Standard Coordinate System Research Articles

Topography of the complete corticopontine projection: From experiments to principal maps

The mammalian brain is characterized by orderly spatial distribution of its cellular components, commonly referred to as topographical organization. The topography of cortical and subcortical maps is thought to represent functional or computational properties. In the present investigation, we have studied map transformations and organizing principles in the projections from the cerebral cortex to the pontine nuclei, with emphasis on the mapping of the cortex as a whole onto the pontine nuclei. Following single or multiple axonal tracer injections into different cortical regions, three-dimensional (3-D) distributions of anterogradely labeled axons in the pontine nuclei were mapped. All 3-D reconstructed data sets were normalized to a standardized local coordinate system for the pontine nuclei and uploaded in a database application (FACCS, Functional Anatomy of the Cerebro-Cerebellar System, available via The Rodent Brain Workbench, http://www.rbwb.org). The database application allowed flexible use of the data in novel combinations, and use of a previously published data sets. Visualization of different combinations of data was used to explore alternative principles of organization. As a result of these analyses, a principal map of the topography of corticopontine projections was developed. This map followed the organization of early spatiotemporal gradients present in the cerebral cortex and the pontine nuclei. With the principal map for corticopontine projections, a fairly accurate prediction of pontine target area can be made for any site of origin in the cerebral cortex. The map and the underlying shared data sets represent a basis for modeling of topographical organization and structure–function relationships in this system.

Internal tectonic structure of the Central American Wadati‐Benioff zone based on analysis of aftershock sequences

Relocated Engdahl et al. (1998) global seismological data for 10 aftershock sequences were used to analyze the internal tectonic structure of the Central American subduction zone; the main shocks of several of these were the most destructive and often referenced earthquakes in the region (e.g., the 1970 Chiapas, 1983 Osa, 1992 Nicaragua, 1999 Quepos, 2001 El Salvador earthquakes). The spatial analysis of aftershock foci distribution was performed in a rotated Cartesian coordinate system (x, y, z) related to the Wadati‐Benioff zone, and not in a standard coordinate system (ϕ, λ, h are latitude, longitude, focal depth, respectively). Available fault plane solutions were also transformed into the plane approximating the Wadati‐Benioff zone. The spatial distribution of earthquakes in each aftershock sequence was modeled as either a plane fit using a least squares approximation or a volume fit with a minimum thickness rectangular box. The analysis points to a quasi‐planar distribution of earthquake foci in all aftershock sequences, manifesting the appurtenance of aftershocks to fracture zones. Geometrical parameters of fracture zones (strike, dip, and dimensions) hosting individual sequences were calculated and compared with the seafloor morphology of the Cocos Plate. The smooth character of the seafloor correlates with the aftershock fracture zones oriented parallel to the trench and commonly subparallel to the subducting slab, whereas subduction of the Cocos Ridge and seamounts around the Quepos Plateau coincides with steeply dipping fracture zones. Transformed focal mechanisms are almost exclusively (>90%) of normal character.

Treeness Triangles: Visualizing the Loss of Phylogenetic Signal

It is well known that molecular data "saturates" with increasing sequence divergence (thereby losing phylogenetic information) and that in addition the accumulation of misleading information due to chance similarities or to systematic bias may accompany saturation as well. Exploratory data analysis methods that can quantify the extent of signal loss or convergence for a given data set are scarce. Such methods are needed because genomics delivers very long sequence alignments spanning substantial phylogenetic depth, where site saturation may be compounded by systematic biases or other alternative signals. Here we introduce the Treeness Triangle (TT) graph, in which signals detectable by Hadamard (spectral) analysis are summed into 3 categories--those supporting 1) external and 2) internal branches in the optimal tree, in addition to 3) the residuals (potential internal branches not present in the optimal tree). These 3 values are plotted in a standard ternary coordinate system. The approach is illustrated with simulated and real data sets, the latter from complete chloroplast genomes, where potential problems of paralogy or lateral gene acquisition can be excluded. The TT uncovers the divergence-dependent loss of phylogenetic signal as subsets of chloroplast genomes are investigated that span increasingly deeper evolutionary timescales. The rate of signal loss (or signal retention) varies with the gene and/or the method of analysis.

Surface similarity-based molecular query-retrieval.

