Symmetric Displacement Research Articles

Unforeseen challenge: bilateral, spontaneous, symmetrical displacement of toric implantable collamer lens: case report

Introduction: The phakic intraocular lenses represent a significant advancement in refractive correction particularly in patients for whom conventional procedures such as laser in situ keratomileusis (LASIK) are contraindicated. To our knowledge, although studies have extensively documented the occurrence and management of implantable collamer lens (ICL) rotation, spontaneous displacement of the ICL has not yet been documented. In this article, we present an interesting case of bilateral ICL displacement. Patient and Clinical Findings: After undergoing bilateral ICL surgery, the patient presented with blurring of vision the next day. On examination, there was symmetrical bilateral displacement of the ICL despite having implanted the maximum size of this lens. Diagnosis, Intervention, and Outcomes: After discussion and analysis, a bilateral explantation of the ICL was performed. Conclusions: Despite taking into consideration all the essential anterior segment parameters for ICL size calculation, there can still be a possibility of ICL displacement.

Maximum likelihood phylogeographic inference of cell motility and cell division from spatial lineage tracing data.

Recently developed spatial lineage tracing technologies induce somatic mutations at specific genomic loci in a population of growing cells and then measure these mutations in the sampled cells along with the physical locations of the cells. These technologies enable high-throughput studies of developmental processes over space and time. However, these applications rely on accurate reconstruction of a spatial cell lineage tree describing both past cell divisions and cell locations. Spatial lineage trees are related to phylogeographic models that have been well-studied in the phylogenetics literature. We demonstrate that standard phylogeographic models based on Brownian motion are inadequate to describe the spatial symmetric displacement (SD) of cells during cell division. We introduce a new model-the SD model for cell motility that includes symmetric displacements of daughter cells from the parental cell followed by independent diffusion of daughter cells. We show that this model more accurately describes the locations of cells in a real spatial lineage tracing of mouse embryonic stem cells. Combining the spatial SD model with an evolutionary model of DNA mutations, we obtain a phylogeographic model for spatial lineage tracing. Using this model, we devise a maximum likelihood framework-MOLLUSC (Maximum Likelihood Estimation Of Lineage and Location Using Single-Cell Spatial Lineage tracing Data)-to co-estimate time-resolved branch lengths, spatial diffusion rate, and mutation rate. On both simulated and real data, we show that MOLLUSC accurately estimates all parameters. In contrast, the Brownian motion model overestimates spatial diffusion rate in all test cases. In addition, the inclusion of spatial information improves accuracy of branch length estimation compared to sequence data alone. On real data, we show that spatial information has more signal than sequence data for branch length estimation, suggesting augmenting lineage tracing technologies with spatial information is useful to overcome the limitations of genome-editing in developmental systems. The python implementation of MOLLUSC is available at https://github.com/raphael-group/MOLLUSC.

A Geometrical Study about the Biparametric Family of Anomalies in the Elliptic Two-Body Problem with Extensions to Other Families

In the present paper, we efficiently solve the two-body problem for extreme cases such as those with high eccentricities. The use of numerical methods, with the usual variables, cannot maintain the perihelion passage accurately. In previous articles, we have verified that this problem is treated more adequately through temporal reparametrizations related to the mean anomaly through the partition function. The biparametric family of anomalies, with an appropriate partition function, allows a systematic study of these transformations. In the present work, we consider the elliptical orbit as a meridian section of the ellipsoid of revolution, and the partition function depends on two variables raised to specific parameters. One of the variables is the mean radius of the ellipsoid at the secondary, and the other is the distance to the primary. One parameter regulates the concentration of points in the apoapsis region, and the other produces a symmetrical displacement between the polar and equatorial regions. The three most used geodesy latitude variables are also studied, resulting in one not belonging to the biparametric family. However, it is in the one introduced now, which implies an extension of the biparametric method. The results obtained using the method presented here now allow a causal interpretation of the operation of numerous reparametrizations used in the study of orbital motion.

Simulation and Experimental Study of Non-Resonant Vibration-Assisted Lapping of SiCp/Al.

