Curvature Mismatch Research Articles

A computational study of artery curvature and endograft oversize influence on seal zone behavior in endovascular aortic repair

Thoracic endovascular aortic repair (TEVAR) is a minimally invasive procedure involving the placement of an endograft inside the dissection or an aneurysm to direct blood flow and prevent rupture. A significant challenge in endovascular surgery is the geometrical mismatch between the endograft and the artery, which can lead to endoleak formation, a condition where blood leaks between the endograft and the vessel wall. This study uses computational modeling to investigate the effects of artery curvature and endograft oversizing, the selection of an endograft with a larger diameter than the artery, on endoleak creation. Finite element analysis is employed to simulate the deployment of endografts in arteries with varying curvature and diameter. Numerical simulations are conducted to assess the seal zone and to quantify the potential endoleak volume as a function of curvature and oversizing. A theoretical framework is developed to explain the mechanisms of endoleak formation along with proof-of-concept experiments. Two main mechanisms of endoleak creation are identified: local buckling due to diameter mismatch and global buckling due to centerline curvature mismatch. Local buckling, characterized by excess graft material buckling and wrinkle formation, increases with higher levels of oversizing, leading to a larger potential endoleak volume. Global buckling, where the endograft bends or deforms to conform to the centerline curvature of the artery, is observed to require a certain degree of oversizing to bridge the curvature mismatch. This study highlights the importance of considering both curvature and diameter mismatch in the design and clinical use of endografts. Understanding the mechanisms of endoleak formation can provide valuable insights for optimizing endograft design and surgical planning, leading to improved clinical outcomes in endovascular aortic procedures.

Detecting radius of curvature (ROC) mismatch among primary mirror (PM) segments.

A segmented primary mirror (PM) is an efficient solution to the problems of a monolithic PM manufacture, testing, transportation, and launch. However, the problem of the radius of curvature (ROC) matching among PM segments will arise, which if not solved will seriously degrade the final imaging quality of the system. Accurately detecting ROC mismatch among PM segments from the wavefront map is of crucial importance for efficiently correcting this kind of manufacturing error, while currently there are few related studies. Based on the inherent relation between the PM segment's ROC error and corresponding sub-aperture defocus aberration, this paper proposes that the ROC mismatch can be accurately estimated from the sub-aperture defocus aberration. Secondary mirror (SM) lateral misalignments will influence the accuracy of estimating ROC mismatch. A strategy is also proposed to reduce the influence of SM lateral misalignments. Detailed simulations are performed to demonstrate the effectiveness of the proposed method for detecting ROC mismatch among PM segments. This paper paves a road for detecting ROC mismatch using image-based wavefront sensing methods.

Anatomic Factors Associated With Osteochondral Allograft Matching for Trochlear Cartilage Defects: A Computer-Simulation Study

Background: Articular step-off between the donor and recipient in osteochondral allograft transplant has been shown to alter contact pressures. Currently, commercial allograft donor selection is primarily based on simple anatomic parameters such as trochlear length, trochlear width, and tibial width. Purpose: To identify anatomic factors associated with optimal graft matching by using a 3-dimensional simulation model. Study Design: Descriptive laboratory study. Methods: Computed tomography images of 10 cadaveric trochlear specimens were obtained to generate 3-dimensional models. Circular defects were created virtually in the recipient trochleae at both superolateral (18.0 mm and 22.5 mm) and central (18.0 mm, 22.5 mm, 30.0 mm) locations. The donor models were virtually projected onto the defect models, and the most optimal graft from any location of the donor specimen was selected. Cartilage incongruity, subchondral bone incongruity, and peripheral articular step-off were calculated for each graft-defect combination. Linear regression models were generated to identify predictors of incongruity, step-off, and the effect of sulcus and sagittal angle mismatch. Akaike information criterion–driven stepwise regression models were generated to identify multivariate predictors. Results: Ideal matches were found for 100% of superolateral defects but for only 15% to 53% of central defects, depending on the defect size. Multivariate stepwise regression identified laterality (odds ratio [OR], 0.54; P = .081), sulcus angle (OR, 0.79; P < .001), sagittal angle (OR, 0.83; P = .001), lateral radius of curvature (OR, 0.81; P < .001), and medial facet width (OR, 0.86; P = .155) as predictors of ideal graft matching. In central defects with proud grafts, increasing sagittal angle and sulcus angle resulted in significantly (P < .001) increased articular step-off, which became sequentially larger with defect size. Conclusion: Sagittal angle, sulcus angle, and lateral radius of curvature mismatch should be used to determine optimal donor allografts, especially in the setting of large (30-mm) central defects. Increasing sulcus angle and sagittal angle mismatch correlated with increasing step-off in proud grafts, whereas sulcus angle and sagittal angle inconsistently correlated with step-off in recessed grafts. Clinical Relevance: Additional descriptive trochlear measurements should be incorporated into the algorithm for donor selection. These findings can be used to identify acceptable mismatch parameters.