BackgroundDiscerning the similarity between molecules is a challenging problem in drug discovery as well as in molecular biology. The importance of this problem is due to the fact that the biochemical characteristics of a molecule are closely related to its structure. Therefore molecular similarity is a key notion in investigations targeting exploration of molecular structural space, query-retrieval in molecular databases, and structure-activity modelling. Determining molecular similarity is related to the choice of molecular representation. Currently, representations with high descriptive power and physical relevance like 3D surface-based descriptors are available. Information from such representations is both surface-based and volumetric. However, most techniques for determining molecular similarity tend to focus on idealized 2D graph-based descriptors due to the complexity that accompanies reasoning with more elaborate representations.ResultsThis paper addresses the problem of determining similarity when molecules are described using complex surface-based representations. It proposes an intrinsic, spherical representation that systematically maps points on a molecular surface to points on a standard coordinate system (a sphere). Molecular surface properties such as shape, field strengths, and effects due to field super-positioningcan then be captured as distributions on the surface of the sphere. Surface-based molecular similarity is subsequently determined by computing the similarity of the surface-property distributions using a novel formulation of histogram-intersection. The similarity formulation is not only sensitive to the 3D distribution of the surface properties, but is also highly efficient to compute.ConclusionThe proposed method obviates the computationally expensive step of molecular pose-optimisation, can incorporate conformational variations, and facilitates highly efficient determination of similarity by directly comparing molecular surfaces and surface-based properties. Retrieval performance, applications in structure-activity modeling of complex biological properties, and comparisons with existing research and commercial methods demonstrate the validity and effectiveness of the approach.

The effect of axis alignment on shoulder joint kinematics analysis during arm abduction

A joint coordinate system allows coherence between the performed movement, its mathematical representation and the clinical interpretation of the kinematics of joint motion. In 2005, the International Society of Biomechanics (ISB) defined a joint coordinate system for the shoulder. To improve kinematics interpretation, the ISB suggested aligning the coordinate systems of the humerus and the scapula. Therefore, the aim of this research project was to determine how the alignment of the joint coordinate system axes can influence the interpretation of shoulder joint kinematics. More precisely, we wanted to investigate if mathematical alignment of the reference and moving coordinate system axes could facilitate the kinematic interpretation of a simple abduction movement without introducing additional coupled motion. An experiment was carried out on eight shoulder cadaveric specimens. Elevation of the arm in the scapular plane (abduction) was recorded using an electromagnetic tracking device. Three-dimensional angular displacements of the arm during elevation in the scapular plane were described using the standard ISB joint coordinate system, and using a modified joint coordinate system for which the axes were mathematically aligned. The results obtained revealed a difference in the interpretation of the starting angles between the ISB joint coordinate system and the aligned coordinate system. No difference was found in the interpretation of the angular range of motion (P<0.01). The aligned coordinate system provided a standardized starting angle of elevation that allows an easier clinical interpretation of shoulder kinematics.

Horizontal Rectus Muscle Anatomy in Naturally and Artificially Strabismic Monkeys

Structural abnormalities of extraocular muscles (EOMs) or their pulleys are associated with some forms of human strabismus. This experiment was conducted to investigate whether such abnormalities are associated with artificial or naturally occurring strabismus in monkeys. Binocular alignment and grating visual acuities were determined in 10 monkeys representing various species using search coil recording and direct observations. Four animals were orthotropic, two had naturally occurring "A"-pattern esotropia, two had concomitant and one had "V"-pattern esotropia artificially induced by alternating or unilateral occlusion in infancy, and one had "A"-pattern exotropia artificially induced by prism wear. After euthanasia, 16 orbits were examined by high-resolution magnetic resonance imaging (MRI) in the quasi-coronal plane. Paths and sizes of horizontal rectus EOMs were analyzed quantitatively in a standardized coordinate system. Whole orbits were then serially sectioned en bloc in the quasi-coronal plane, stained for connective tissue, and compared with MRI. Nerve and EOM features were analyzed quantitatively. Quantitative analysis of MRI revealed no significant differences in horizontal rectus EOM sizes or paths among orthotropic or naturally or artificially strabismic monkeys. Histologic examination demonstrated no differences in EOM size, structure, or innervation among the three groups, and no differences in connective tissues in the pulley system. The accessory lateral rectus (ALR) EOM was present in all specimens, but was small, inconsistently located, and sparsely innervated. Characteristics of the ALR did not correlate with strabismus. Major structural abnormalities of horizontal rectus EOMs and associated pulleys are unrelated to natural or artificial horizontal strabismus in the monkeys studied. The ALR is unlikely to contribute to horizontal strabismus in primates. However, these findings do not exclude a possible role of pulley abnormalities in disorders such as cyclovertical strabismus.