SiCp/Al is a difficult-to-machine material that makes it easy to produce surface defects during machining, and researchers focus on reducing the surface defects. Vibration-assisted machining technology is considered an effective method to reduce surface defects by changing the trajectory and contact mode of the abrasive. Aiming at the problem of SiCp/Al processing technology, a vibration-assisted lapping device (VLD) is designed, and elliptical motion is synthesized by a set of parallel symmetrical displacement output mechanisms. The working parameters of the device were tested by simulation and experiment, and the lapping performance was verified. Then, the effects of removal characteristics and process parameters on surface roughness and lapping force were analyzed by simulation and experiment. Simulation and experimental results show that frequency and amplitude that are too low or too high are not conducive to the advantages of NVL. The best surface quality was 54 nm, obtained at A = 8 μm and f = 850 Hz.

A Laser Triangulation Displacement Sensor Based on a Cylindrical Annular Reflector

The ellipticity of the spot caused by laser jitter has a significant effect on the measurement accuracy of the traditional laser triangulation method. In order to overcome the influence of laser characteristics on measurement and improve the accuracy of displacement measurement, this paper proposes a measurement model for a laser displacement sensor based on a cylindrical annular reflector. A physical prototype is designed through parameter optimization using NSGA-II, and a two-step detection algorithm is proposed for the imaging ring of the prototype. The algorithm performs contour thinning after rough positioning of the imaging annular ring, and then performs precise detection. Through physical experiments, it is verified that the repeatability error of this method can reach below 0.02%, and the accuracy is significantly improved compared to traditional laser triangulation displacement sensors. Meanwhile, the measurement results of displacement show linearity. The optical path design of this sensor is simpler than the previously proposed rotational symmetrical laser triangulation displacement sensor, which has good application prospects.

Raman study of layered breathing kagome lattice semiconductor Nb3Cl8

Niobium chloride (Nb3Cl8) is a layered two-dimensional semiconducting material with many exotic properties including a breathing kagome lattice, a topological flat band in its band structure, and a crystal structure that undergoes a structural and magnetic phase transition at temperatures below 90 K. Despite being a remarkable material with fascinating new physics, the understanding of its phonon properties is at its infancy. In this study, we investigate the phonon dynamics of Nb3Cl8 in bulk and few layer flakes using polarized Raman spectroscopy and density-functional theory (DFT) analysis to determine the material’s vibrational modes, as well as their symmetrical representations and atomic displacements. We experimentally resolved 12 phonon modes, five of which are A 1g modes while the remaining seven are Eg modes, which is in strong agreement with our DFT calculation. Layer-dependent results suggest that the Raman peak positions are mostly insensitive to changes in layer thickness, while peak intensity and full width at half maximum are affected. Raman measurements as a function of excitation wavelength (473–785 nm) show a significant increase of the peak intensities when using a 473 nm excitation source, suggesting a near resonant condition. Temperature-dependent Raman experiments carried out above and below the transition temperature did not show any change in the symmetries of the phonon modes, suggesting that the structural phase transition is likely from the high temperature P 1 phase to the low-temperature R phase. Magneto-Raman measurements carried out at 140 and 2 K between −2 and 2 T show that the Raman modes are not magnetically coupled. Overall, our study presented here significantly advances the fundamental understanding of layered Nb3Cl8 material which can be further exploited for future applications.

Design and compression-induced bandgap evolution of novel polygonal negative stiffness metamaterials

The paper proposes a novel polygonal negative stiffness (NS) metamaterial composed of folded beams and stiffening walls, which exhibits excellent performance in attenuating waves over a broad frequency range and shows compression-induced bandgap evolution characteristics. Dispersion relation and bandgaps for the propagation of elastic waves in NS metamaterials are calculated utilizing a semi-analytical periodic spectral method (PS-SAFE). The results demonstrate that broadband bandgaps can be achieved in the proposed polygonal NS metamaterials. Mode analysis and transmission spectrum are utilized to explain the underlying mechanisms of wave attenuation. Furthermore, appropriate deformation conditions are applied to the NS metamaterials to realize compression-induced bandgap evolution, which shows that compression-induced configuration variations significantly impact the frequency range and bandwidth of the bandgaps. As the deformation increases, folded beams enter the elastic instability stage, and the internal stress change strongly influence the vibration displacement modes, leading to various symmetric and antisymmetric displacement vibration modes within a similar frequency range, forming low-frequency broadband bandgaps. This work provides valuable insights into the design of advanced materials for low-frequency broadband wave attenuation.

