Through the use of different indices of heavy metal contamination (geo-accumulation index (Igeo), improved Nemerow index (IIN) and potential ecological risk index (RI)), the degree of pollution caused by mining activities in two areas, Colquirrumi and Julcani, which have a high density of mining sites in operation, was determined. The values obtained from these indices indicated that the Colquirrumi region was the most contaminated, followed by Julcani. The area of La Zanja, despite being free of mining operations, presented slight diffuse pollution. Several positive correlations were obtained, with a high level of significance, between pH, organic carbon content, cation exchange capacity, and the Cr, Pb and Ni concentrations of the soils. The spatial distribution of the heavy metals was realized by means of the interpolation method of ordinary kriging. The results obtained and the experience gained in this work were necessary to facilitate the identification of soil contamination processes in high altitude areas of the Andes Western Cordillera (Peru) as a basis for taking appropriate measures when restoring soils, during mine closure processes, and to protect the quality of soil resources.Concentrations of seven heavy metals  and one metalloid (As) as well as various parameters  were analyzed in 77 soil samples collected in the mining areas of La Zanja and Colquirrumi (Department of Cajamarca) and Julcani (Department of Huancavelica). Our study proposed geochemical baseline values for heavy metals in a natural region (La Zanja) from samples collected during the period of the environmental impact study (2006), that is, from an earlier period which occurred at the beginning of the exploitation of the current gold mine. The baseline values obtained were as follows: 8.26 mg·kg Heavy metals in soils have been identified as essential components of the environment and the food chain and as important factors inhuman health ,3,4,5,6.Background level is a measure that is used to differentiate between the concentration of the natural compound and the concentrations with an anthropogenic influence in a given environmental sample ,8. The cThe calculation of environmental geochemical baselines is necessary to assess the current state of the environment and to provide guidelines and quality standards in environmental legislation and policy-making, especially in the evaluation of contaminated soils and in environmental risk assessment . NumerouThe analysis of the environmental impacts of a mining activity is made through the difference between the situation of the environment before the activity was conducted, and after the development and cessation of mining activity. The investigation of the baseline of a territory represents a measure of the geochemical variations of its surface formations (rocks and soils) and is considered of great interest, not only from a scientific and mining point of view, but also constitutes a very important tool for environmental planning, environmental health, and sustainable development policies worldwide . If an egeo), the potential ecological risk index (RI), the improved Nemerow index (IIN), etc., of the surface horizons of soils.The first step in a baseline study is to define the thresholds of toxicity for the different pollutants, where the normal values of potentially polluting substances present in natural soils without human influence (known as the background level) are calculated, which corresponds to the normal value of an element in a given environment ,23. The In this study, a geostatistical approach was adopted to calculate the spatial distribution of the geochemical anomalies of this region of the Peruvian Andes, specifically, the spatial distribution of the concentrations of seven heavy metals and one metalloid  in soils using the Inverse Distance Weighting (IDW) and ordinary Kriging interpolation methods . The spaStudies of soil contamination by heavy metals need to focus on identifying areas with a high risk of contamination. Samples from these types of areas usually have atypical spatial values at the local level . The fungeo, IIN, and RI) in the superficial horizons of soils; (3) to obtain geochemical maps revealing the degree of contamination of soils by heavy metals; and (4) to evaluate the correlations between heavy metal concentrations and soil properties . This environmental research study aimed to understand the influence of mining activity on the environmental contamination of high altitude areas within the provinces of Cajamarca (3200–3900 m) and Huancavelica (4100–4400 m) in the Western Cordillera de Los Andes (Peru). The results of this study will contribute to the creation of an environmental database of the soils and waters of the Cajamarca and Huancavelica regions (Peru), which will provide the authorities with monitoring data on the pollution caused by mining activities and will assist in the development of appropriate management strategies to control the contamination of heavy metals in soils and waters.The main objective of this study was: (1) to analyze the concentrations of eight heavy metals  to calculate the background level in three mining areas of the provinces of Cajamarca and Huancavelica  and calculate the geochemical baseline in La Zanja; (2) for purposes of comparison, to calculate several indices of heavy metal contamination , 88 km north of the city of Cajamarca and south-west of the district of Bambamarca. The La Zanja Project is in the village of La Zanja , in the district of Pulán, Province of Santa Cruz de Succhabamba, Department of Cajamarca. The Department of Huancavelica is in the south-central zone of the Western Cordillera of the Andes. It has borders in the North with the Department of Junín, in the East with Ayacucho, the South with the Departments of Ica and Ayacucho, and in the West with Ica and Lima. The mining site of Julcani is in Angaraes Province (Huancavelica), District of Cochaccasa.The Departments of Cajamarca and Huancavelica are located at high altitudes above sea level (between 3200–4400 m), with very rainy climates (between 800–1300 mm) and cold temperatures (average temperature of the year between 5–13 °C), with an evapotranspiration between 900–1140 mm. The climate is sub-humid, with seasonal rains and frequent periods of drought. Seasons of intense rain occur between the months of November and April. In the upper parts of the mountain range, temperatures drop below 0 °C.From a geological perspective, the mining area of Colquirrumi-Sinchao is constituted by folded sedimentary rocks from the Cretaceous period that have been improved by stocks, dykes and sills composed of diorite and granodiorite of the Miocene Half-Superior. All these bodies are located within a NW-SE regional course that includes the well-known mineral deposits of Colquirrumi, Hualgayoc, San Agustín, Shinchao, Constancia, Cerro San José, Cerro Corona, Minas Congas, Galeno, Michiquillay-Lambayeque, Mansita, San Agustín, Tres Cruces, etc.The mineral deposits of the Hualgáyoc district are of different types: veins, mantles, bodies and porphyries with disseminated mineralization, and in stockwork which contain complex ores of Ag-Zn-Pb (Colquirrumi) and Cu-Ag-Au-Zn (Sinchao) from meso to epithermal. The Colquirrumi-Sinchao deposit is a replacement in the form of limestone and sandstones, which are covered with volcanic materials. Towards the NE appears a stock of medium-fine grain diorite and quartz-diorite porphyries. The igneous activity continues with the location of dacite domes and volcanic rhyolites and/or dacites that partially cover the other units. The final phase consists of rhyolitic dikes that cut epithermal mineralization. The ore is composed of chalcopyrite, tetrahedrite, galena, sphalerite and as gangue pyrite, quartz, chalcedony, and iron oxides ,35. In HIn the deposit of the Zanja are rocks of volcanoclastic origin, consisting of a sequence of tuffs, tuffs and lavas, of andesitic, dacitic, and rhyolitic nature, belonging to the Llama, Porculla and Volcanic Huambo formations . The geoThe studied area of Julcani was geologically formed by a series of sedimentary rocks of Paleozoic-Mesozoic age including: (1) phyllites and sandstones of lower Devonian age (Excelsior Group), where these rocks are strongly deformed in syncline folds and anticline orientations NW; (2) a sequence of conglomerates, sandstones and shales, known as red layers (Mitu Group) that overlie, in erosive discordance, the metamorphosed and folded rocks of the Excelsior Group from the Permian period; (3) limestones and sandstones (Pucará Group) that usually contain abundant chert from the Triassic-Jurassic age; and (4) a volcanic sequence that occurred in the surroundings of Julcani comprised of dacites to rhyolites in a grouping of volcanic centers orientation WNW-ESE (Julcani Formation), and these volcanic materials have been dated to 10.4 Ma (upper Miocene).In Julcani, deposits of economic value have been identified  in mineralization located and genetically related to the Julcani volcanic center, which comprises a grouping of volcanic dacitic centers to the WNW-ESE, composed of pyroclastic rocks, lavas, endogenous domes and dikes. It is a filonian type deposit of fracture fillings with metallic content of Ag, Pb, Cu in the form of a system of irregular veins with bonanza bodies and gaps placed in pyroclastic rocks of the Julcani Formation. Most deposits in this mining district are within a volcanic sequence (Miocene), among them we have the following mines: Herminia, Mimosa, Sacramento, Estela, Temtadora, Nuestra Señora del Carmen, Rita, Achillia, etc. Another mineralized zone is of phyllites (Lower Devonian), where the mines are the Pucará, Bernabé and Contaglapampa .The morphological inventory and the sampling of the soils has been realized by considering all units of soils that have been developed based on different types of rocks that exist in this territory. Thus, the selection of sampling points of the soil profiles has been based on lithological criterion, since in natural soils, the heavy metals present are inherited directly from the parent rock. In addition, the content of heavy metals  produced by primary dispersion caused by the mineralization of the parent rock (background level) has been characterized, independently of that produced for mining activity, for this purpose, all horizons (A- and B- and subsurface-C or R-) of the soils were sampled. The sampling strategy focused specifically on the surface horizons (A and B) and deep or bedrock (C or R); the latter being unlikely to be contaminated by atmospheric deposition.Four sub-samples of replicate soils were randomly collected at each sampling point within a 1.5 m × 1.5 m grid and mixed to obtain a composite sample of about 750 g in weight. In this study, a total of 77 soil samples were collected (77 × 4 subsamples = 308). Samples were air-dried and sieved through a 2 mm mesh. The determination of the physical and chemical properties was carried out as per traditional methods of soil analysis: organic matter by oxidation with potassium dichromate, granulometric analysis using the Robinson pipette method, pH (water 1:1) and capacity cation exchange (CEC) using the ammonium acetate method. The total contents of heavy metals in soil were analyzed as per the procedure recommended by the European Union International Organization for Standardization (ISO) standard 11466. Extraction was performed with a mixture of nitric acid and hydrochloric acid in a microwave oven, with determination by inductively coupled plasma mass spectrometry (ICP-MS) . The analysis was carried out by the Chemical Analysis Service of the University of Salamanca through the digestion of samples in a microwave oven , using the standard USEPA method 3052. To calibrate the equipment, standard solutions (panreac) of 1000 mg/L of all metals were used, which were calibrated from 10–100 ppb.SPSS software v.23.0  was used for statistical analysis. The results have allowed us to obtain different values of interest: arithmetic mean, geometric mean, median, range, standard deviation, coefficient of the variable, kurtosis, correlation analysis between heavy metals and soil properties. In addition, various pollution indices have been calculated in order to determine the levels of contamination of heavy metals in soils. The geographic information system (GIS) analysis  with extensions Spatial analysis tools and geostatistical analyst has calculated the degree of spatial variability of each heavy metal using ordinary kriging . KrigingiS) = the