Standardizing the atomic description, axis and centre of biological ion channels

A general representation of the atomic co-ordinates of a biological ion channel is obtained from a definition of channel axis and centre. Through rotation and translation of the channel, its centre becomes the origin of the standard co-ordinate system, and the channel axis becomes the system's z-axis. A method for determining the channel axis and centre based on the concepts of mass centre and mass moment of inertia is presented. The method for determining the channel axis can be directly applied to channels that adhere to two specific conditions regarding their geometry and mass distribution. Specific examples are given for Gramicidin A (GA), and the mammalian potassium channel Kv1.2. For channels that do not adhere to these conditions, minor modifications of these procedures can be applied in determining the channel axis. Specific examples are given for the outer membrane bacterial porin OmpF, and for the staphylococcal pore-forming toxin α-hemolysin (αHL). The definitions and procedures presented are made in an effort to establish a standard basis for performing, sharing, and comparing computations in a consistent manner.

MapCruncher

Current large-scale interactive web mapping services such as Virtual Earth and Google Maps use large distributed systems for delivering data. However, creation and editorial control of their content is still largely centralized. The Composable Virtual Earth project's goal is to allow seamless interoperability of geographic data from arbitrary, distributed sources. MapCruncher is a first step in this direction. It lets users easily create new interactive map data that can be layered on top of existing imagery such as road maps and aerial photography. MapCruncher geographically registers and reprojects the user's map into a standard coordinate system. It then emits metadata that makes it easy for anyone on the Internet to find the published map data and import it. Interactive maps them become distributed, seamlessly composable building blocks -- similar to images in the early days of the Web.

Cortical electrode localization from X-rays and simple mapping for electrocorticographic research: The “Location on Cortex” (LOC) package for MATLAB

Medically refractory epilepsy accounts for more than 30% of the epilepsy population. Scalp EEG electrodes have limited ability to localize seizure onset from deep structures and implantation of subdural electrodes with long term monitoring provides additional information. Apart from clinical application, this patient population provides a unique opportunity for acquiring electrocorticography data in research paradigms. We present a method for rapid localization of electrodes using lateral and anterior–posterior X-rays. Skull landmarks and proportions are used for co-registration with the standardized Talairach coordinate system. This MATLAB-based “Location on Cortex” (LOC) package facilitates rapid visualization of clinical and experimental data in a user-friendly manner.

Visualizations of Wave Dynamics in a Wedge Waveguide with Non-Penetrable Boundaries: Normal-, Adiabatic-, and Intrinsic-Mode Representations

Many natural or man-made guiding environments are characterized by physical parameters that render the wave equation non-separable in any of the standard coordinate systems. In particular, in the absence of transverse-longitudinal separability, it is not possible to define discrete or continuous normal modes (NM) that individually satisfy the transverse boundary conditions and that propagate longitudinally without coupling to other modes. When transverse-longitudinal separability is only weakly perturbed, one may define local (adiabatic) modes that adapt smoothly, without inter-mode coupling, to the slowly changing conditions. Adiabatic modes (AM) fail in cutoff regions, and can be made uniform there by intrinsic modes (IM), which are synthesized by a spectral continuum of adiabatic modes. These concepts have been elucidated and validated previously by investigating the wave dynamics in a simple test environment: a wedge waveguide with non-penetrable boundaries, viewed either in coordinate-separable cylindrical coordinates that yield exact field solutions in terms of normal mode, or in non-separable rectangular coordinates that yield approximate field solutions in terms of adiabatic modes and intrinsic modes. The present article is intended as a tutorial to enhance the utility and understanding of these analytical formulations through visualizations of the dynamic interaction between the various wave species, implemented through an educational MATLABtrade package. The visualizations for the full range of ray, mode, and hybrid options, parameterized in the spectral wavenumber domain, has been explored by us previously for the inherently separable canonical environment of a line-source-excited parallel-plate waveguide. In our present investigation of the wedge waveguide, we shall not attempt to mimic the variety of options because of the substantial complications and subtleties inherent in their rectilinearly weakly-non-separable implementation. For our purposes here, a single specific option suffices to address the normal-mode, adiabatic-mode, and intrinsic-mode phenomenologies. Throughout this article, the intended audience is expected to be familiar with asymptotic methods for the evaluation of integrals.