Angular correlations on causally-coherent inflationary horizons

We develop a model for correlations of cosmic microwave background (CMB) anisotropy on the largest angular scales, based on standard causal geometrical relationships in slow-roll inflation. Unlike standard models based on quantized field modes, it describes perturbations with nonlocal directional coherence on spherical boundaries of causal diamonds. Causal constraints reduce the number of independent degrees of freedom, impose new angular symmetries, and eliminate cosmic variance for purely angular 2-point correlations. Distortions of causal structure from vacuum fluctuations are modeled as gravitational memory from randomly oriented outgoing and incoming gravitational null shocks, with nonlocally coherent directional displacements on curved surfaces of causal diamonds formed by standard inflationary horizons. The angular distribution is determined by axially symmetric shock displacements on circular intersections of the comoving sphere that represents the CMB photosphere with other inflationary horizons—those centered on it, and those that pass through an observer’s world line. Displacements on thin spheres at the end of inflation have a unique angular power spectrum that approximates the standard expectation on small angular scales, but differs substantially at large angular scales due to horizon curvature. For a thin sphere, the model predicts a universal angular correlation function with an exact ‘causal shadow’ symmetry, , and significant large-angle parity violation. We apply a rank statistic to compare models with WMAP and Planck satellite data, and find that a causally-coherent model with no shape parameters or cosmic variance agrees with the measured better than a large fraction () of standard model realizations. Model-independent tests of holographic causal symmetries are proposed.

Construction-Monitoring Analysis of a Symmetrical Rigid Frame Tied Steel Box Arch Bridge in Southwest China Based on Segmental Assembly Technique

Tied steel box arch bridges are increasingly being used due to their attractive appearance, high load-bearing capacity, and good stress performance. Their construction involves multiple processes and factors. Construction monitoring can ensure that such a bridge remains in its intended stress and linear states during and after construction. This helps to minimize deviations from the design state at every stage of construction. Using the segmental assembly construction technique, this study conducted construction monitoring of the alignment and force at each stage of the reconstruction of bridges using MIDAS Civil software. The construction monitoring analysis indicated that the arch rib and lattice beam were correctly placed, thereby meeting the specified requirements for arch rib closure. Displacement errors between the measured and theoretical values at each stage of construction fell within an allowable range, resulting in overall smooth bridge alignment. The measured stress in the main arch and the lattice beam generally corresponded to the theoretical stress derived from the control section stress of the entire bridge. The deviation between the cable force of the suspender and the tie rod and theoretical value fell within 10%, indicating good stress reserve. The symmetrical monitoring points in the analyzed rigid-frame tied steel box arch bridges exhibited symmetrical displacement, stress, and cable force results under various working conditions. This observation further confirms the effectiveness of construction monitoring using the segmental assembly technique.

A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

A locking-free stabilized embedded discontinuous Galerkin method for linear elasticity with strong symmetric stress and continuous displacement trace approximation

The influence of equine hoof conformation on the initiation and progression of laminitis.

The health and performance of horses are significantly affected by diseases associated with the hoof. Laminitis is a critical hoof disease that causes pain and, potentially, severe hoof and bone pathology. To generate an equine hoof finite element (FE) model to investigate the impact of normal and toe-in hoof conformations on the degeneration (decrease in elastic modulus) of the laminar junction (LJ), as occurs in chronic laminitis. Computer software modelling. A hoof FE model was generated to investigate the biomechanics of hoof laminitis. A 3D model, consisting of nine components, was constructed from computed tomography scans of an equine left forelimb hoof. The model was loaded with 100 cycles of trotting. Two different centres of pressure (COP) paths representing normal and toe-in conformations were assigned to the model. LJ injury was modelled by degenerating the tissue's elastic modulus in the presence of excessive maximum principal stresses. FE models successfully showed findings similar to clinical observations, confirming third phalanx (P3) dorsal rotation, a symmetric distal displacement of the P3 (2 mm at the lateral and medial sides) in the normal model, and an asymmetric distal displacement of the P3 (4 mm at the lateral and 1.5 mm at the medial side) in the toe-in model. The proximal distance between P3 and the ground after LJ degeneration in the current model was significantly different from experimental measurements from healthy hooves (P< 0.01). The inability to account for variations in population geometry and approximation of boundary conditions and system relations were the limitations of the current study. The distribution of LJ tissue degeneration was symmetric at the quarters in the normal hoof and in comparison, there was a lateral concentration of degeneration in the toe-in model.