Modified Stoney’s equation with anisotropic substrates undergoing large deformations

Thin film deposition is a key fabrication step in several opto-mechanical and electronics applications. For instance, thin film coatings can act as reflective interfaces, protective coatings or they can be used to modify the thermal behavior of the film-substrate system. For effective design, it is important to understand the deformation of the system in response to residual stresses during thin film deposition. The widely used Stoney’s equation to measure this deformation assumes isotropic elasticity of the substrate together with infinitesimal strains and rotations. In this work we relax both constraints, where we study the deformation of commonly used substrates made of single crystal Si(001) and Si(111) wafers that undergo large rotations. We derive relations between normalized substrate curvature and thin film mismatch strain and validate our analysis with numerical results. The methodology presented can be used for more accurate understanding of a broad range of film-substrate systems in semiconductors.

Binding, Unbinding and Aggregation of Crescent-Shaped Particles on Tubular Membranes

The binding of crescent-shaped nanoparticles (CNPs) on nanoscale tubular membranes is investigated through systematic coarse-grained molecular dynamics simulations of an implicit-solvent model. The CNPs adhere through their concave side to the outer surface of the tubular membrane. The binding/unbinding transitions are found to be irreversible, with the threshold binding energy, Eb, being higher than that of the unbinding threshold, Eu. Furthermore, the difference Eb-Eu increases with increasing either the CNP’s arclength, Lnp, or curvature mismatch, m=Rt/Rnp, where Rnp is the CNP’s radius of curvature and Rt is the tube’s radius. We also investigated the arrangement of a CNP on the tube and found that for m smaller than a Lnp-dependent m∗, the CNP lies perpendicularly to the tubule. However, for m<m∗<1, the CNP is tilted with respect to the tubule’s axis, with the tilt angle that increases with decreasing m. for m>1 (or m<m) and high Lnp, the NPs self-assemble into chains.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes.

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength Lnp or curvature mismatch μ = Rc/Rnp, where Rc and Rnp are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either Lnp or μ. NPs with curvature larger than that of the tubule (μ > 1) lie perpendicularly to the tubule's axis. However, for μ smaller than a specific arclength-dependent mismatch μ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing μ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for μ > 1 and high values of Lnp, the NPs self-assemble into linear chains, and lie side-by-side. For μ < μ* and high Lnp, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Local curvature mismatch may worsen the midterm functional outcomes of osteochondral allograft transplantation.

This study aimed to determine the magnitude of local curvature matching in the sagittal plane between an implanted graft and the condylar region receiving the graft and to analyze its effect on clinical outcomes in patients undergoing osteochondral allograft transplantation (OCA). Patients who underwent knee OCA between 2016 and 2019 without circumferential step-off and were matched with a donor in accordance with the conventional matching process were included. The magnitude of donor-host local curvature matching was measured using postoperative sagittal magnetic resonance imaging data with Syngo (Siemens Medical Solutions, Forchheim, Germany) and GeoGebra (GeoGebra GmbH, Linz, AU) software. In addition to radiological evaluation, ROC analysis was performed to compare the patient-reported outcome measures (PROMs) obtained during the 2-year follow-up period among the patients in the SagA group, who had a graft match in the sagittal plane; SagB group, who had low convexity of the graft in the sagittal plane; and SagC group, who had high convexity of the graft in the sagittal plane in accordance with the determined indices. The study included 27 patients who fulfilled the inclusion criteria, and the mean clinical scores of the SagC group were not statistically significantly higher than those of the other groups at any timepoint during the follow-up. The mean Tegner, IKDC, total KOOS and SF-12 physical and mental health scores of the SagC group were lower than those of the other two groups at various follow-up time points, particularly at month 24 (p < 0.05). There were no significant differences between the SagA and SagB groups in the PROMs at any of the follow-up time points (n.s.). The significant differences observed between the SagC group and the other groups in the mean KOOS scores for function in daily living and function in sport and recreation were also observed between the SagA and SagB groups at the follow-ups (p < 0.05). During OCA, a local curvature mismatch between the donor and the host involving large graft convexity may have a negative impact on midterm clinical outcomes. A preoperative analysis of the convexity relationship between the defect site and the graft region in the hemicondylar allograft to be used may enhance donor-host matching. The local analysis method described in the current study may also facilitate graft supply by ensuring donor-host matching without condyle-side and size matching. III.