measured value at the location i; iλ = an unknown weight for the measured value at location i; S0 = the location of the prediction; and N = the number of measured values.In this work, the applied kriging method was the ordinary one which assumes that the distance or direction between the sample points reflects a spatial correlation that can be used to explain the surface variation.The predominant soils in these sectors located at high altitudes of the Andes Mountains are of little development, being located in steep areas with strong slopes . Most soThe Andes mountain range is subject to intense erosive processes that increase sediment and soil trawling to the bottoms of valleys or depressions. It is in these zones where erosion processes dominate over edaphic processes, where soils have small development (Dystric Regosols and Gleyic Cambisols) and are developed on sloping landslides. These soils differ from the previous ones in that the superficial horizon has a low or moderate content of organic matter (4.65%) and, therefore, a brown color. Cambisols are characterized by having a subsurface horizon (Bw), of alteration (horizon of diagnostic cambium), and are brownish-gray or yellowish-brown color.In the studied area, rocky outcrops that are associated to soils with little thickness with the denomination of Umbric Leptosols are also frequent, and limestone rocks have been observed with Rendzic Leptosols and Calcic Kastonozems. In some areas, there are small depressions where water accumulates , and the reducing environment favors the accumulation of organic matter, giving rise to Fibric Hemic and Sapric Histosols (Pebbles). In the “valley bottoms” originating from rivers, streams and streams that run through the studied area, recent alluvial sediments have been deposited, consisting of gravel and sand with a thickness to the order of two meters. The soils that have developed in the current channel of streams and rivers are classified as Dystric Fluvisols.A classification of these soils has been made by considering their morphology and analytical data, by the taxonomy of the World Reference Base (WRB). The statistical data of the main studied properties of the soils of the Zanja, Colquirrumi, and Julcani are presented in In this study, our aim was to understand the natural contents of the soils  to detect the intensity of the contamination of the soils and to compare the results with norms or regulations of other countries worldwide ,39.In the statistical analysis of this study, the data of the most superficial horizons (A and B) and underlying (C) horizons were treated separately. The more superficial horizons or solum were those that provided information on the levels of pollution caused by the processes of soil formation and by anthropogenic sources, whereas the underlying horizon (bedrock) exclusively represents the lithogenic contributions, since there is little probability of contamination through atmospheric deposition . It is fThe average values of the heavy metals obtained from the statistical analysis of the soils of La Zanja can be seen in Background levels of the Ni, Cu, Hg, As, and Pb metals were above the world average. The Zn content was equivalent to the world average, and the concentration of Cr was lower than the world average. The highlight of the mining area of La Zanja was the high content of Cd soils, since it had a value higher than the world's top ranking sample.−1, compared to the world average of 15 mg·kg−1 and a global range between 2 and 200 mg·kg−1 [−1 [−1) when compared to the world average. Furthermore, in numerous soil samples, Cu content exceeded the values of the world average (12 mg·kg−1), and in some soils Cu values reached between 100 and 500 mg·kg−1. As for Zn, the background level (165.6 mg·kg−1) obtained in this study exceeded the world average values of 40 mg·kg−1. In some soil samples, values higher than 3000 mg·kg−1 were reached. Of the soil samples collected in Colquirrumi, only three did not exceed the world average (20 mg·kg−1) regarding As content, where the background level (218.1 mg·kg−1) was up to 11 times higher than most other countries in the world, although the range reached as high 250 mg·kg−1. Large As abnormalities have been observed in some soil samples, with values to the order of 1000 mg·kg−1. Finally, it was noted that the values of the background levels of Cd and Hg were high, to the order of 15 and 70 times above the world averages. To summarize, from the study of heavy metals in soils in the mining area of Colquirrumi, we must highlight the geochemical anomalies in Pb, As, Cd, Hg, Cu, and Zn.As for the values obtained from the Colquirrumi soils, it is worth noting the abnormally high values across all samples for Pb content, where the background level was 1539 mg·kg mg·kg−1 , althougkg−1 [−1 . Obtaini−1). However, the concentrations of Zn and As were slightly higher than those obtained in other countries. The background levels of Pb, Cd, and Hg obtained from Julcani were 13, 14, and 34 times higher, respectively, than the levels obtained in soils from other parts of the world.In relation to the values obtained in the soils of Julcani, it is necessary to point out the following: Cr, Ni, and Cu metals presented background and reference levels considered inferior to those described in the literature regarding other parts of the world. None of our soil samples exceeded the world average values, in terms of the Cr content. For Ni content, only two soil samples exceeded the values of the world average fund level  and the improved Nemerow index (IIN).Using the pollution factor and Nemerow Index to determine pollution levels in the La Zanja area showed that most soil samples (70%) were contaminated, 20% were moderately contaminated, and 10% were strongly contaminated, mainly by Cr, As, and Pb. These data does not represent the reality observed on the land itself of the environmental conservation status of the territory, since La Zanja was a natural area without any type of mining when the samples were collected in 2006. Therefore, the soil samples obtained in this area were expected to appear low or very low on the contamination indices. These results question the validity of these indices to calculate the degree of soil contamination. In agricultural soils and in less industrialized areas of the Northern Plateau of Spain , the usegeo is calculated from equation (Equation (2)) [i is the measured concentration of the i metal examined in the soil, and Bi is the background level of the i metal. The factor 1.5 was used to correct possible variations in the background values of a particular metal in the environment. The Igeo for the eight heavy metals studied are summarized in geo of the analyzed heavy metals allowed the analysis of the single factor contamination index to evaluate the presence of each individual metal and its level of contamination in the study area.The Iion (2)) :Igeo = lIN shows the degree of general pollution caused by the simultaneous presence of the nine heavy metals. In La Zanja, considering the Igeo, most soils were included in Class 0 (Igeo ≤ 0) and Class 1 (0 < Igeo ≤ 1), that is, uncontaminated to slightly contaminated, with 67.7% and 17.8% of the samples, respectively, and only some soils in Class 2 (1 < Igeo ≤ 2), which were moderately contaminated by Cr, As, and Pb in 5.45% of the samples. Soils were not included in Classes 3, 4, 5, and 6 (from moderately contaminated to extremely contaminated). In Colquirrumi, samples of the soils studied were included in all classes ranging from uncontaminated to extremely contaminated soils: Class 0 (48.1% of the samples), Class 1 (16.3%), Class 2 (20.9%), Class 3 (5.4%), Class 4 (9.3%), Class 5 (0%), and Class 6 (16.3%). In Julcani, the soils, were classified as Class 0 (54.2%), Class 1 , Class 3 (5.6%), and Class 4 (1.4%), which ranged from uncontaminated to heavily contaminated.However, the Igeo, the levels of contamination (from low to high) of the heavy metals in the superficial horizons of the soils was as follows: La Zanja < Julcani < Colquirrumi.By considering the IIN was calculated by Equation (3):geomax is the maximum Igeo value of all metals in a sample, and Igeoave is the arithmetic mean of the Igeo. In La Zanja, when considering the IIN, the soils ranged from non-contaminated to moderately contaminated: 20% of samples were in Class 0 (IIN < 0.5), 50% in Class 1 (0.5 ≤ IIN < 1), and 30% of soils in Class 2 (1 ≤ IIN < 2). However, it should be pointed out that the small degree of contamination indicated by this index may be due to anthropogenic processes , which led to an increase in geological concentrations in the soils of La Zanja. The main external sources of heavy metals in the soils of this area are through diffuse pollution, and wet and dry deposition caused by metallic mining and the processing of minerals from bordering areas that has led to the accumulation over the long-term use of heavy metals. In Colquirrumi, all soil samples were classified as moderately contaminated Class 2 (33.3% of soil samples) to the highly contaminated Class 3  based on the IIN. The soils of the Julcani area were considered as non-contaminated to highly contaminated: Class 0 (22.2% of the samples), Class 1 (22.2%), Class 2 (22.2%), and Class 3 (33.3%). By using the IIN, heavy metal contamination levels (from low to high) from soil surface horizons are as follows: La Zanja < Julcani < Colquirrumi.The Iri) evaluates the toxicity of trace elements in sediments and has been extensively applied to soils [The ecological risk index :Tr is the toxicity coefficient of each metal whose standard values are Hg = 40, Cd = 30, As = 10, Co = 5, Cu = 5, Ni = 5, Pb = 5, Cr = 2, and Zn = 1 [fi is the contamination factor (Cfi = Ci/Bi), where iC is the measured concentration of the pollutant, and iB is the level of geological background.To calculate the Ed Zn = 1 ,49; and To calculate the potential response rate to the toxicity of all the studied heavy metals (RI), we use Equation (5):The potential ecological risk index (RI) index reflects the general situation of pollution caused by the simultaneous presence of the eight heavy metals .Considering the individual ecological risk index (Er), the levels of heavy metal contamination of the surface horizons of La Zanja soils were considered to be of low contamination risk (Er < 40), with only one soil sample (14.3%) with a considerable risk of contamination (80 ≤ Er < 160) per Hg.In Colquirrumi, a majority of the samples (87%) were considered to have a low risk of contamination (Er < 40); a small percentage of samples (4.2%) were considered to have a moderate contamination risk (40 ≤ Er < 80) from Cr, Ni, As, and Hg; 8.2% of the samples presented a considerable risk of contamination (80 ≤ Er < 160) for Cd and Hg; and only 0.6% of the soil samples had a very high risk of contamination (160 ≤ Er < 320) per Hg.In Julcani, it was also seen that the majority of the samples (86.1%) were considered to be at low risk of contamination (Er < 40); a small percentage (6.9%) of samples were considered to have a moderate contamination risk (40 ≤ Er < 80) from metals As, Cd, Hg, and Pb; 2.8% of samples presented a considerable risk of contamination (80 ≤ Er < 160) for Hg; and 4.2% of soil samples had a high risk of contamination (160 ≤ Er < 320) from As and Hg.If we consider the individual ecological risk (Er) index, the levels of contamination (from lowest to highest) by heavy metals from the surface horizons of soils were as follows: La Zanja < Julcani < Colquirrumi.When considering the RI of all the metals studied, the contamination levels were as follows: in La Zanja, all soil samples (100%), present low ecological risk of potential contamination (RI < 150). In Colquirrumi, 38.1% of the samples had a low ecological risk of potential contamination (RI < 150); 57.1% presented a moderate ecological risk potential (150 ≤ RI < 300); and 4.8% faced a significant potential ecological risk (300 ≤ RI < 600). In Julcani, 44.4% of soil samples presented a low ecological risk of potential contamination (RI < 150); 44.4% had a moderate ecological risk of potential contamination (150 ≤ IR < 300); and soils with a considerable risk of contamination (300 ≤ RI <600) were in the minority (11.1%).Furthermore, when considering the potential ecological risk index (RI), the levels of contamination (from low to high) from heavy metals from the superficial horizons of soils were as follows: La Zanja < Julcani < Colquirrumi.The use of the geostatistical method of ordinary kriging spatial interpolation