Design and Optimization for a New XYZ Micropositioner with Embedded Displacement Sensor for Biomaterial Sample Probing Application.

An XYZ compliant micropositioner has been widely mentioned in precision engineering, but the displacements in the X, Y, and Z directions are often not the same. In this study, a design and optimization for a new XYZ micropositioner are developed to obtain three same displacements in three axes. The proposed micropositioner is a planar mechanism whose advantage is a generation of three motions with only two actuators. In the design strategy, the proposed micropositioner is designed by a combination of a symmetrical four-lever displacement amplifier, a symmetrical parallel guiding mechanism, and a symmetrical parallel redirection mechanism. The Z-shaped hinges are used to gain motion in the Z-axis displacement. Four flexure right-circular hinges are combined with two rigid joints and two flexure leaf hinges to permit two large X-and-Y displacements. The symmetrical four-lever displacement amplifier is designed to increase the micropositioner's travel. The displacement sensor is built by embedding the strain gauges on the hinges of the micropositioner, which is developed to measure the travel of the micropositioner. The behaviors and performances of the micropositioner are modeled by using the Taguchi-based response surface methodology. Additionally, the geometrical factors of the XYZ micropositioner are optimized by teaching-learning-based optimization. The optimized design parameters are defined with an A of 0.9 mm, a B of 0.8 mm, a C of 0.57 mm, and a D of 0.7 mm. The safety factor gains 1.85, while the displacement achieves 515.7278 µm. The developed micropositioner is a potential option for biomedical sample testing in a nanoindentation system.

The stability of low-pitched von Mises trusses with horizontal elastic supports

Abstract. Purpose. The work’s aim is to study the horizontal supports stiffness impact, which simulate the conditions for supporting the domes upper tier on the von Mises trusses' stability. Methodology. A three-hinged truss' deformed scheme under applying a concentrated vertical load in the ridge joint was considered. An analytical method was used to obtain a generalized equation for the three-hinged trusses' stability criterion to determine the critical load depending on the design system's parameters such as the rods' inclination angle, the rods' stiffness, and the horizontal elastic supports stiffness. A two transcendental equations' system for the dependence of the load on vertical and horizontal displacements taking into account the rods' compression was obtained. Such equations' system's analytical solution through a generalized parameter - a variable rods' angle tangent, made it possible to obtain one equation for the dependence of the vertical load on the vertical and symmetric horizontal supports' displacement. The truss' stability numerical studies were carried out depending on the structure's design geometry. Findings. An analytical expression of the dependence for the load on the structure, which was reduced to the rod’s stiffness depending on the rods’ angle to the horizontal stiffness of the supports, was obtained. The low-pitched double-rod three-hinged trusses' nonlinear deformation nature depending on the elastic supports' stiffness and the rods' angle was confirmed. It was found that with the two-rod low-pitched three-hinged systems’ nonlinear deformation nature the ridge joint's snap-through effect takes place. It was found that the relative reduced critical load value decreases along with the rods' inclination angle decrease depending on the horizontal supports' stiffness. Scientific innovation. On the theoretical studies basis of the three-hinged two-rod low-pitched trusses with elastic horizontal supports deformed scheme a generalized analytical equation for the such systems' solution was obtained. The generalized analytical solution models the dome system annular elements stiffness through the horizontal supports' stiffness and determines the general lower tier elements stiffness effect on the dome uppermost tier structural system stability. Practical value. The obtained analytical equation makes it possible to determine the dome annular elements rational design parameters to ensure the upper tier stability.

Influence of optical mode polarization state on the Brillouin gain spectrum in optical microfibers

During the stimulated Brillouin scattering (SBS) process, when the two H E 11 modes in the pump light and scattered light have different polarization states, between which is an angle θ , the Brillouin gain spectrum characteristics in a microfiber are studied in detail. The difference of θ directly changes the generated optical force distribution. When 0 ≤ θ ≤ π / 2 , for the T R 0 n acoustic mode in forward SBS and the L 0 n acoustic mode in backward SBS, the corresponding Brillouin gain values have a clear cosine-like functional relationship with θ . Considering the change of optical force, the T R 0 n and L 0 n acoustic modes with symmetrical displacement distributions of center circles are the key features to realize the change of gain with θ . The characteristics of gain value with θ may provide interesting theoretical enlightenment for Brillouin applications involving angles, such as Brillouin sensors and acousto-optic modulators.