Three-dimensional curvature mismatch of the acetabular radius to the femoral head radius is increased in borderline dysplastic hips.

Whether borderline hip dysplasia is pathologic remains unclear. In order to evaluate the three-dimensional joint congruity, this study sought to answer the question: are borderline dysplastic hip curvature mismatch and eccentricity between the acetabulum and the femoral head different from dysplastic or control hips three-dimensionally? The 113 hips, categorized as: dysplastic (LCEA ≤ 20°), 47 hips; borderline (20° ≤ LCEA < 25°), 32 hips; and control (25° ≤ LCEA < 35°), 34 hips; were evaluated. Three-dimensional (3D) femoral and coxal bone models were reconstructed from CT images. Using a custom-written Visual C++ routine, the femoral head and acetabular radii of curvature, and the femoral head and the acetabular curvature center were calculated. Then the ratio of the acetabular radius to the femoral head radius (3D curvature mismatch ratio), and the distance between the acetabular curvature center and the femoral head center (3D center discrepancy distance) were calculated. These indices were compared statistically among the three groups using Tukey’s post hoc test. The mean 3D curvature mismatch ratio in the borderline (1.13 ± 0.05) was smaller than in the dysplasia (1.23 ± 0.08, p < 0.001), and larger than in the control (1.07 ± 0.02, p < 0.001). The mean 3D center discrepancy distance in the borderline (3.2 ± 1.4 mm) was smaller than in the dysplasia (4.8 ± 2.3, p < 0.001) and larger than in the control (1.6 ± 0.7, p < 0.001). These results demonstrated that three-dimensional congruity of the borderline dysplastic hip is impaired, but its incongruity is not as severe as in dysplastic hips. The 3D curvature mismatch ratio and the 3D center discrepancy distance can be valuable signs of joint congruity in patients with borderline dysplasia. However, future studies are necessary to clarify any associations between curvature mismatch and pathogenesis of osteoarthritis in borderline dysplasia.

Sampling moiré method: a tool for sensing quadratic phase distortion and its correction for accurate quantitative phase microscopy.

The advantages of quantitative phase microscopy (QPM) such as label-free imaging with high spatial sensitivity, live cell compatibility and high-speed imaging makes it viable for various biological applications. The measurement accuracy of QPM strongly relies on the shape of the recorded interferograms, whether straight or curved fringes are recorded during the data acquisition. Moreover, for a single shot phase recovery high fringe density is required. The wavefront curvature for the high-density fringes over the entire field of view is difficult to be discerned with the naked eye. As a consequence, there is a quadratic phase aberration in the recovered phase images due to curvature mismatch. In the present work, we have implemented sampling moiré method for real-time sensing of the wavefront curvature mismatch between the object and the reference wavefronts and further for its correction. By zooming out the interferogram, moiré fringes are generated which helps to easily identify the curvature of the fringes. The wavefront curvature mismatch correction accuracy of the method is tested with the help of low temporal coherent light source such as a white light (temporal coherence ∼ 1.6 µm). The proposed scheme is successfully demonstrated to remove the quadratic phase aberration caused due to wavefront mismatch from an USAF resolution target and the biological tissue samples. The phase recovery accuracy of the current scheme is further compared with and found to better than the standard method called principle component analysis. The proposed method enables recording of the corrected wavefront interferogram without needing any additional optical components or modification and also does not need any post-processing correction algorithms. The proposed method of curvature compensation paves the path for a high-throughput and accurate quantitative phase imaging.