In vivo three‐dimensional skeletal alignment analysis of the hindfoot valgus deformity in patients with rheumatoid arthritis

The purpose of this study was to analyze the skeletal alignment of the hindfoot valgus deformity in patients with rheumatoid arthritis using bone models reconstructed from three-dimensional computerized tomography data. Computed tomography was performed on 21 feet of patients with rheumatoid arthritis, and magnetic resonance imaging was taken of 10 normal feet of eight volunteers. An image processing system was used to create bone models and analyze the three-dimensional displacement of the calcaneus, talus, navicular, and cuboid bones. With a standard coordinate system in the distal tibia and a local coordinate system in each bone of the hindfoot, three rotational parameters and three translational parameters were used to evaluate the relative displacement. The talus showed plantar flexion. Both the calcaneus and navicular bones had valgus and lateral shift displacements. However, the cuboid had no displacement relative to the calcaneus, and the navicular showed no displacement relative to the cuboid. The calcaneus, navicular, and cuboid bones have the same pattern of deformity in patients with rheumatoid arthritis. This three-dimensional image-based technique successfully quantified the hindfoot valgus deformity resulting from rheumatoid arthritis and is beneficial for better understanding the deformity pathomechanism.

A note on the dipole coordinates

A couple of orthogonal coordinates for dipole geometry are proposed for numerical simulations of plasma geophysics in the Earth's dipole magnetic field. These coordinates have proper metric profiles along field lines in contrast to the standard dipole coordinate system that is commonly used in analytical studies for dipole geometry.

Reliability of Digital Versus Conventional Cephalometric Radiology: A Comparative Evaluation of Landmark Identification Error

The purpose of this study was to determine whether direct digital lateral cephalometric radiographs are of equal value in diagnosis and treatment planning as conventional cephalometric radiographs by investigating differences in landmark identification on direct digital and conventional cephalometric radiographs. An evaluation of precision and the distribution of landmark identification error at each cephalometric landmark was undertaken. Ten observers, all orthodontists or postgraduate orthodontic residents, identified 19 landmarks twice on 6 digital images and 6 conventional cephalometric films obtained from the records of 6 patients at the University of Alabama School of Dentistry Graduate Orthodontic Clinic. Patient records selected were of adults with existing pretreatment conventional cephalometric films and posttreatment direct digital cephalometric images on file. Landmark identification recordings were transferred into a standardized coordinate system, adjusted for magnification differences, and evaluated separately along both the x- and the y-coordinates. Statistically significant differences in landmark identification error were found along the x-coordinate for A point (Apt) and along the y-coordinate for anterior nasal spine (ANS) and condylion (Co). These statistically significant differences, as well as those found to be not statistically significantly different, were all below 1 mm, indicating that even the statistically significant differences between the two methods of image acquisition were unlikely to be of clinical significance. Each landmark exhibited its own unique pattern of landmark identification error, the magnitude and distribution of which must be taken into consideration when selecting landmarks for use in cephalometric analysis or when interpreting these analyses for diagnostic or treatment planning purposes. The results of the present study indicate similar precision and reproducibility in landmark identification using both direct digital images and conventional lateral cephalometric head films. The purpose of this study was to determine whether direct digital lateral cephalometric radiographs are of equal value in diagnosis and treatment planning as conventional cephalometric radiographs by investigating differences in landmark identification on direct digital and conventional cephalometric radiographs. An evaluation of precision and the distribution of landmark identification error at each cephalometric landmark was undertaken. Ten observers, all orthodontists or postgraduate orthodontic residents, identified 19 landmarks twice on 6 digital images and 6 conventional cephalometric films obtained from the records of 6 patients at the University of Alabama School of Dentistry Graduate Orthodontic Clinic. Patient records selected were of adults with existing pretreatment conventional cephalometric films and posttreatment direct digital cephalometric images on file. Landmark identification recordings were transferred into a standardized coordinate system, adjusted for magnification differences, and evaluated separately along both the x- and the y-coordinates. Statistically significant differences in landmark identification error were found along the x-coordinate for A point (Apt) and along the y-coordinate for anterior nasal spine (ANS) and condylion (Co). These statistically significant differences, as well as those found to be not statistically significantly different, were all below 1 mm, indicating that even the statistically significant differences between the two methods of image acquisition were unlikely to be of clinical significance. Each landmark exhibited its own unique pattern of landmark identification error, the magnitude and distribution of which must be taken into consideration when selecting landmarks for use in cephalometric analysis or when interpreting these analyses for diagnostic or treatment planning purposes. The results of the present study indicate similar precision and reproducibility in landmark identification using both direct digital images and conventional lateral cephalometric head films.