allowed us to predict the spatial distribution of the concentrations of each metal in the areas not sampled , based oIn the area of La Zanja, the distributions of the heavy metals Ni, Cd, and Pb were similar as they had the highest concentrations in the NW and W of the studied area, in the superficial horizons of Profiles 13 and 17–19, which developed on rock alterations  and on a porphyritic rhyolitic dome. These anomalies were located in two current areas of exploitation in Au and Ag mines (in the San Pedro Sur and Pampa Verde fields). The highest concentration of Cu was in the SW quadrant of the zone in Sample 14. The Cr content was abnormally high in the NE quadrant of the zone . The highest concentration of Zn occurred as a concentric circle in the SW quadrant of the studied area in Sample 14, and As dominated in the W-limit of the zone (Soil 12). With regard to Hg content, a geochemical anomaly existed where Profile 18 was sampled.In the Colquirrumi zone, the Zn and Cd heavy metal distributions were quite similar since they presented the highest concentrations in the NE and N corners of the studied area, in the surface horizons of the Profiles 6  in the case of Zn, and in Profile 9 (developed on limestones and marls of the Pariatambo Formation) in the case of Cd. Furthermore, the distributions of heavy metals As and Hg  in soils developed on marls, shales and limestones of the Chulec Formation. The highest Pb content was in the NW quadrant in Sample 5 (soil developed on monzonites and granodiorites). The Cu value identified a geochemical anomaly in the form of two concentric circles located in the N (Soil 6) and SE (Soil 8). Ni was present in the SW quadrant (Soils 4 and 7), and finally, the highest concentration of Cr was in the NW quadrant (Soil 4) and in the eastern half of the area (Soils 8 and 9).In the Julcani zone, the distributions of the heavy metals Ni, Cd, Hg, and Pb were similar and showed a decrease in the form of concentric circles, from the center of the zone towards the periphery . The contents of Cu, Zn, and As were abnormally high in the SE part of the studied region , which meant that there may have been several contaminations from point sources. The Cr value indicated a higher distribution in the form of two concentric circles located in the SE and E of the investigated area .IN and RI) were depicted that reflected the overall pollution situation caused by the simultaneous presence of the eight heavy metals in the three areas studied , soil contamination rates (I studied .Soils studied in the Andes Mountains (Peru) were characterized by geochemical baselines with high concentrations of potentially toxic heavy metals. The average concentrations of some elements were much higher than the values obtained from other parts of the world, particularly for Pb, Cu, Zn, As, Cd, and Hg.geo, IIN, and RI) have been used as tools to diagnose pollution. Data revealed that the soils were uncontaminated, or slightly contaminated at La Zanja ; significantly contaminated at Colquirrumi ; and moderately contaminated in Julcani .Several pollution indices . Therefore, there was a great difference in calculating the percentage and the degree of contamination in soils, through the use of different contamination indices. Thus, it is our belief that the INM was much more accurate in assessing the environmental risks of heavy metal contamination.If we conducted an environmental risk assessment using the Nemerow index, the soils of La Zanja (virgin zone without the presence of mining operations) have values ranging between contaminated and heavily contaminated soils; however, using the improved Nemerow index IThe distribution patterns of heavy metal concentrations were mainly influenced by the lithology and geochemistry of the parent rock and by the existence of metallogenic belts in the studied area.It is our goal to see that the results of this study contribute to the creation or be added to an environmental database of soils in this mining region of the Peruvian Andes, and to facilitate the development of management strategies and remediation of soils contaminated by heavy metals.


In this paper, aluminum alloy samples were fabricated by selective laser melting (SLM) and subsequently T2 heat treatment was undertaken. In order to obtain comprehensive results, various experiments on densification, hardness, tensile strength, bending strength and microstructure characterization were carried out. The results show that densification of samples after T2 heat treatment does not vary very much from the SLMed ones, while the Brinell hardness and strength decreases to about 50%. Moreover, the plasticity and fracture deflection increases about 3 fold. The effects on the microstructure and the mechanical properties of the SLMed aluminum alloy samples and subsequent T2 heat treatment were studied. Selective laser melting (SLM) is a new type of rapid prototyping technology that appeared in the 1990s. In the SLM process, a high-energy laser beam selectively melts metal powder completely and then the melted area metal rapidly cools and solidifies to form metal parts with high densification and precision. There are quite a few advantages of the SLM process, such as design freedom, time reduction, cost saving and structure strength etc.2O3-TiN composites via a novel ball milling + addictive sintering process with the electrical percolation threshold value decreasing from 29% to 15% [In recent years, many experiments have been conducted on the preparation of titanium alloy, cobalt chromium alloy and iron-based alloy by SLM. Chlebus et al. studied the fabrication of Ti-Al-Nb alloy by SLM and suggested that by improving the process parameters, the titanium alloy parts exhibit better performance than traditionally processed components . Kempen % to 15% .Compared with titanium alloy, cobalt chromium alloy and iron-based alloy, studies on SLM aluminum alloy are relatively late. Prior to 2011, there were very limited reports regarding SLM aluminum alloy. With the continuous development of SLM equipment, some research institutes have gradually carried out studies on SLM alloy ,7,8,9,10Based on the process characteristic of rapid heating and cooling, there is large inner stress in the SLM samples. As the inner stress increases, the samples will deform and even crack, resulting in the dramatic degeneration of the material performance which conforms to research by Hitzler . Hitzler2 cubes and the rotation of 67° between the adjacent layers. The directly formed samples without any heat treatment were marked as SLMed samples as built. X- and Y-axis orientated parallel and normal to the building direction of the SLM. In the cross-section of the samples, the powder was set as the X-Y plane exposure to the laser source.Gas-atomized AlSi10Mg powder with the particle distribution range of 20~60 μm was used as the raw material for the SLM process. All the samples were produced on the Renishaw  AM250 machine, equipped with a 400 W fiber laser beam. Samples were fabricated using laser power of 400 W, scanning speed of 1000 mm/s, hatching space of 175 μm and a layer thickness of 25μm. Layers were scanned by chessboard strategy with the 5 × 5 mmThe main purpose of T2 treatments to eliminate internal stress, stabilize dimension size and improve the plasticity of the samples. The specific parameters of T2 heat treatment for the SLMed AlSi10Mg samples are: heating up to 380 °C, holding for 45 min and then air cooling.After the T2 heat treatment, mechanical tests of the samples parallel and normal to the building direction of the SLM were done. For a convenient comparison, the testing conditions of T2 heat-treated samples are the same as those made by SLM. The density was tested according to Archimedes principle of drain age. The hardness test was performed according to the standard EN IOS 6506-1. The tensile test was examined based on the national standard GB/T 228-2002. The bending test was evaluated according to national standard YB/T 5349-2014.3 and 85% distilled water (volume fraction) and investigated using a Zeiss Axiovert 200 optical microscope  a Nova NanoSEM 450 scanning microscope.To study the microstructure, the samples were sectioned, ground and polished using the standard metallographic procedures. Afterwards, the samples were etched using a solution containing 10% HF, 5% HNOThe densifications of the SLMed samples and T2 heat-treated samples are shown in The Brinell hardness results of the samples treated by T2 heat treatment are shown in The tensile results of samples treated by T2 heat treatment are shown in Perpendicular to the building direction of the SLM, tensile strength is 171.7 MPa, which is similar to that of the samples parallel to the building direction of the SLM. The elongation is 16.5%, which is nearly 2 times of that of the samples parallel to the building direction of the SLM. Compared with the SLMed samples, the strength decreases about 50%, and the plasticity increases about 2.5 times.After T2 heat treatment, the strength of the samples clearly decreased, and the plasticity is clearly improved. During the SLM process, the melt rapidly forms and solidifies, and large internal stress accumulates in the samples. T2 heat treatment largely eliminates the residual internal stress, resulting in a decrease in the strength and increase in the plasticity of the samples. After T2 heat treatment, the difference of the strength and plasticity of the samples parallel and perpendicular to the building direction of the SLM decreases, and the degree of anisotropy becomes smaller.After T2 heat treatment, the tensile fracture surface of the sample shown in As shown in The bending results of the SLMed samples parallel to the building direction of the SLM indicates that the average bending strength is 600 MPa, the prescribed non-proportional bending strength is 345 MPa, and the fracture deflection is 6.5 mm. Perpendicular to the building direction of the SLM, the average bending strength is about 660 MPa, the prescribed non-proportional bending strength is about 365 MPa, and the fracture deflection is 10 mm.The bending results of T2 heat-treated samples after T2 heat treatment are shown in Perpendicular to the building direction of the SLM, the average bending strength is 366.7 MPa, the prescribed non-proportional bending strength is 178 MPa, and the fracture deflection is 37.6 mm. Compared with the SLMed samples, the strength decreases about 44%, and the fracture deflection increases about 2.7 times.The results show that the texture of the samples after T2 heat treatment is obviously weakened. The samples restore and recrystallize, which leads to the decrease in strength and increase in plasticity. The difference of strength and plasticity between the different directions decreases. The above results are consistent with the tensile results.The bending fracture of the samples after T2 heat treatment is shown in The optical microstructure of the samples perpendicular to the building direction of the SLM after T2 heat treatment is shown in The SEM images of the samples perpendicular to the building direction of the SLM after T2 heat treatment are shown in The optical microstructure of the samples parallel to the building direction of the SLM after T2 heat treatment is shown in The SEM images and elemental analysis of the samples parallel to the building direction of the SLM after T2 heat treatment are shown in The results show that during the T2 heat treatment, the solid solution of Si in the matrix has enough time to diffuse, precipitate, absorb on the original Si crystal nucleus building a new crystal nucleus and grow into a new particle. The amount of Si particles increases and the volume decreases in the samples after T2 heat treatment. T2 heat treatment is a stress relief annealing, which promotes the homogenization and eliminates the internal stress of the samples. After T2 heat treatment, the boundary of molten pool disappears and becomes vague. The precipitates at the molten pool boundary dissolves in the matrix, and the microstructure of the samples is homogenized. In the process of the SLM, supersaturated solid solution is formed due to non-equilibrium solidification, and the solubility of Si in Al matrix can reach as high as 10%. This results in a large amount of supersaturated Si elements precipitates and forms a large amount of dispersed Si phase during the T2 heat treatment. Si is uniformly distributed in the matrix, and there is no obvious trend of distribution along the grain boundary, which is beneficial to the plasticity rise of the samples. However, the yield strength and tensile strength of the samples are greatly reduced when the grain boundary pinning effect is lost.(1)Compared with the SLMed samples, the densification is not very different. T2 heat treatment has no obvious influence on the densification of the SLMed samples.(2)After T2 heat treatment, the Brinell hardness, tensile strength, and bending strength of the SLMed samples decrease about 50%. The plasticity and fracture deflection clearly increases, and the anisotropy decreases.(3)The T2 heat treatment promotes the homogenization of elements, and the precipitates in the molten pool boundary dissolves in the matrix. The samples undergo recrystallization, Si particle size grows and tends to form spherical. The internal stress of the samples is effectively released.The effects of T2 heat treatment on the densification, hardness, tensile properties, bending properties, and microstructure of SLMed aluminum alloy samples have been studied. The main conclusions are as follows:


CD1 genes encode cell surface molecules that present lipid antigens to various kinds of T lymphocytes of the immune system. The structures of CD1 genes and molecules are like the major histocompatibility complex (MHC) class I system, the loading of antigen and the tissue distribution for CD1 molecules are like those in the class II system, and phylogenetic analyses place CD1 between class I and class II sequences, altogether leading to the notion that CD1 is a third ancient system of antigen presentation molecules. However, thus far, CD1 genes have only been described in mammals, birds and reptiles, leaving major questions as to their origin and evolution. In this review, we recount a little history of the field so far and then consider what has been learned about the structure and functional attributes of CD1 genes and molecules in marsupials, birds and reptiles. We describe the central conundrum of CD1 evolution, the genomic location of CD1 genes in the MHC and/or MHC paralogous regions in different animals, considering the three models of evolutionary history that have been proposed. We describe the natural killer (NK) receptors NKR-P1 and ligands, also found in different genomic locations for different animals. We discuss the consequence of these three models, one of which includes the repudiation of a guiding principle for the last 20 years, that two rounds of genome-wide duplication at the base of the vertebrates provided the extra MHC genes necessary for the emergence of adaptive immune system of jawed vertebrates. Caesar Milstein, who along with Georges Koehler had discovered and developed monoclonal antibody (mAb) technology, was asked to choose the first antigen for the newly established cluster of differentiation antigen (CD) nomenclature, and he chose CD1 to be the cell surface molecule recognised by the mAb NA1/34 raised against human thymocytes  with the help of mAb from Karsten Skjødt and Jan Salomonsen in the lab of Morten Simonsen  became available , two expressed sequences from the Chinese alligator  and one expressed sequence and another intact sequence not found to be expressed from the Siamese crocodile . Similarly, CD1 sequences have been identified in three marsupials, a single gene each in the bandicoot  and the Tasmanian devil , but a single pseudogene in the American opossum   genes in humans and chickens  together and the three reptile isotypes together . However, analysis of the extracellular domains placed chickens separate from reptiles for the α1 domain, but within the reptile cluster for the α2 and α3 domains  but not for CD1A and CD1E. The same is true for the expressed marsupial sequences, IsmaCD1 and SahaCD1 which end with putative tyrosine-based motifs , with the ModoCD1 pseudogene sequence terminated before the transmembrane region. The two crocodilian CD1.1 sequences also have short tails with putative tyrosine-based motifs (both YQDI), but the two CD1.2 sequences are different, with two leucines at the C-terminus of a short cytoplasmic tail (a putative di-leucine motif) in AlsiCD1.2, but a potential tyrosine-based motif (YTRP) in the middle of a longer tail in CrisiCD1.2 . The lizard CD1 also has a longer tail, with a potential tyrosine-based motif (YEDV) in the middle. The chicken molecules also differ, with a short tail ending in leucine-isoleucine (a putative di-leucine motif) for CD1.2, but a potential tyrosine-based motif (YGGC) in the middle of a much longer tail in CD1.1  showed that RNA was very well expressed in spleen for chicken CD1.1 and CD1.2 , SahaCD1 (and CrsiCD1.1 and CD1.2 by quantitative RT-PCR), as well as lymph node for SahaCD1, thymus for IsmaCD1, and bursa for chicken CD1.1 and 1.2. Weaker expression was found for SahaCD1 in the lung and uterus, and much weaker for IsmaCD1 in the spleen. Good expression was found for both chicken isotypes in the bone marrow, thymus, lung and the ileum from intestine (and liver for chicken CD1.2), as well as in splenic B cells and CD8 (but not CD4) T cells. Weaker expression of CrsiCD1.1 and CD1.2 was found by quantitative RT-PCR for lung, kidney and small intestine. Expression at the protein level has only been determined for chicken CD1.1 molecules. The mAb CB3  an MHC paralogous region on chromosome 1 , with the CD1 genes in other mammals in comparable (syntenic) regions. In addition to the human MHC on chromosome 6, there are (at least) three other MHC paralogous regions that have many genes  similar to those in the MHC, located on chromosomes 1, 9 and 19. The existence of these four paralogous regions was taken by Masanori Kasahara  the lack of CD1 genes in most or all fish. In fact, no CD1 sequence has been found in any amphibian or fish by a variety of analyses. Among the most sensitive has been a search based on a hidden Markov model (HMM) that found all of the known class I genes  and predicted many other class I genes that have been verified but failed to find any identifiable CD1 genes in the genomes of the lizard green anole, the frog Xenopus, and eventually in reptiles  the two rounds of genome-wide duplication at the base of the vertebrates. This prediction is consistent with the fact that no classical MHC genes, T cell receptor (TcR) genes, antibody genes or recombination activating genes (RAGs) have been discovered in jawless fish  landed near an existing paralogous region during the fragmentation and rearrangement of chromosomes in the lineage leading to mammals, and therefore are not really a part of the MHC paralogous region on human chromosome 1 . It is not quite clear when this movement might have taken place, since the CD1 pseudogene on chromosome 2 in opossum is clearly located in a region with genes syntenic to the human CD1 region, while the CD1 gene of Tasmanian devils is reported to be on the same chromosome as the MHC  examples might be that there is a cluster of tightly linked paralogous genes with either the CD1/FcRn genes embedded in the middle and obviously part of the paralogous region, or located some way off and obviously not part of the paralogous region. Sadly, the situation is more complex than is usually presented Fig. . The genThe CD1 genes are found in the middle of the 76 Mb covering the original paralogous genes on chromosome 1, relatively close to some well-defined paralogous genes such as LMNA, SPTA1, PBX1 and RXR. This finding is most easily accommodated by the CD1 genes being part of the region before duplication, but it remains possible that the CD1 genes were inserted into the middle of an existing paralogous region. In contrast, the FcRn gene is located at one end of the 47-Mb region containing the paralogous genes on chromosome 19, relatively far away (and across the centromere) from the bulk of those paralogous genes , considered to be most primitive of all birds  has a single CD1 gene together with TAP2 and class I genes, and the north island brown kiwi  has five CD1 genes, three together without other recognisable genes, and two together with tenascin. The mallard duck (Anas platyrhynchos) has four CD1 genes on three contigs, two together with a zinc finger, one with tenascin and one with nothing recognisable. The swan goose (Anser cygnoides domesticus) also has four CD1 genes on three contigs, two together with tenascin, TRIM7/butyrophilin-like, C4/α2-macroglobulin-like and two MHC class I genes, one with APOBEC4, and one with dynactin. This last constellation of genes is most intriguing, with class I genes typical of the mammalian class I region, tenascin typical of the mammalian class III region, TRIM7 and butyrophilin typical of the mammalian extended class I region, and α2-macroglobulin found in mammalian natural killer complex (NKC). As mentioned above, it has been suggested long ago that the NKC and the MHC were originally adjacent, as part of the primordial MHC  are the CD1 genes found next to recognisable MHC genes Fig. . For insOverall, it would appear that the CD1 genes can be found in the MHC and more than one of the MHC paralogous regions, apparently even in the same species. One explanation would be that CD1 genes were present in all four paralogous regions in the last common ancestor of reptiles, birds and mammals, and have been differentially silenced in each lineage, indeed in each species. However, if CD1 genes were present in all four paralogous regions, were they originally present in amphibians and the many thousands of different fish species, and are now lost? Another explanation might be that CD1 genes can move around in the genome, perhaps preferentially between genomic regions with some level of sequence homology, as might be expected for MHC paralogous regions. This possibility leads us to consider another unexpected finding in the chicken MHC, the presence of the lectin-like NK receptor and potential ligand.One of the many surprises that arose from the first genomic sequence of the chicken MHC was the presence of two genes that encoded lectin-like domains with apparent transmembrane exons located as in type II membrane proteins, located head-to-head in opposite transcriptional orientation. The one called B-NK was very clearly most closely related to a well-defined NK receptor in mammals, NKR-P1, and was found to be expressed in chicken NK cell clones  on chromosome 19 or in the MHC on chromosome 6, or near to any of the MHC paralogous regions  gene(s) and ligand (CLEC2) gene(s) are found to be located  in the natural killer complex (NKC), together with other lectin-like receptor genes such as KLRG1  and other signature genes such as TMEM52b, GABARAPL1 and αAs for the CD1 genes, we proposed that B-NK and B-lec were present in the primordial MHC before the two rounds of genome-wide duplication, and then these genes were differentially silenced in different paralogous regions of the lineage leading to mammals and to birds. We proposed that the NKC and the MHC were originally one region, in which both receptors and ligands were present in order to co-evolve , while B-lec was virtually monomorphic (Rogers and Kaufman Taeniopygia guttata), is located on the Z sex chromosome , has both a KLRB1 gene and a CLEC2 gene in between SLC1a1 and CDC37L1.It seemed possible to explain the appearance of a multigene family of B-lec genes with a single B-NK gene in and around the MHC of chickens and other galliforms, but it was a shock to find that the B-NK and B-lec gene pair in a passerine bird, the zebra finch , the low-coverage whole genome sequences for a wide variety of birds , the MHC of chickens and/or mammals  and the avian Z chromosome (including SLC1A1). Although this collection of genes is spread over 150 Mb, their presence all on the same chromosome is consistent with the idea that all three regions in birds were once together in a reptilian ancestor.In the genome sequence of the lizard, the green anole  as well as the generation of monoclonal antibodies which can be used to determine tissue expression, study cell biology and isolate molecules to determine the lipids bound, which in turn will allow the production of lipid-CD1 multimers to discover the responding cells. A crucial but much more difficult step is to determine the role of each of these CD1 molecules in response to particular diseases . Once all of these tasks are accomplished, it may become possible to pick out the important patterns that have governed the details of CD1 evolution, in order to understand which features have been selected and which features are due to chance. The journey to understand the lectin-like NK receptors and their ligands is likely to be similar but much more complicated, given the enormous complexity of NK cell biology.Overshadowing the comparative biology of both the CD1 and lectin-like NK receptors is the question of their genomic histories. For nearly 20 years, a guiding principle for the evolution of adaptive immunity has been the concept of genome-wide duplications at the base of the vertebrates leading to the extra genes that provided the potential to evolve an adaptive immune system. A large literature has explored this concept , and it remains a powerful way to organise and explain the disparate data that have been gathered. However, the Hughes-Dascher model completely repudiates this view, with the original adaptive immune system of jawed vertebrates envisaged to have appeared next to one of the paralogous regions after the two rounds of genome-wide duplication. Is it possible, after all of the sound and fury, that genome-wide duplication is in fact irrelevant to the origin and evolution of the adaptive immune system of the jawed vertebrates?Despite our own published models and beliefs, the existing data do not allow us to choose definitively between the dogma of Kasahara and the catastrophic antithesis of Hughes and Dasher. The analogous adaptive immune system of VLRs discovered in jawless fish does not provide clear evidence one way or the other, since the jawless fish have undergone at least one round of genome-wide duplication (Flajnik and Kasahara