Models for membrane curvature sensing of curvature generating proteins

The curvature-sensitive localisation of proteins on membranes is vital for many cell biological processes. Coarse-grained models are routinely employed to study the curvature-sensing phenomena and membrane morphology at the length scale of a few micrometres. Two prevalent phenomenological models exist for modelling the experimental observations of curvature sensing: (1) the spontaneous curvature (SC) model and (2) the curvature mismatch (CM) model, which differ in their treatment of the change in elastic energy due to the binding of proteins on the membrane. In this work, the prediction of sensing and generation behaviour by these two models are investigated using analytical calculations as well as dynamic triangulation Monte Carlo simulations of quasispherical vesicles. While the SC model yields a monotonically decreasing sensing curve as a function of the vesicle radius, the CM model results in a non-monotonic sensing curve. We highlight the main differences in the interpretation of the protein-related parameters in the two models. We further propose that the SC model is appropriate for modelling peripheral proteins employing the hydrophobic insertion mechanism, with minimal modification of membrane rigidity, while the CM model is appropriate for modelling curvature generation using scaffolding mechanism where there is significant stiffening of the membrane due to protein binding.

Properties of Asymmetric Membranes from Coarse Grained Molecular Dynamics Simulations

Biological lipid membranes exhibit compositional asymmetry between the leaflets of the bilayer. This fact leads to membranes which exhibit properties not found in single-component lipid bilayers, such as spontaneous curvature and differential stress. Molecular dynamics simulations can be, and have been utilized to study these effects, but all-atom simulations are relatively slow and size-restrictive compared to more coarse grained models. However, simulation of asymmetric membranes with highly coarse-grained models has been difficult in the past due to the accelerated dynamics of various processes, notably transbilayer lipid motion (flip-flop), which leads to the decay of asymmetric states in simulation before statistically significant measurements can be made. We propose a version of the highly coarse grained Cooke lipid model, gently reparameterized to strongly suppresses flip-flop, and employ it to probe elastic properties of membranes with stress asymmetry and leaflet spontaneous curvature mismatch. We also calculate and present lateral stress profiles for the different cases to illustrate the changes that take place on a local level throughout the bilayer leaflets as a result of asymmetry.

Controllable Bending of Bi-hydrogel Strips with Differential Swelling

Bi-hydrogel strips consisting of a highly swelling layer and a non-swelling layer are investigated in this study, in which the differential swelling capabilities and mismatch strain in the composite structure drive the strips into a bending configuration when being exposed to solvents. A modified analytical model originated from Timoshenko theory on bi-material beam is proposed to predict the swelling-induced bending shape of the bi-hydrogel strips, with explicit relations of bending curvature and mid-span deflection versus mismatch strain. Different sets of experiments were performed to verify the analytical model and its solutions, in which the swelling-induced mismatch strain was systematically tuned by the selection of saline concentration. The broad agreements between the theoretical and experimental results indicate that the modified analytical model can be used to guide the design of morphing elements by modulating layer-by-layer mismatches in gel composites to produce precise and complex shape transformations for practical applications.

Novel Eye Plaque Designs for Brachytherapy of Iris and Ciliary Body Melanoma and the First Clinical Application

Background: While traditional eye plaque brachytherapy can be used for the treatment of iris melanoma, it faces challenges of poor patient tolerability due to cornea-plaque touch caused by radius of curvature mismatch and potential dosimetric inaccuracy from incomplete coverage. We present novel plaque designs and the first clinical application of the plaques for iris melanoma. Methods: Two dome-shaped plaques (EP2132 and EP1930) were designed to vault above the cornea to treat tumors of the iris and ciliary body. Image-based treatment planning of the first 2 clinical cases using the EP2132 plaque covered the tumor base plus a 2 mm margin and the involved ciliary body with at least 75 Gy to the tumor apex. Results: The tumors decreased in size following treatment. The patients tolerated the treatment well. There was no adverse event associated with the traditional iris plaques, such as decreased vision, pain, corneal edema, glaucoma, or cataract. Conclusion: The novel dome-shaped plaques for the treatment of iris melanoma provide effective dose distribution, improved surgical maneuverability, and increased tolerability for the patient. This plaque model can be used to treat iris melanoma of various sizes, configurations, and locations, including the ciliary body. The need for a customized plaque platform for each patient is minimized.