Nonlocal active metamaterial with feedback control for tunable bandgap and broadband nonreciprocity

In this paper, a nonlocal active metamaterial with feedback control is proposed. For a metamaterial with a symmetric feedback signal, the tunable bandgap and negative effective stiffness are discussed. Symmetric displacement feedback control significantly broadens the bandgap, and combined with velocity feedback control can rapidly attenuate the vibration amplitude. In the metamaterial with an asymmetric feedback signal, the spatial symmetries of the control force are broken by the asymmetrical feedback signal. The non-Hermitian skin effects are achieved by asymmetrical feedback signal. The modes of localized are determined by topological properties with winding number, and the asymmetrical feedback control gain can change the topological properties with winding number. The imaginary parts of the wavenumber are also asymmetrically distributed in space. Theoretical analysis shows that nonlocal active metamaterials with asymmetric feedback signals can achieve nonreciprocal wave propagation and directional amplification across a broad frequency range. Numerical results verify that this metamaterial possesses the characteristics of nonreciprocal wave propagation and directional amplification. The nonlocal active metamaterials in this paper can not only achieve superior bandgap tuning, but also nonreciprocal wave propagation and directional amplification. Function switching between bandgap control and nonreciprocity can be realized by switching the feedback control signal.

Mechanism of Triphosphate Hydrolysis by Human MAT2A at 1.07 Å Resolution.

Human methionine adenosyltransferase MAT2A provides S-adenosyl-l-methionine (AdoMet) for methyl-transfer reactions. Epigenetic methylations influence expression patterns in development and in cancer. Transition-state analysis and kinetic studies have described the mechanism of AdoMet and triphosphate formation at the catalytic site. Hydrolysis of triphosphate to pyrophosphate and phosphate by MAT2A is required for product release and proceeds through a second chemical transition state. Crystal structures of MAT2A with analogues of AdoMet and pyrophosphate were obtained in the presence of Mg2+, Al3+, and F-. MgF3- is trapped as a PO3- mimic in a structure with malonate filling the pyrophosphate site. NMR demonstrates that MgF3- and AlF30 are bound by MAT2A as mimics of the departing phosphoryl group. Crystallographic analysis reveals a planar MgF3- acting to mimic a phosphoryl (PO3-) leaving group. The modeled transition state with PO3- has the phosphorus atom sandwiched symmetrically and equidistant (approximately 2 Å) between a pyrophosphate oxygen and the water nucleophile. A catalytic site arginine directs the nucleophilic water to the phosphoryl leaving group. The catalytic geometry of the transition-state reconstruction predicts a loose transition state with characteristics of symmetric nucleophilic displacement.

A Few Points of the Engineering Logic Discussed in ITER EDA on Evaluation of Halo- and AVDE-Induced Loads in Tokamaks

All tokamaks are designed to withstand a certain number of energetic electromagnetic (EM) transients caused by uncontrolled terminations of plasma pulses, including symmetric and asymmetric plasma vertical displacement events: VDEs and AVDEs. These events generate significant pulsed EM loads in all conductive components and coils. Axially symmetric transient EM loads induced by VDEs without Halo current have been calculated well since the 1980s; however, Halo-related EM load components and lateral loads associated with AVDEs still cause discussions. The author worked on fast plasma and EM transients in tokamaks quite a while ago then deviated to other areas but has been keeping track of the topic since. He is aware of discussions of the modelling of Halo currents and of significant scatter present in current estimates for AVDE-induced lateral loads and contends that some points of engineering logic formulated earlier on this topic may help reduce these uncertainties. This article summarises a few points of the engineering understanding developed in informal discussions within the ITER EDA team with the purpose to preserve these points for all tokamak developments.