All authors agree that posterior crossbite is a malocclusion that affects mandibular growth and may lead to skeletal asymmetry but there are few data on which age these modifications are easily quantifiable.For this study, the researchers used x-ray records of 217 children between 6 and 9 years of age, in the mixed dentition stage and with unilateral posterior crossbite. All the horizontal variables were traced and evaluated by the principal researcher, using the tpsDig version 2 computer program. Subsequently, a descriptive and statistical analysis was carried out, using the SPSS 17.0 for Windows program.p<0.005) for the entire sample (H3-H4), in the group of boys (H3-H4) and in the 7-year old age group (H1-H2 and H3-H4). Differences were observed in the size of the horizontal measures between the crossbite side and the non-crossbite side. Some of these differences were significant as a function of the sex and age of the study sample.After analysing the vertical mandibular traces on the x-rays, the researchers found, in all cases, quantifiable differences between the crossbite side and the non-crossbite side. The differences between horizontal variables were statistically significant ( Key words:Crossbite, Mandibular asymmetry, Panoramic. Patients with unilateral crossbite present occlusal, postural and functional alterations, which can lead to a reduction in bite force, asymmetrical muscular activity, joint problems and changes, not only in the position of the mandible, but also in its movements. If this pathology persists throughout the patient´s growth, it facilitates the development of skeletal asymmetry .There are different opinions about the manner in which this malocclusion affects mandibular growth and the development of skeletal asymmetry. Some researchers have observed that a unilateral posterior crossbite at an early age leads to bone development of an asymmetrical mandibular ramus with larger vertical dimensions. They have frequently observed, on the crossbite side, the presence of a condyle in a more posterior position -5.Different authors have tried to evaluate and determine the precision of images and measurements of the mandible using orthopantomography -10. TheyOrthopantomography has also been used to determine the patient’s skeletal pattern and mandibular foramen ,18. CurrIt is therefore not known at what age skeletal asymmetry provokes quantifiable bone changes in paediatric patients. We analysed panoramic x-rays of patients at early ages, in order to evaluate bone development, keeping in mind the crossbite side.To evaluate possible alterations in bone development that may be caused by malocclusion, by studying panoramic x-rays of a sample of children with unilateral crossbite. At the same time, to verify through these routine examinations at an early age whether any bone changes occurring are quantifiable, whether they increase with the age of the patient, and whether they are observed equally in both sexes.The study sample consisted of 645 patients attending a Diagnostic Radiology Centre over the last five years. All the children were recruited randomly. Afterwards, photographic and radiographic (orthopantomographic) records were taken. General medical data were recorded. The parents or guardians of all the children signed an informed consent form authorising the use of the records for research purposes, in compliance with the Data Protection Law.Subsequently, the following criteria were applied for inclusion:• Healthy patients, in first-phase mixed dentition, with a unilateral posterior crossbite.• No history of having received corrective treatment for malocclusion.• Photographic records that allow for precise diagnosis of the malocclusion under study.• Panoramic x-rays of sufficient quality to be evaluated.And for exclusion:• Patients with any orofacial pathology, dysmorphology, or syndrome that might cause alterations in normal development and/or growth.• The presence of dental/periodontal alterations that might affect or interfere with the diagnosis of crossbite.• Patients who use orthodontic appliances.After applying these criteria, the selected sample consisted of 217 children between 6 and 9 years of age. The median age of the sample was 7.5 years.The photographic diagnosis protocol included a series of digital photographs taken by the examiner himself, meeting the same technical requirements. The photographic series included extraoral projections while at rest , and intraoral  in occlusion and at maximum opening . The photographs were evaluated by the principal researcher using a computer (with a 30-inch screen), for a maximum of 20 patients per session, and the image was magnified when required. The following variables were taken into account: the number of teeth involved, the deviation from the median line, and the type of anterior and/or posterior crossbite.Likewise, all the x-rays were taken using the same technical specifications, and the verbal instructions were the same for all the patients. The x-rays were again examined by the principal researcher. In case of duplication, the best-quality photograph was selected. All the photographs were analysed using a computer and a 30-inch monitor, as well as the software programme tpsDig version 2. A maximum of 20 x-rays were examined in each session. Initially, the digital image from the x-ray was captured and a zoom was used to enlarge or reduce it by 10% each time, facilitating anatomical recognition of structures of interest. The anatomical points for the study were then located. Finally, the traces and estimates of horizontal measurements were made, at the level of the mandibular body:Variable H1: Distance between the most protruding and highest point of the right condyle and the perpendicular V0.Variable H2: Distance between the highest, most protruding point of the left condyle and the perpendicular V0.Variable H3: Distance between the highest, most protruding point of the right coronoid apophysis and the perpendicular VO.Variable H4: Distance between the highest, most protruding point of the left coronoid apophysis and the perpendicular VO.Variable H5: Distance between the bisector of the right mandibular angle and the perpendicular VO.Variable H6: Distance between the bisector of the left mandibular angle and the perpendicular VO.p< 0.05). Post hoc tests were also performed to determine the differences between the medians for each age range and for each of the measurements. Following the last measurement, after 20 days had passed, the principal researcher randomly selected 20% of the total measurements, to take them again. A paired T test was applied to detect systemic error.The measurements obtained were subjected to statistical analysis using the SPSS 17.0 for Windows program. A linear model was employed to determine the inter-subject factors. A Student’s T-Test was applied to each of the measurements individually, comparing at all times the side that had the crossbite with the non-crossbite side. The median, standard deviation and N value for each of the measurements in the total sample were found. In each of the results, a check was made to see whether there were significant differences at 95% , greater length was found in variables H2, H4 and H6, corresponding to the left side, compared to variables H1, H3 and V5 on the right side. All the horizontal estimations were always greater on the side without malocclusion. These results showed that only the differences between the horizontal variables H3-H4 were statistically significant.Analysis of the lengths of the horizontal variables in the sample of boys with RUPC reflected greater length in the H2, H4 and H6 variables corresponding to the left side, compared to the H1, H3 and V5 variables on the right side. Once again, as in the total sample, there was only significance in the difference between the left and right horizontal variables H3-H4.Analysis of the lengths of the horizontal variables in the sample of girls with RUPC showed greater length in the H1 and H5 variables corresponding to the right side, compared to the H2 and H6 variables on the left side. In this study group, the length of the H3 variable on the right side was less than the H4 variable on the left side, just as in the total sample, and in the boys. On this occasion, no statistically significant differences were observed in any of the variables .Analysis of the lengths in the age 6 sample showed greater length in the H2, H4 and H6 variables on the side without malocclusion, compared to the H1, H3 and H5 variables on the side with malocclusion. No statistically significant differences were found in any of the differences between variables . Analysis of these same lengths in the age 7 sample also showed greater length in the H2, H4 and H6 variables on the side without malocclusion, compared to the H1, H3 and H5 variables on the side with malocclusion. In this age range, statistically significant differences were observed between the H1-H2 and H3-H4 study variables. Analysis of horizontal lengths in the age 8 sample showed greater length in the H2 and H4 variables on the side without malocclusion; however, greater length was observed in the H5 variable on the side with malocclusion. None of the differences between variables were significant in this group. Finally, analysis of the length of the study variables in the age 9 sample found greater lengths for the H1 and H5 variables on the side with malocclusion. No statistically significant differences were found in any of the differences between variables  , Table 2There are few studies in the literature that evaluate asymmetry and possible quantifiable skeletal changes at an early age using routine x-ray projections such as orthopantomography ,21. Someet al. , with respect to the size of the mandibular body.Durval Given the scarcity of studies analysing mandibular symmetry through the use of horizontal metric variables traced on panoramic x-rays, we find it difficult to compare our results with those of other, similar research projects.In the total sample, in the group of boys aged 6 and 7, we observed larger mandibular dimensions on the side without malocclusion. However, in the sample of girls aged 8 and 9, some of the variables corresponding to the side with malocclusion were greater, although on this occasion no significance was found. We can say that age and sex can alter bone size, keeping in mind the study variables.In our study, differences were observed in the size of the horizontal measurements, keeping in mind the side with the malocclusion. Some of these differences were significant as a function of the sex and age of the study sample.Although efficient and precise diagnostic methods exist, panoramic x-rays, because they are a habitual and very accessible record, continue to be used frequently in the diagnosis of different pathologies, even though analysis of the tracing of linear and angular measurements does not represent a real projection of the object under study. However, it might be of help in diagnosing possible mandibular bone changes in patients with unilateral posterior crossbite.