Analysis of waves in Saturn's dayside magnetosphere: Voyager 1 observations

Magnetic field fluctuations were observed in the data of Voyager 1 on its inbound leg in Saturn's magnetosphere from about 19 to 8.4 Saturn radii, during the interval 7–17 hours before closest approach. These low‐amplitude oscillations had the appearance of irregular micropulsations. The wave periods in the spacecraft frame varied between ≈1 and 20 min with a tendency to be inversely correlated with the field strength. An eigenfunction analysis yielding wave propagation direction as a function of frequency showed that at and near peak frequency two distinct types of waves were present, one propagating along field lines (within 30°) usually at the higher frequencies considered, (4–14) × l0−3 Hz, and the other propagating along (the azimuthal direction in a standard spherical coordinate system) at lower frequencies, (0.8–4) × l0−3 Hz. The power spectral density (in (nT)2/Hz) at the peaks tended to be inversely related to frequency over the full set of frequencies. An interpretation of these results is that Alfven waves are propagating along field lines at the higher frequencies with wavelengths between 1/4 and 1/2 RS. These occur in both the mantle and plasma sheet. The waves traveling along , which are observed to occur in the low‐latitude plasma mantle, are apparently manifestations of rapidly corotating MHD waves with large compressional components and are probably due to the operation of the centrifugal flute instability at the plasma sheet‐mantle boundary. For both types, wave absorption occurs with a high‐frequency cutoff at or near the gyrofrequency of O+ (and/or N+). Our results establish the framework for MHD waves within Saturn's outer magnetosphere, and it is expected that the Cassini mission, for which orbit insertion occurred on 1 July 2004, will add considerably to that presented here.

Virtual 10–20 measurement on MR images for inter-modal linking of transcranial and tomographic neuroimaging methods

It is important to create a link between stereotaxic coordinates and head-surface-based positioning systems in order to share data between tomographic and transcranial brain mapping studies. In our previous studies, we established the probabilistic correspondence of the international 10–20 positions to the standard stereotaxic coordinate systems and made a reference database. However, its expansion required the physical marking of the 10–20 positions and the subsequent acquisition of MR images. To avoid such tedious procedures, we developed a virtual 10–20 measurement algorithm that can be applied to reanalyze any structural MR image that covers the whole head. As in the physical 10–20 measurements, with the reference points given, the algorithm automatically determines each 10–20 position step by step. Using the virtual 10–20 measurement method, we reanalyzed the MR images of 17 healthy subjects for whom we had determined 10–20 positions by physical marking in our previous study. The acquired 10–20 positions were normalized to the Montreal Neurological Institute (MNI) stereotactic coordinates and compared with the positions previously determined by physical measurements. 10–20 positions determined using the virtual and physical methods were roughly consistent. Average standard deviations for virtual and physical methods were 7.7 mm and 9.0 mm, respectively. There was a systematic shift in the virtual method, likely due to the absence of hair interference. We corrected the shift with affine transformation. The virtual 10–20 measurement method proved to be an effective alternative to physical marking. This method will serve as an essential tool for expanding the reference database and will further strengthen the link between tomographic and transcranial brain mapping methods.

Pig brain stereotaxic standard space: Mapping of cerebral blood flow normative values and effect of MPTP-lesioning

The analysis of physiological processes in brain by position emission tomography (PET) is facilitated when images are spatially normalized to a standard coordinate system. Thus, PET activation studies of human brain frequently employ the common stereotaxic coordinates of Talairach. We have developed an analogous stereotaxic coordinate system for the brain of the Göttingen miniature pig, based on automatic co-registration of magnetic resonance (MR) images obtained in 22 male pigs. The origin of the pig brain stereotaxic space (0, 0, 0) was arbitrarily placed in the centroid of the pineal gland as identified on the average MRI template. The orthogonal planes were imposed using the line between stereotaxic zero and the optic chiasm. A series of mean MR images in the coronal, sagittal and horizontal planes were generated. To test the utility of the common coordinate system for functional imaging studies of minipig brain, we calculated cerebral blood flow (CBF) maps from normal minipigs and from minipigs with a syndrome of parkisonism induced by 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP)-poisoning. These maps were transformed from the native space into the common stereotaxic space. After global normalization of these maps, an undirected search for differences between the groups was then performed using statistical parametric mapping. Using this method, we detected a statistically significant focal increase in CBF in the left cerebellum of the MPTP-lesioned group. We expect the present approach to be of general use in the statistical parametric mapping of CBF and other physiological parameters in living pig brain.

