A new method of calculating crown projection area and its comparative accuracy with conventional calculations for asymmetric tree crowns

This paper introduces a new method of calculating crown projection area(CPA),the area of level ground covered by a vertical projection of a tree crown from measured crown radii through numerical interpolation and integration.This novel method and other four existing methods of calculating CPA were compared using detailed crown radius measurements from 30 tall trees of Eucalyptus pilularis variable in crown size,shape,and asymmetry.The four existing methods included the polygonal approach and three ways of calculating CPA as the area of a circle using the arithmetic,geometric and quadratic mean radius.Comparisons were made across a sequence of eight non-consecutive numbers(from 2 to 16)of measured crown radii for each tree over the range of crown asymmetry of the 30 trees through generalized linear models and multiple comparisons of means.The sequence covered the range of the number of crown radii measured for calculating the CPA of a tree in the literature.A crown asymmetry index within the unit interval was calculated for each tree to serve as a normative measure.With a slight overestimation of 2.2%on average and an overall mean error size of 7.9%across the numbers of crown radii that were compared,our new method was the least biased and most accurate.Calculating CPA as a circle using the quadratic mean crown radius was the second best,which had an average overestimation of 4.5%and overall mean error size of 8.8%.These two methods remained by and large unbiased as crown asymmetry increased,while the other three methods showed larger bias of underestimation.For the conventional method of using the arithmetic mean crown radius to calculate CPA as a circle,bias correction factors were developed as a function of crown asymmetry index to delineate the increasing magnitude of bias associated with greater degrees of crown asymmetry.This study reveals and demonstrates such relationships between the accuracy of CPA calculations and crown asymmetry and will help increase awareness among researchers and practitioners on the existence of bias in their CPA calculations and for the need to use an unbiased method in the future.Our new method is recommended for calculating CPA where at least four crown radius measurements per tree are available because that is the minimum number required for its use.

Accuracy Assessment of a Novel Radiographic Method to Evaluate Guided Bone Regeneration Outcomes Using a 3D-Printed Model

The aim of this study was to evaluate the accuracy and reproducibility of a morphological contour interpolation(MCI)based segmentation method for the volumetric measurement of bone grafts around implants.Three 3D-printed models(one with a cylinder and two with a geometrically-complex form)were fabricated to simulate implant placement with a simultaneous guided bone regeneration(GBR)procedure.All models were scanned using a cone beam computed tomography(CBCT)instrument with the same parameters.The true volumes of the bone grafts in the models were assessed using computer-aided calculation(controls).For the test measurements,both manual and MCI-based methods were used.A comparison between the measured and true volumes was performed to evaluate the accuracy.The coefficients of variation of repeated measurements were calculated to evaluate the reproducibility.In addition,the execution time was recorded and a comparison between the two methods was performed.The high accuracy of the MCI-based method was found with differences between the measured value and actual volume,which never exceeded 7.3%.Excellent reproducibility was shown,with coefficients of variation never exceeding 1.1%.A shorter execution time was observed for the MCI-based method than for the manual method.Within the confines of this study,the MCI-based method may be suitable for volumetric measurements of grafted bone around implants.

The research of space-time coupled spectral element method for acoustic wave equations

A space-time coupled spectral element method based on Chebyshev polynomials is presented for solving time-dependent wave equations.Acoustic propagation problems in1＋1,2＋1,3＋1 dimensions with the Dirichlet boundary conditions are simulated via space-time coupled spectral element method using quadrilateral,hexahedral and tesseractic elements respectively.Space-time coupled spectral element method can obtain high-order precision over time.With the same total number of nodes,higher numerical precision is obtained if the higher-order Chebyshev polynomials in space directions and lower-order Chebyshev polynomials in time direction are adopted.Numerical illustrations have indicated that the space-time algorithm provides higher precision than the semi-discretization.When space-time coupled spectral element method is used,time subdomain-by-subdomain approach is more economical than time domain approach.