The mean density of each receptor type over all cortical layers and of each of the three major strata varies between cortical regions. In a single cortical area, the multi-receptor fingerprints of its strata  differ in shape and size indicating regional and laminar specific balances between the receptors. Furthermore, the three strata are clearly segregated into well definable clusters by their receptor fingerprints. Fingerprints of different cortical areas systematically vary between functional networks, and with the hierarchical levels within sensory systems. Primary sensory areas are clearly separated from all other cortical areas particularly by their very high muscarinic M2 and nicotinic α4β2 receptor densities, and to a lesser degree also by noradrenergic α2 and serotonergic 5-HT2 receptors. Early visual areas of the dorsal and ventral streams are segregated by their multi-receptor fingerprints. The results are discussed on the background of functional segregation, cortical hierarchies, microstructural types, and the horizontal (layers) and vertical (columns) organization in the cerebral cortex. We conclude that a cortical column is composed of segments, which can be assigned to the cortical strata. The segments differ by their patterns of multi-receptor balances, indicating different layer-specific signal processing mechanisms. Additionally, the differences between the strata-and area-specific fingerprints of the 44 areas reflect the segregation of the cerebral cortex into functionally and topographically definable groups of cortical areas , and reveals their hierarchical position  sensory to higher sensory and finally to multimodal association areas).We measured the densities (fmol/mg protein) of 15 different receptors of various transmitter systems in the supragranular, granular and infragranular strata of 44 areas of visual, somatosensory, auditory and multimodal association systems of the human cerebral cortex. Receptor densities were obtained after labeling of the receptors using quantitative HighlightsDensities of transmitter receptors vary between areas of human cerebral cortex.Multi-receptor fingerprints segregate cortical layers.The densities of all examined receptor types together reach highest values in the supragranular stratum of all areas.The lowest values are found in the infragranular stratum.Multi-receptor fingerprints of entire areas and their layers segregate functional systemsCortical types  differ in their receptor fingerprints. Cortical layers—as defined in classical architectonic studies  were removed at autopsy. Subjects had given written consent before death and/or had been included in the body donor program of the Department of Anatomy, University of Düsseldorf, Germany, which also requires written consent by the donor. All procedures complied with the requirements defined by the local ethical committee. Post mortem delay before deep freezing was between 8 h and 18 h. Causes of death were cardiac arrest, lung edema, and myocardial infarction. After having separated each hemisphere into approximately 3 cm thick slabs, the slabs were shock frozen in isopentane at −40°C and stored at −80°C in airtight plastic bags until further processing. Thus, brain tissue was not treated with any chemical fixation substances. The total post mortem delay, including the deep freezing step, varied between 8 h and 18 h.in vitro receptor autoradiography, or stained for the visualization of cell bodies , acetylcholine , noradrenaline , serotonin , and dopamine (D1) were identified using tritium-labeled ligands according to previously published receptor protocols  with a large scale cryostat microtome. Alternating sections were processed for quantitative  Merker,  or of my Merker,  using si®, Amersham) or brain tissue scales (with a known protein density) containing step-wise increasing radioactivity concentrations. Protein content in the homogenate used to create the brain tissue scales had previously been determined by means of the Lowry method  together with plastic , E is the efficiency of the scintillation counter , B is a constant representing the number of decays per unit of time and radioactivity (Ci/min), bW the protein weight of a standard (mg), aS the specific activity of the ligand (Ci/mmol), DK the dissociation constant of the ligand (nM), and L the free concentration of the ligand during incubation (nM). Thus, the gray value of each pixel in a digitized autoradiograph, which can be color coded for visualization purposes, codes for a receptor concentration per unit protein  at saturation of ligand-receptor complexes.where Equidistant receptor profiles oriented vertically to the cortical surface were extracted by means of a minimum length algorithm from the linearized autoradiographs  and ventral (V2v) parts of the secondary visual cortex  and 45 (45a) in Broca’s region; Amunts et al., superior parietal areas 5L and 5M . Threshold was set at p ≤ 0.05. Subsequently, one-sample t-tests were carried out for each receptor type to determine whether its density in a given area differed significantly from the mean density of that receptor over all examined areas . Since these tests were only carried out for the receptor types for which the ANOVA was found to be significant, p values (threshold p ≤ 0.05) of the one-sample t-tests must not corrected for multiple testing. The same procedure was applied to densities measured in each of the three strata.To determine whether the density  of each receptor type separately was homogeneously or not homogeneously distributed over the 44 areas, ANOVA tests were carried out and p < 0.000), a pairwise comparison between all areas was also performed. The p values of these subsequent discriminant analyses were not corrected for multiple comparisons, because the Omnibus test was significant and the subsequent tests were performed as post hoc tests. This procedure was carried out for the fingerprints of the mean densities over all layers as well as for those of each of the three strata.For the question whether the 44 areas significantly differed in their receptor fingerprints, a discriminant analysis was carried with “area” as a grouping factor. This enables the determination of homogeneity or inhomogeneity of the fingerprints between areas. Since the discriminant analysis over all areas indicated a highly significant inhomogeneity of the fingerprints between the areas  of 15 different transmitter receptors for glutamate, GABA, acetylcholine, dopamine, noradrenaline and serotonin were measured in the three strata  of 44 cytoarchitectonically defined iso- and periarchicortical areas of the human brain. Additionally, the mean density of each receptor over all cortical layers  was calculated. All original data are provided in Supplementary Table S2.A, GABAB, M1, M2, α1, α2 and 5-HT1A receptors , 11 , lateral part of area 37 (M1), PGp (M3), 32 (nicotinic α4β2), 6 (α1), and 36 (5-HT1A). The lowest densities of AMPA receptors are reached in the posterior cingulate area 23, NMDA receptors in area 4, kainate receptors in area V2d, GABAergic GABAA receptors and GABAA/BZ binding sites in the motor cortex , and of GABAB receptors in area 45. Muscarinic M1 and M2 receptors have their minima in area 4, M3 receptors in area V4v, nicotinic α4β2 receptors in area 2, adrenergic α1 receptors in area 44, adrenergic α2 receptors in area 38, serotonergic 5-HT1A receptors in area V1, serotonergic 5-HT2 receptors in area FG1, and dopaminergic D1 receptors in premotor area 6. Despite of this considerable regional heterogeneity of the maximal and minimal mean areal densities of single receptor types, regional preferences can be detected. NMDA, GABAA, GABAA/BZ, M2, α2, 5-HT2, and D1 receptors all reach high densities in the primary visual cortex V1, whereas the same receptor types (except α2 and 5-HT2) and the M1 receptor show very low densities over all layers in primary motor and premotor areas.Figure strata-specific densities of each receptor type (Supplementary Table S2), the courses of all three strata seem to run nearly parallel to each other throughout all cortical areas , and in the anterior cingulate area 32 (nicotinic α4β2). The supra- and infragranular strata reach coincident maxima in the orbitofrontal area 11 (AMPA) and the premotor area 6 , whereas such coincident maxima of granular and infragranular layers are found in areas 11 (kainate) and 3b (α2) . In all other areas the density of this receptor is low, and shows no clear-cut local preference.Large differences between 5-HTd Figure . The dene Figure , since t2 receptor, which reaches highest densities in the granular stratum of most areas, and the α1 and 5-HT1A receptors, which in some areas present higher densities in the infragranular than in the granular stratum.In most areas a canonical sequence of receptor densities from highest values in the supragranular stratum, intermediate values in the granular layer IV, and lowest values in the infragranular stratum is found. Exceptions from this rule are seen for the kainate receptor, which shows highest densities in the infragranular stratum, the Mz-score normalized . The regional-specific expression of all receptors studied constitutes the receptor fingerprint of an area or a stratum. We generated four receptor fingerprints per cortical area, visualizing the mean areal density, as well as the density in its supragranular, granular and infragranular strata. This is done for both the absolute . After these Omnibus tests, a pairwise comparison between all combinations of areas revealed some significant inter-areal differences, but most comparisons did not reach significance (Supplementary Tables S3–S6).Discriminant analyses of the fingerprints over all layers, and separately for the three strata shows that the fingerprints of all 44 areas are heterogeneous , the proportional changes in densities between cortical areas remain constant when comparing different brains; e.g., in all examined brains, V1 contained higher overall NMDA, GABAIn conclusion, the sizes of absolute fingerprints, and thus the density of all receptors together in each area or stratum, are regional-specific and show a canonical sequence (supragranular to granular to infragranular) of the strata from large to small fingerprints.shape, and thus in the regional balance between multiple receptors can be better visualized.Using the normalized fingerprints, differences in the 4β2 receptor densities in the granular layers of the core regions of the primary somatosensory (3b) and auditory (41) cortices. Within each of the three sensory systems, the fingerprints are most similar between primary and early sensory areas . Furthermore, the fingerprints of early unimodal visual areas  are more similar to V1and V2 than to the hierarchically higher visual areas (areas FG1 and FG2 of the fusiform gyrus). Notably, the fingerprints of the early visual areas of the dorsal stream  differ from those of the ventral stream . The primary visual area V1 shows considerably higher normalized densities of NMDA, GABAA, GABAA/BZ, M2, α2, 5-HT2 and D1 receptors in all strata than the primary somatosensory  and auditory (41) areas  differ from those of the areas of the temporal and occipital lobes  and the secondary and multimodal auditory/temporal areas  systematically differ. Particularly, the normalized density of the α1 receptors in the premotor cortex (area 6) contributes to the segregation of