Invariant surface alignment in the presence of affine and some nonlinear transformations

In this paper, we introduce a non-iterative geometric-based method to align 3D brain surfaces into standard coordinate system, which is based on a novel set of surface landmarks (e.g., inflection and/or zero torsion points residing on parabolic contours), which are intrinsic and are computed from the differential geometry of the surface. This is in contrast to existing methods that depend on anatomical landmarks that require expert intervention to locate – a very hard task. The landmarks are local and are preserved under affine transformations. To reduce the sensitivity of the landmarks to noise, we use a B-Spline surface representation that smoothes out the surface prior to the computation of the landmarks. The alignment is achieved by establishing correspondences between the landmarks after a sorting of the landmarks based on derived absolute invariants (volumes confined between parallelepipeds spanned by sets of the landmark point quadruplets). The method is tested for intra- and inter-brain alignments while entertaining affine, cubic and fourth-order polynomial nonlinear transformations using distance mapping as well as comparison with an expert alignment, and promising results are obtained. When comparing our automatic alignment with that of an expert we arrived at complete agreement for the more difficult case of partial alignment of sectional slab materials of five rats with an atlas (a whole brain of rat). This perfect alignment was only based on the surface structure for our procedure, whereas it was based on the staining and the external and internal structures for the expert.

A standard local coordinate system for multipole refinements of the estrogen core structure

A comparative charge density study on a series of estrogen derivatives has been initiated. The study utilizes the Hansen–Coppens atom-centred multipole model to describe the valence electron density distribution. Direct comparison of the population parameters for each estrogen after the respective multipole refinements requires standardization of the atom-centred local coordinate systems. Such a standard coordinate system for the common estrogen core is reported, taking advantage of the shape of those multipoles which have the spatial characteristics ofsp2andsp3hybrid orbitals. Additionally, populating these principal multipoles at the beginning stage of the refinements improves the stability of these large highly correlated calculations.

Advances in biomolecular simulations: methodology and recent applications.

Molecular dynamics simulations are widely used today to tackle problems in biochemistry and molecular biology. In the 25 years since the first simulation of a protein computers have become faster by many orders of magnitude, algorithms and force fields have been improved, and simulations can now be applied to very large systems, such as protein-nucleic acid complexes and multimeric proteins in aqueous solution. In this review we give a general background about molecular dynamics simulations, and then focus on some recent technical advances, with applications to biologically relevant problems.

A New Terrain-Following Vertical Coordinate Formulation for Atmospheric Prediction Models

Most numerical weather prediction models rely on a terrain-following coordinate framework. The computational mesh is thus characterized by inhomogeneities with scales determined by the underlying topography. Such inhomogeneities may affect the truncation error of numerical schemes. In this study, a new class of terrainfollowing coordinate systems for use in atmospheric prediction models is proposed. Unlike conventional systems, the new smooth level vertical (SLEVE) coordinate yields smooth coordinates at mid- and upper levels. The basic concept of the new coordinate is to employ a scale-dependent vertical decay of underlying terrain features. The decay rate is selected such that small-scale topographic variations decay much faster with height than their large-scale counterparts. This generalization implies a nonlocal coordinate transformation. The new coordinate is tested and compared against standard sigma and hybrid coordinate systems using an idealized advection test. It is demonstrated that the presence of coordinate transformations induces substantial truncation errors. These are critical for grid inhomogeneities with wavelengths smaller than approximately eight grid increments, and may overpower the regular-grid truncation error of the underlying finite-difference approximation. These results are confirmed by a theoretical analysis of the truncation error. In addition, the new coordinate is tested in idealized and real-case numerical experiments using a nonhydrostatic model. The simulations using the new coordinate yield a substantial reduction of small-scale noise in dynamical and thermodynamical model fields.