Multiscale modeling of skeletal muscle to explore its passive mechanical properties and experiments verification

<abstract> <p>The research of the mechanical properties of skeletal muscle has never stopped, whether in experimental tests or simulations of passive mechanical properties. To investigate the effect of biomechanical properties of micro-components and geometric structure of muscle fibers on macroscopic mechanical behavior, in this manuscript, we establish a multiscale model where constitutive models are proposed for fibers and the extracellular matrix, respectively. Besides, based on the assumption that the fiber cross-section can be expressed by Voronoi polygons, we optimize the Voronoi polygons as curved-edge Voronoi polygons to compare the effects of the two cross-sections on macroscopic mechanical properties. Finally, the macroscopic stress response is obtained through the numerical homogenization method. To verify the effectiveness of the multi-scale model, we measure the mechanical response of skeletal muscles in the in-plane shear, longitudinal shear, and tensions, including along the fiber direction and perpendicular to the fiber direction. Compared with experimental data, the simulation results show that this multiscale framework predicts both the tension response and the shear response of skeletal muscle accurately. The root mean squared error (RMSE) is 0.0035 MPa in the tension along the fiber direction; The RMSE is 0.011254 MPa in the tension perpendicular to the fiber direction; The RMSE is 0.000602 MPa in the in-plane shear; The RMSE was 0.00085 MPa in the longitudinal shear. Finally, we obtained the influence of the component constitutive model and muscle fiber cross-section on the macroscopic mechanical behavior of skeletal muscle. In terms of the tension perpendicular to the fiber direction, the curved-edge Voronoi polygons achieve the result closer to the experimental data than the Voronoi polygons. Skeletal muscle mechanics experiments verify the effectiveness of our multiscale model. The comparison results of experiments and simulations prove that our model can accurately capture the tension and shear behavior of skeletal muscle.</p> </abstract>

The Methodology of Creating Variable Resolution Maps Based on the Example of Passability Maps

The paper presents the methodology for creating variable resolution maps, which was developed by the author and implemented to generate passability maps. These studies are used in military applications and crisis management in order to determine the possibility of crossing the area off-road. They may significantly facilitate the process of planning rescue or search operations. The developed methodology uses source data in the form of a spatial database to generate maps consisting of Voronoi polygons. The proposed solution automates the process of creating such maps, which was realized in practice by developing a dedicated IT system. It served to generate a series of passability maps in various configurations, which were then thoroughly compared. The conducted research demonstrated that variable resolution passability maps may successfully replace maps that consist of sometimes several dozen times higher numbers of primary fields. This enables reducing the amount of data stored in computer memory and shortens the time necessary to access visualization and information analysis on passability maps.

On Koenig's theorem for integer functions of finite order

Показано, что теорема Кенига о нулях аналитической функции, примененная к логарифмической производной целой функции конечного порядка, приводит к алгоритму отыскания нулей, для которого областями сходимости являются многоугольники Вороного искомых нулей. Так как диаграмма Вороного последовательности нулей составляет множество меры нуль, то алгоритм имеет глобальную сходимость. Дана оценка скорости сходимости. Для итераций высших порядков, которые строятся с помощью теоремы Кенига, рассмотрено влияние кратности корня на область сходимости и приводится оценка скорости сходимости. It is shown that Koenig's theorem on zeros of analytic functions applied to the logarithmic derivative of an integer function of finite order leads to an algorithm of finding zeros whose convergence domains are the Voronoi polygons of the zeros to be found. Since the Voronoi diagram of a sequence of zeros is a set of measure zero, this algorithm is globally convergent. The rate of convergence is estimated. For higher-order iterations that are constructed using Koenig's theorem, the effect of root multiplicity on the convergence domain is considered and the convergence rate is estimated for this case.