this area from the primary motor cortex (area 4).The normalized fingerprints of motor areas 4 and 6 completely contrast with those of all sensory areas. Additionally, the high density of α3 receptors in the angular group, and a lower density of this receptor in the supramarginal group which resembles only that of the average over all 44 areas. Notably, the fingerprints of PGa and the postcentral areas 5L and 5M are very similar, although the latter areas are not located in the inferior parietal lobule. Additional to their high M3 receptor density, the supragranular and granular strata of 5L, 5M, PGa and PGp show a GABAA/BZ density clearly above average. Thus, both receptors largely contribute to the similarity of the fingerprints between these four parietal areas and segregate them from PFm and PFt.Multimodal association regions are located in the prefrontal, temporal and parietal lobes including the precuneus region. Areas of the inferior parietal lobule are clearly segregated by different shapes of receptor fingerprints into two different groups: the supramarginal group with areas PFm and PFt, and the angular group with areas PGa and PGp. Both groups of fingerprints are separated by the high to very high density of the muscarinic MDo the fingerprints of the three strata build separate, strata-specific clusters if all cortical areas are compared?Do the fingerprints over all layers and/or the stratum-specific fingerprints systematically differ by their shapes and sizes between cortical areas? Do these variations indicate principal aspects of functional and topographical segregation, as well as hierarchical organization?In a next step the area- and stratum-specific fingerprints were tested to answer two questions:A multidimensional scaling analysis of the stratum-specific fingerprints shows three clusters Figure , which cThe hierarchical cluster analysis of fingerprints of mean areal receptor densities separates all early visual areas from the rest of the cortex already after the first branching in the dendrogram Figure . The higThe fingerprints of the supragranular stratum Figures , 9A agaiThe fingerprints of the granular stratum Figures , 9B cleaThe fingerprints of the infragranular stratum Figures , 9C do nThe cluster analyses of stratum-specific fingerprints Figures , 9 highl4β2 receptor in the granular layers of all three primary sensory areas, and of the M2 receptor in the same layer of V1 and early visual areas of the ventral stream, as well as in the primary auditory cortex (area 41). In these areas, the density of the nicotinic α4β2 and the M2 receptors in the granular layer exceeds that of the supragranular stratum, which is the stratum with the highest receptor density in most areas. The general rule of a sequence in receptor densities from highest levels in the supragranular strata and lowest in the infragranular strata of all 44 areas is only violated by the kainate, noradrenergic α1 and serotonin 5-HT1A receptors where the canonical sequence from highest to lowest levels is changed in some or most areas.In summary, the fingerprints of the different strata differed greatly and enabled a separation of these strata-specific fingerprints into three clusters Figure . Only thThe new aspect of this study is the large scale cross area comparison of stratum-specific receptor fingerprints. It has been demonstrated that the densities of various transmitter receptors vary considerably between different cytoarchitectonically defined areas in the human cerebral cortex  and the M1 receptor reach very low densities in primary motor and premotor areas. Furthermore, the mean areal densities of GABAA, GABAA/BZ, M2, 5-HT2 and D1 receptors are higher in the early visual areas than in other isocortical regions. This latter finding is in sharp contrast to the regional distribution of kainate receptors, which are present at exceptionally low densities in all areas of the visual system. The multimodal association areas of the prefrontal and temporal cortices are characterized by high GABAB densities above the mean of all areas. The higest AMPA and kainate receptor densities are found in areas of the prefrontal association cortex or in this region and in the temporal association cortex, respectively. Low densities of the M2 receptor were found in the temporal and prefrontal association cortices, whereas the nicotinic receptor reached highest mean areal densites in the prefrontal and lowest densities in the temporal association cortex. Very high α1 and 5-HT1A receptor densities are found in the entire temporal cortex, particularly in the multimodal temporal association areas. In conclusion, primary sensory and multimodal association areas frequently showed a segregation by receptor densities. In some cases even prefrontal and temporal association areas can be separated by the distinct levels of their receptor expression. Thus, densities of single receptors are not randomly distributed over the entire cortex, but vary according to a general classification scheme into sensory, motor and multimodal areas.As previously stated  are also consistent with previous reports in the macaque monkey . The size of the fingerprints, scaled by absolute mean areal or stratum-specific densities, reflects the sum of the densities of all receptors, and shows considerable regional variations. Since the absolute densities of AMPA, NMDA, GABAThe size of the absolute fingerprint of a cortical area is defined by the sum of the densities of all receptors measured in that area. Since we measured all receptor types in all areas, and the absolute fingerprints are identically scaled, the sizes of fingerprints enable a comparison of the densities (fmol mg/protein) between all 44 areas, and reveal area- as well as strata-specific differences, thus demonstrating the regional heterogeneity of receptor expression . In conclusion, the normalized fingerprints clearly demonstrate locally specific roles of certain receptor types which lead to different balances between the receptors in the here studied areas and possibly to such different balances in all other regions of the cerebral cortex. That is a hint to a regional specificity of the receptor-mediated mechanisms of information processing.E.g., the high MSince both the different sizes and shapes of fingerprints reflect the regional and stratum-specific balances between receptors, a multidimensional scaling analysis of the fingerprints was performed. It shows that each stratum and each area have a characteristic fingerprint and thus, specific levels of total receptor densities and balances between the receptors Figure . This anOnly exceptions from this general finding are the positions of the fingerprints of the granular stratum in motor areas 4 and 6, which are shifted into the range of the infragranular cluster, and the concomitant shift of the supragranular fingerprints into the granular cluster. This shift of stratum-specific fingerprints of areas 4 and 6 to the “wrong” clusters may be caused by the method with which we defined the position of their layer IV . In the vast majority of the literature, areas 4 and 6 are described as being agranular, i.e., lacking a layer IV  play an important role here for the special position of particularly primary secondary areas. Although the function of the single receptor types has been intensely studied, the here important aspect of the role of the different receptor types within the cortical microcircuitry is, however, presently largely unknown. Our results on strata- and area-specific fingerprints and their relationships to general classification schemes of the cortex may be seen as a stimulus to study the specific functional role of these recepotr types in a systemic environment. Beside the distinct position of primary and early sensory unimodal areas, it must be emphasized that also the separation of the cluster of all prefrontal areas  from other multimodal association areas with separate clusters for the infraparietal and temporal regions is a strong hint to the analytical potential of the hierarchical receptor fingerprint analysis as a tool to understand principal rules of cortical segregation also in higher functional and multimodal systems.The degree of similarity between the fingerprints of the three strata and of all layers together was analyzed by hierarchical cluster analyses which revealed a considerable regional heterogeneity, but also some notable general rules. Early visual areas were clearly separated from the rest of the cortex if we focus on the supragranular stratum and on all layers together, thus emphasizing similar receptor balances in this stratum over all these areas. The analysis of the fingerprints of the granular stratum emphasizes the exceptional organization of layer IV in V1 and the similaritiy of these fingerprints in the ventral visual stream in contrast to the dorsal visual stream, since areas V3d and V3A are clearly separated from the cluster of the ventral stream areas. The infragranular stratum does not separate dorsal and ventral stream areas from each other. Therefore, we can conclude, that organizational principles of the visual cortex  are recognizable by the fingerprints, but to different degrees in the different strata. A further general finding was the close similarity of the receptor fingeprints of the primary and secondary somatosensory and auditory areas. This is most clearly seen in the supra- and infragranular strata, as well as in the fingerprints of all layers together. This leads again to the conclusion that primary and secondary sensory areas are clearly different from higher unimodal or multimodal cortices by their receptor balances. As discussed above, specific receptor types (MIt is remarkable that the receptor fingerprints of the primary somatosensory area 3b and the primary auditory cortex (area 41) are very similar and cluster together, while both fingerprints largely differ from that of the primary visual cortex V1. Therefore, fingerprints seem to reflect differences in modalities of sensory systems. The similarity of the fingerprints of areas 41 and 3b may be explained by their similar functional properties, i.e., mechanoreception, whereas the input in V1 is clearly different. Thus, V1 has to comply with different functional requirements compared to the auditory and somatosensory systems. Comparable differences can also be found for the unimodal sensory areas and their fingerprints. The fingerprint of area 2 (somatosensory cortex) is very similar to that of area 42 (secondary auditory cortex), and both clearly differ from the fingerprint of the secondary visual cortex V2. Finally, the fingerprints of areas 44 and 45, which are subdivisions of Broca’s language region, consistently cluster together in all strata and in the entire cortical width. All these findings suggest a modality-specific component of the shape of receptor fingerprints.The different levels of branching are indicated in the hierarchical cluster analyses. The highest possible number of clusters after k-means analysis was determined. All areas belonging to the same cluster in the supragranular, granular or infragranular strata, as well as to a cluster defined at the level of the mean over all layers are then labeled with the identical color. The resulting map indicates a subdivision of the cortex based on the similarity or dissimilarity of the regional-specific fingerprints in the different strata or entire areas. These maps are remarkable similar, since they assign in most cases the same areas to one cluster irrespective of the stratum in which the fingerprints have been yielded. Notably, the clusters comprise neighboring areas in many cases, but it must be emphasized, that the criterion of topographical neighborhood expresses at the same time a grouping of the areas according to different modalities or principal classifications into primary sensory, motor or higher multimodal association areas. Interestingly, area 38 does not cluster with the other multimodal temporal areas, but with areas on the supramarginal gyrus  and with the temporo-occipital transition zone . The latter areas have been attributed to the language network of Wernicke’s region  reflect the segregation of the cerebral cortex into functionally and topographically definable groups of cortical areas , and reveal their hierarchical position  sensory to higher sensory and finally to multimodal association areas) within sensory systems.This study was carried out in accordance with the recommendations of “Experimentelle wissenschaftliche Studien an Gewebeproben von Gehirnen und Organen von Körperspendern, Ethics Committee of the Medical Faculty of the Heinrich-Heine University Düsseldorf” with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the “Ethics Committee of the Medical Faculty of the Heinrich-Heine University Düsseldorf.”KZ and NP-G conceived of and designed the study, analyzed data, drafted the manuscript and figures. NP-G acquired data. KZ obtained funding.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