Asymmetric serviceability limit states of symmetrically loaded segmental tunnel rings: Hybrid analysis of real-scale tests

Serviceability limit states (SLS) of segmental circular tunnel rings, subjected to symmetric loading, may experience asymmetric deformations. This is investigated herein, based on real-scale experiments and structural analysis. Single segmental rings, consisting of six tubbings and six joints, were subjected to 24 point loads, simulating ground pressure until convergence-related SLS were reached. Structural analysis is based on transfer relations, representing analytical solutions of the linear theory of thin circular arches. One symmetric mode and two antisymmetric modes of rigid-body displacements of the investigated segmental rings are described analytically. The vertical-to-horizontal convergence ratio of the symmetric mode is compared with convergence ratios, measured close to the SLS obtained in the tests. This allows for categorization of the tests as symmetric and asymmetric problems. The structural behavior of two asymmetric tests is analyzed by means of a generalized hybrid method. The term “hybrid” applies insofar as the external loading and the data from monitoring of the displacements during the tests are used as input. It is “generalized” in order to allow for consideration of the asymmetric structural behavior, thus abandoning the restriction to symmetry. The relative rotations of the joints are determined such that they refer to symmetric and antisymmetric rigid-body displacements and that the simulated convergences reproduce the measured values. Applying this concept to the two tests, it is shown that the asymmetry develops in a progressive rather than in a stepwise fashion. It refers to different forms of structural behavior of joints that nominally transmit the same normal forces and bending moments. It is concluded that the asymmetry results from small initial imperfections rather than from asymmetric external loading.

Accuracy of three digital scanning methods for complete-arch tooth preparation: An in vitro comparison

Statement of problemThe accuracy of digital scanning for complete dental arch and implant-supported complete-arch restorations has been reported. However, research addressing the accuracy of digital scanning methods for complete-arch tooth preparation is lacking. PurposeThe purpose of this in vitro study was to compare the accuracy of intraoral scanning, impression scanning, and cast scanning for complete-arch preparation. Material and methodsMaxillary and mandibular jaw typodonts with 28 teeth prepared for complete crowns were used as reference casts and digitized as reference data sets with a desktop scanner. Three digital scanning methods were applied. First, the reference casts were each scanned 10 times with an intraoral scanner to generate the intraoral scanning group data sets. Second, the reference casts were each captured 10 times by using polyvinyl siloxane impression material, and the impressions were scanned with a desktop scanner to generate the impression scanning group data sets. Third, the impressions obtained in the impression scanning group were used to make gypsum casts which were then digitized with a desktop scanner to generate the cast scanning group data sets. Accuracy was determined by trueness and precision. Three-dimensional deviations of the prepared arches and anterior and posterior segments were measured from root mean square values and depicted on color-difference maps. Differences among test groups were analyzed by using a 1-way ANOVA and the post hoc Bonferroni test for normally distributed data or the Kruskal-Wallis test with Bonferroni correction for non-normally distributed data (α=.05). ResultsThe trueness of the maxillary arch was significantly higher in the impression scanning group than in the cast scanning and intraoral scanning groups (P<.05), but no significant differences were found among the 3 groups of the mandibular arch (P>.05). The precision of both arches was significantly higher in the impression scanning and intraoral scanning groups than in the cast scanning group (P<.05). Color maps showed horizontal symmetrical displacement in the intraoral scanning group relative to the reference data sets and within-group unilateral distal-end distortion. Irregular arch deformations were noted in the impression scanning group, and buccal and occlusal expansion occurred in the anterior-posterior direction in the cast scanning group. Pooled data for anterior teeth indicated that the trueness was lowest in the intraoral scanning group; however, that for the maxillary anterior teeth did not differ, while that for the mandibular anterior teeth differed significantly among groups (P<.05). For the posterior teeth, deviation was the lowest in the impression scanning group, and significant differences were noted in both arches among the 3 groups (P<.05). ConclusionsOf the methods tested, impression scanning was the most accurate for the creation of a digital cast of a complete prepared arch.

Analysis of field free region formed by parametric positioning of a magnet pair for targeted magnetic hyperthermia

One of the challenges that arise in the practical applications of magnetic fluid hyperthermia (MFH) is the limited control of magnetic nanoparticle oscillations. In this study, we investigated to manipulate field free region (FFR) form and location by symmetric and asymmetric displacements of a magnet pair (MP). Finite element method (FEM) simulation was used to predict gradient patterns (GPs) in the workspace. An experiment platform was produced and point probe measurements are taken. It is observed that FFR form and position can be manipulated with parametric distance and angle changes. FFR can shrink and its form can be transformed to the linelike or point-like areas. Focus of FFR can be moved off-center, and it can be directed to different parts of the target object. The mapping of GP produced by a MP for the use of targeted MFH is discussed for the first time in this study. And the findings provide insight into which GP is appropriate in which situations in targeted MFH.