip with around 777 K. For the Brown Swiss bulls genotyped with the Illumina BovineSNP50 BeadChip, genotypes have been imputed to the Illumina BovineHD BeadChip based on a reference set of 727 Brown Swiss cows and 153 bulls using a combination of family and population imputation implemented in the software FImpute . After qGenotype and phenotype data is available from the authors on request.Cross-validation was performed in different k-fold scenarios with k = 2, 3, …, 10, 15 or 20. This resulted in different sizes of training sets with different values of k. With a k-fold cross-validation, k-1 folds are used to predict the remaining fold and this procedure is repeated so that each fold is predicted once. Animals were assigned to the folds randomly. For the evaluation of the GBV prediction, the correlation as  e.g. , where  Genomic breeding values were predicted using genomic best linear unbiased prediction (GBLUP) based on the modelReml 3.0  and wereIn the following, we will describe available deterministic equations for prediction of the level of accuracy from the literature and modifications of these formulas we will conduct.Daetwyler et al. Goddard et al. b included to account for the finite number of markers. Note that if Goddard et al. Assuming a finite w) and the accuracy of genomic breeding values assuming all causal variants are known and considered so thatAccording to The factor w and avoiding any further definition of b. This leads to prediction equation G3 defined asEquations G1 and G2 of w and w and –D2, G1–G3, respectively) and A maximum likelihood approach was used to determine the value of w remain the only parameters in all considered equations to be adjusted. Searching for the maximal likelihood was done using the function “optimize” in R w in D2 and G3).Most of the parameters used in w (in D2) and then predicted the accuracies for a training set in the size of the training set used for the 20-fold cross-validation runs with the whole Holstein Friesian data set (i.e. 5′413 bulls). For this we chose 4′000 bulls randomly out of the whole sample and performed a variance component estimation and all k-fold cross-validation runs  for the different subsets. Afterwards, we maximized the likelihood as described above. Since there may be a sampling effect when using a random subset of 4′000 bulls, we repeated the whole procedure ten times so that we had predictions for ten different subsets of 4′000 bulls. The range of predicted values for a training set size of 5′413 bulls then was compared with the empirical accuracy from a 20-fold cross-validation with our whole data set, i.e. with a training set size of 5′413 bulls.In many applications the prediction accuracy obtained with the data, especially the training set size, at hand is not sufficient. In such cases it would be desirable to be able to determine accurately the required training set size to achieve a pre-defined level of accuracy of genomic prediction. We tried to mimic this exercise to compare the usefulness of a model accounting for the fact that the finite marker set does not account for the full genetic variation (model D2) with that of a model not doing so (model D1). We used subsets of 4′000 Holstein-Friesian bulls to derive the optimal number of The mean and standard errors of the empirical accuracies obtained from the different cross-validation schemes in the Holstein Friesian data are displayed in Drosophila melanogaster, can also be used to estimate the model parameters and in our case would lead to very similar results (results not shown).Our observed accuracies were far away from the bounds of correlation coefficients (−1 and 1) and apparently normally distributed: The results of the Shapiro Wilk test showed that for all k-fold results with 42′551 SNPs in the Holstein Friesian data set the null hypothesis “normally distributed” was not rejected in a single case with p<0.01. Therefore, no further transformation of the data was necessary. Other approaches, like the least squares principle used by In the following, we will first describe the results for the estimates of In w and w was in all cases between 0.87 and 0.91, suggesting that with the given marker set the accuracy of prediction will not approach 1 even if a very large training set is used. According to Dekkers (2007) the squared value of w represents the proportion of genetic variance associated with the markers which in our case would range between 75.5 per cent (milk yield with model G3) and 82.3 per cent (somatic cell score with model D2). This indicates that a large proportion, but not the complete genetic variation in our data set is captured by the SNP set at hand.Maximum likelihood estimates for w) the curves could accommodate a different slope of the empirical accuracy values more flexibly than with the one-parameter equations, which are bound to have their origin in w when reducing the number of SNPs but the extent of the decrease was limited, so that even with 10′000 SNPs a high percentage of the genetic variance  is captured and not much is gained by applying a more than four-fold SNP density. For the optimal number of Since we observed that only a specific fraction of the genetic variance was captured by the available SNP set we were interested in studying the effect of different SNP densities on the shape of the curve of expected accuracies and the respective parameters. Results of the maximum likelihood estimation using equations D2 and G3 with different marker set sizes in the Holstein Friesian data set are given in Based on our previous results, we next tried to describe the relationship between the estimates of w obtained and the underlying marker density.w, is a function of the natural logarithm of the SNP density. Using the Holstein Friesian data, we found that a functionWe hypothesize that the maximum accuracy that can be obtained, bly well . With anz depending on the marker density using our suggested maximum likelihood approach. We used D2 for the expected value with As we had cross-validation results based on different marker densities available, we were also interested in finding a global function for estimating w with different SNP sets can be seen in w kept constant in both traits  when decreasing the number of markers up to a point of around 19′000 SNP from where on it decreased considerably. This indicates that the percentage of genetic variance captured with a given SNP set did not increase further when using more than 19′000 SNPs in this data set. w as well as D2 for modeling the expected accuracy for both traits and the full SNP set of 627′306 SNPs. As already