The process of stem cell myogenesis  includes several stages characterized by the expression of certain combinations of myogenic factors. The first part of this process is accompanied by cell division, while the second part is mainly associated with direct differentiation. The mechanical cues are known to enhance stem cell myogenesis, and the paper focuses on the stem cell differentiation under the condition of externally applied strain. The process of stem cell myogenic differentiation is interpreted as the interplay among transcription factors, targeted proteins and strain-generated signaling molecule, and it is described by a kinetic multi-stage model. The model parameters are optimally adjusted by using the available data from the experiment with adipose-derived stem cells subjected to the application of cyclic uniaxial strains of the magnitude of 10%. The modeling results predict the kinetics of the process of myogenic differentiation, including the number of cells in each stage of differentiation and the rates of differentiation from one stage to another for different strains from 4% to 16%. The developed model can help better understand the process of myogenic differentiation and the effects of mechanical cues on stem cell use in muscle therapies. Effective models have recently been proposed for a variety of cells under different conditions where mechanical factors are involved. They include analyses of spreading on patterned substrates278914et al. have recently shown that the application of strains to the myogenic environment significantly enhances the outcome of ASC differentiation21et al.Huri In the present paper, we consider stem cell myogenesis and focus on its differentiation part  as well 0, n1, and n2) are not discussed in the present paper, although the values of no, n1, and n2 affect the cell density feedback factor determined by the total number of cells. In addition, the cells in stage 2 contribute to the number of cells in stage 3 through asymmetric division. Wherever the characteristics of earlier stages 0, 1, and 2 enter the current model of stem cell myogenic differentiation or are graphically presented they are treated according to Deshpande et al.The focus of our model of stem cell myognenic differentiation is the kinetics of expression of myogenic factors, MyoD, myogenin and MHC, and the effect of the applied strain. We formulate our model in terms of the number of cells in the distinct stages of myogenesis which are determined by particular combinations of the expressed factors . In termThe kinetics of stem cell myogenic differentiation can be described by the following equations3), cell death , asymmetric division in previous stage 2 , and direct differentiation into next stage 4 (differentiation function D3). The terms on the right-hand side of 3), direct differentiation into next stage 4 , and cell death . The terms on the right-hand side of 4) and cell death . In equations (−1 (day−1) and the coefficient, 1 − r2, describing differentiation via asymmetric division is dimensionless. Both functions describing direct differentiation have units of number of cells/time (number of cells/day). The function f(ntot) (dimensionless) describes the feedback signal affecting the rates of cell number in different stages if the total cell number approaches a threshold .Here, the right-hand sides on equations , 2, 3 gi3 and D4, describes the actuation by the corresponding transcription factor  of the next myogenic factor . It is also assumed that the two transcription factors induce the –expression of their corresponding targets by means of a signaling molecule, S generated by the application of strain  toward myogenin (expressed in stage 4) production. The change in the myogenin production occurs via binding of the transcription factor, MyoD to the myogenin promoter. The duration of this binding is much shorter than that of the resulting production of myogenin  is dimensionless). If the MyoD transcription activity is pre-conditioned by the effect of the signaling molecule, S then the total [MyoD] concentration in 4) the number of MyoD molecules affected by S can be found from the steady state solution of the corresponding kinetic equationHere [MyoD] is the concentration of MyoD and ks (units of concentration) is a constant characterizing S/MyoD interaction (if the mechanism of such interaction is direct binding then ks is the dissociation constant), and [S] is the concentration of the signaling molecule. We now take into account that MyoD transcriptional activity takes place in all cells belonging to state 3 and re-write the right-hand site relationship (5) asHere, k0] where [S0 ] is the concentration coefficient, and ε is the strain coefficient equal to 1 for the 10%- amplitude the applied strain). Now, we divide the numerator and denominator in the S-function in the right-hand site of 0], and in addition, divide the numerator and denominator of the right-hand side of 3 in its final formHere, 3 is the parameter characterizing the n4 production , s/[S0], and 3 and 3 is a linear function of n3, and β3 is the coefficient of proportionality between the two. On the other hand, for large concentrations of S  and n5 (by increasing). An increase in 3, n4, n5, and ntot. In this case, the transition of cells in stage 3 into stage 4 is smaller resulting in more cells in stage 3 and fewer cells in stage 4. With the constant 4, resulting in a smaller initial slope of n5(t) but in larger values of n5 in later days. In terms of the effect of the constant, 3, but larger values of 5(t) and smaller values of n5 at later times. However, the total number of cells remains approximately the same due to the balance between n4 and n5. Thus, the parameters, β3 and β4 enhance differentiation, while the constants, 0, but more general functions of strain will be discussed as well.The concentration of signaling molecules, S, is determined by the applied strain, ε(t). Although the strain is cyclic for one hour of each day, we assume that S is the total number of signaling molecules produced during this relatively short, transient period of time that determines the signaling molecule’s interaction with transcription factors, MyoD and myogenin, for the rest of each day. The results below will be obtained assuming that S is proportional to the magnitude of the strain, εet al.th stage, and the results are compared with the model data in terms of the n’s. The converse approach of converting the n’s to myogenic factors is, however, more advantageous in our case because the experimental data2, n3, n4, n5, and ntot into the corresponding data in terms of the differentiation factors and compare them with the experimental results for Desmin, MyoD, MHC, and the total cell number.There are two possible ways to compare the modeling results with the previously obtained experimental data3, β4, We use the comparison with the experimental data to compute the optimal values of the model parameters, β5 and the times (days) of reaching these maxima. For these predictions, we use the parameters of the differentiation functions obtained from the optimization. Other parameters involved are the n3-and ntot-thresholds, and, for the consistency, they were chosen to be close to those used in the previous analysisIn 5 exhibits an approximately linear increase with a slope which is greater for larger strains. Note, that the magnitudes of n5-slopes are correlated with the preceding slopes of cell number in stage n3  reaches its maximal value which is greater for larger strains ))5-slope,3-function has two characteristic parts, a linearly increasing section whose slope increases with the strain and a decreasing section that behaves similarly for all strains   and n3, the function, D3 then reaches the time where the differentiation becomes weak but it is greater for smaller strains. Our model for the strain dependence of differentiation results in the clear saturation of the D3-function for larger strains  its maximal value. After this, D4 decreases and tends to zero more sharply for larger strains . The rise in cell number in stage 4 triggers the appearance and increase in cell number in stage 5. Following this, the cell number in stage 4 decreases, and finally, cells in all stages, from 0 to 4, disappear as they are differentiated into the latest stage 5. The kinetics of cells expressing particular factors is, however, different. The numbers of cells expressing Desmin, MyoD, myogenin, and MHC all increase with time  . Then D3 strains . The maxstage n4 . In summith time  consiste3 reaches the prescribed threshold and through the Desmin-related proliferation term in the n3-rate )The model presented here differs in several important aspects from the previous versionIn conclusion, we have developed a novel model of stem cell myogenic differentiation accompanied by the application of the mechanical strain. The model describes the differentiation kinetics and its association with the strain-dependent signaling. The model parameters optimally fit the experimental data for ASCs subjected to the strain of a particular magnitude, and the model results predict the stem cell behavior for different strains. The developed conceptual approach provides a better understanding of the interplay among myogenic factors involved, and it can help in the broader analysis of different stem cells and extracellular matrices (including 3-D microenvironment) used in cell therapies of skeletal muscle dysfunctions.5  is introduced a function of total cell number, ntot, total cell number threshold, A feedback factor, f. 3, β4, In order to optimize  the parameters, βHow to cite this article: Deshpande, R. S. and Spector, A. A. Modeling Stem Cell Myogenic Differentiation. Sci. Rep.7, 40639; doi: 10.1038/srep40639 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.