SETTLEMENT STRUCTURE OF EARLY MEDIEVAL GROUPS IN THE TRANS-URALS

The article considers the settlement of Early Medieval population in the Trans-Urals (4th–9th centuries AD). The study is based on the data about the location of monuments attributed to the Bakal culture, which are re-corded on the territory of the Tobol-Ishim interfluve and its water system in the area of the modern forest-steppe belt. The relevance of the study is determined by the following points: presentation of new data on the monu-ments of the Bakal culture; analysis of the settlement system and landscape use in the specified period; identifica-tion of economic areas characteristic of the early medieval population. In this study, the authors used the methods and approaches of landscape and settlement archaeology. In addition to the spatial and morphological character-istics, the source database includes data on the Earth's digital model drawing on SRTM30 data. The analysed materials (81 monuments — 36 hillforts, 40 villages, 5 burial grounds) were collected in one geoinformation sys-tem; the authors proposed an improved classification of fortified villages, which provides the opportunity to char-acterise the economic structure of the Bakal groups in a new way. The hillforts comprise 27 terrace settlements located on the high bedrock coasts of rivers, as well as 9 floodplain fortified settlements situated on isolated hills. When identifying economic zones on the basis of constructed Thiessen (Voronoi) polygons, it was found that there was one or, less often, two fortified villages (hillforts) in the centre of one zone. Settlements were located not far from the centre (most often in a floodplain). The analysis of direct visibility from the settlements showed that direct visual watch was kept over the villages in the floodplain, with the visibility zones covering large flood-plain sectors, thereby providing fairly tight control of the territory. It was established that the burial grounds were located in the immediate vicinity of fortified villages. The analysis revealed a correlation between the location of the village and the economy of the Bakal population, where cattle, prevailing in quantity, played an important role. This is due to the presence of large fortified settlements located in floodplains, whose population kept livestock. The authors established a system of the settlement and space-related occupation of the Medieval population in the Trans-Urals, with hillforts being the main centres used to control the territory simultaneously performing the functions of political, trade and economic centres.

An Algorithm based on the Weighted Network Voronoi Diagram for Point Cluster Simplification

Points on maps that stand for geographic objects such as settlements are generally connected by road networks. However, in the existing algorithms for point cluster simplification, points are usually viewed as discrete objects or their distances are considered in Euclidean spaces, and therefore the point cluster generalization results obtained by these algorithms are sometimes unreasonable. To take roads into consideration so that point clusters can be simplified in appropriate ways, the network Voronoi diagram is used and a new algorithm is proposed in this paper. First, the weighted network Voronoi diagram is constructed taking into account the weights of the points and the properties of the related road segments. Second, the network Voronoi polygons are generated and two factors (i.e., the area of the network Voronoi polygon and the total length of the dilated road segments in the polygon) are considered as the basis for point simplification. Last, a Cartesian coordinate system is built based on the two factors and the point clusters are simplified by means of the “concentric quadrants”. Our experiments show that the algorithm can effectively and correctly transmit types of information in the process of point cluster simplification, and the results are more reasonable than that generated by the ordinary Voronoi-based algorithm and the weighted Voronoi-based algorithm.

Voronoi polygons quantify bias when sampling the nearest plant

The design bias in the sample mean obtained from sampling the trees nearest to points randomly and uniformly distributed over a forested area can be exactly quantified in terms of the Voronoi polygons (V polygons) surrounding each tree in the forest of interest. For this sampling method, the V polygon for a prospective sample tree is its inclusion zone. The sides of such polygons are perpendicular to a line joining adjacent trees and equidistant from these trees. For any individual tree attribute Y, the design bias in such a sample mean for estimating the population mean of Y will be equal to the covariance between Y and V-polygon area V divided by the mean V-polygon area. The bias as a percent of the population mean of Y is the product of the correlation coefficient between Y and V and the coefficients of variation for Y and V multiplied by 100. This implies that attempts to estimate the means of commonly measured individual tree variables such as DBH, basal area, and crown diameter or the area from sampling trees nearest to randomly located points will likely be positively biased, and the magnitude of that bias will depend on the strength of the linear relationship to the V-polygon area, as well as the variability among the V-polygon areas and the variable of interest. It is not obvious whether increment core data will be positively or negatively biased, because this depends on the characteristics of the forest of interest. The main conclusion of the study is that the bias formula derived for unweighted estimation from sampling the tree nearest to a point indicates that bias in the range of 5%–10% or greater can occur in many forest populations.