seen with the Holstein Friesian data, D2 with optimized values for the number of w fitted the shape of the curve of empirical values very well.To check the results in an independent data set, we applied the maximum likelihood approach based on D2 also on the Brown Swiss data set. Empirical values from the 2- to 20-fold cross-validation when using the full SNP set are shown in w and the marker density for the Brown Swiss data set (same approach like in the Holstein Friesian data set). The results are shown in 2 of 0.998 for milk yield, for example. However, with any further increase of the marker density , the weighting factor did not increase anymore but stayed on a constant level We also tested the relationship between the weighting factor Next we studied if our approach can be used to extrapolate the accuracy of prediction beyond the data set used to determine the model parameters. For this, the maximum likelihood approach was applied to ten data sets of 4′000 Holstein Friesian bulls which were the basis of cross-validation runs as described above. w ranged between 0.874 and 0.906 for the different data sets while the optimal number of In The aim of our study was to use empirical data to find a deterministic prediction equation for the accuracy of genomic breeding values that accounts for factors like sample size of the training set and marker density used that fits our data best. We used a maximum likelihood approach to validate different equations to predict the accuracy of GBV. We showed that the likelihood of our approach was best when the estimates of There are different possible reasons why the accuracy of genomic prediction with a specific SNP set may not reach one even if the number of training animals is infinite. First of all, only a fraction of the variance generated by QTL will be tagged by SNPs, i.e. the marker density is too low. Furthermore arrays like the Illumina BovineSNP50 BeadChip were designed such that the allele frequencies of the markers are more or less uniformly distributed  which lew can be interpreted as the maximum accuracy that can be achieved with the specific marker set in the population at hand assuming an infinite training set size. In our case, we found w to be in a range of ∼0.875 to 0.9 while the accuracies we could obtain with ∼5′700 bulls in our Holstein Friesian data set empirically were around 0.8. This means that most of the possibly achievable accuracy is already obtained when having ∼5′000 bulls in the training set. Genomic heritability (i.e. heritability in the GBLUP model) may be another good indicator of how much genetic variance is captured by the SNPs. Estimates of genomic heritability in our data sets (results not shown) were higher than the estimated squared w (representing the proportion of genetic variance captured by the SNPs), but behaved completely similar in trend  compared to w2.The weighting factor Having the estimates of w. He observed four data points within US Holstein data sets for different training set sizes. However, he did not use different k-fold cross validation but validated his theory by augmenting the training set with new animals, including cows, to achieve larger training set sizes. The maximum genetic variance that is captured by the SNP set depends also on the population studied. Adding cows thus may bias the results since a higher genetic variance is expected in the cow population compared to the highly selected group of progeny tested bulls.Daetwyler w in principle should be trait specific, but if conventional estimated breeding values  are used as quasi-phenotypes for genomic prediction differences between traits should not be large as long as estimated breeding values are sufficiently accurate and homogeneous. Daetwyler The maximum genetic variance found in his study was All numbers of w squared. With b will approach 1 very fast. For example, when b would be 0.982 and therefore the square root of b (i.e.w) would be >0.99, which is clearly higher than found in experiments with real data  of the form z is a trait-specific regression coefficient. Such a linear relationship has also been found by w which can represent the maximal achievable accuracy did not differ much between our runs with different number of SNPs in the Holstein data set. We could not study what will happen with further increasing the marker density in Holstein Friesian, since we did not have access to a sufficiently large set of individuals with high density marker genotypes.We found a clear linear relationship between the reciprocal of the logarithm of the marker density and the maximal achievable accuracy  in such formulas can be limited when they are derived with the suggested goodness-of-fit-approach.These results indicate that further parameters have to be found that can determine the proportion of genetic variance explained and the SNP density at which the plateau is reached. They also illustrate that calculating an expected value of w were derived with a subset of 4′000 bulls. The overestimation was not dramatic for this example, but 5′413 is not that much bigger than 4′000. However, if the difference between the number of individuals used for fitting the curve and the size of the reference set for which the accuracy is to be predicted increases, the upward bias will accumulate. Especially, as it is expected that number of animals in the training sets will increase in real studies up to ten thousands of training animals, it is critical that a prediction equation is able to fit the slope of the increasing accuracy correctly.We further showed that model D2 allowed a realistic extrapolation of prediction accuracies with increasing training set sizes, while model D1 systematically overestimated the accuracy for a training set of 5′413 Holstein Friesian bulls when the model parameters w can be chosen in a way that they describe the underlying population and trait as good as possible, but it is not the goal to obtain exact predictions of accuracies for specific animals in the prediction set. As shown by many studies (e.g. e. Further approaches still need to be developed for the “before data collection” case.Equations to predict the accuracy of genomic breeding values are often derived for the simple case of a random set of animals that are not related e.g.  or show ies e.g.  the relaWe suggest a comprehensive model for the average accuracy of genomic breeding values and demonstrate how the model parameters can be estimated using a systematic cross-validation based on empirical data. Integrating all results, we suggest the model.The suggested modification of the original equation of