The Binding and Aggregation of Anisotropic Nanoparticles on Cylindrical Lipid Membranes

Golgi and endoplasmic reticulum in eukaryotic cells owe their complex membrane conformations to specialized curvature inducing proteins. Using coarse-grained molecular dynamics simulations, we investigated the aggregation and binding of anisotropically curved nanoparticles to cylindrical lipid membranes that are reminiscent of the BAR-domain containing proteins. Here we consider only the case where the nanoparticle–nanoparticle interaction is repulsive and only the concave surface of the nanoparticle interacts attractively with the lipid head groups. We found that the ability of a nanoparticle to bind to a cylindrical membrane depends on the nanoparticle-lipid interaction strength, mismatch in nanoparticle-membrane curvature, and the nanoparticles's arclength. In particular, we found that the minimum interaction strength required for a single nanoparticle binding increases with mismatch in nanoparticle-membrane curvature or increasing the nanoparticle arclength. Additionally, nanoparticles were found to accommodate a tilt angle on cylindrical membranes having a radius of curvature less that of the bound nanoparticles. This tilt angle is well maintained for nanoparticles with large arclength, while shorter nanoparticles are able to rotationally diffuse more freely. These results are consistent for larger numbers of nanoparticles where they aggregate into various structures depending on nanoparticle-lipid interaction strength, mismatch in nanoparticle-membrane curvature, and the nanoparticle's arclength. This aggregation by many nanoparticle is reminiscent of protein aggregates formed by the BAR-protein family, in spite of the simplicity of our nanoparticles.

Self-assembly of convex particles on spherocylindrical surfaces.

The precise control of assembly and packing of proteins and colloids on curved surfaces has fundamental implications in nanotechnology. In this paper, we describe dynamical simulations of the self-assembly of conical subunits around a spherocylindrical template, and a continuum theory for the bending energy of a triangular lattice with spontaneous curvature on a surface with arbitrary curvature. We find that assembly depends sensitively on mismatches between subunit spontaneous curvature and the mean curvature of the template, as well as anisotropic curvature of the template (mismatch between the two principal curvatures). Our simulations predict assembly morphologies that closely resemble those observed in experiments in which virus capsid proteins self-assemble around metal nanorods. Below a threshold curvature mismatch, our simulations identify a regime of optimal assembly leading to complete, symmetrical particles. Outside of this regime we observe defective particles, whose morphologies depend on the degree of curvature mismatch. To learn how assembly is affected by the nonuniform curvature of a spherocylinder, we also study the simpler cases of assembly around spherical and cylindrical cores. Our results show that both the intrinsic (Gaussian) and extrinsic (mean) curvatures of a template play significant roles in guiding the assembly of anisotropic subunits, providing a rich design space for the formation of nanoscale materials.

Mechanism of Shiga Toxin Clustering on Membranes.

The bacterial Shiga toxin interacts with its cellular receptor, the glycosphingolipid globotriaosylceramide (Gb3 or CD77), as a first step to entering target cells. Previous studies have shown that toxin molecules cluster on the plasma membrane, despite the apparent lack of direct interactions between them. The precise mechanism by which this clustering occurs remains poorly defined. Here, we used vesicle and cell systems and computer simulations to show that line tension due to curvature, height, or compositional mismatch, and lipid or solvent depletion cannot drive the clustering of Shiga toxin molecules. By contrast, in coarse-grained computer simulations, a correlation was found between clustering and toxin nanoparticle-driven suppression of membrane fluctuations, and experimentally we observed that clustering required the toxin molecules to be tightly bound to the membrane surface. The most likely interpretation of these findings is that a membrane fluctuation-induced force generates an effective attraction between toxin molecules. Such force would be of similar strength to the electrostatic force at separations around 1 nm, remain strong at distances up to the size of toxin molecules (several nanometers), and persist even beyond. This force is predicted to operate between manufactured nanoparticles providing they are sufficiently rigid and tightly bound to the plasma membrane, thereby suggesting a route for the targeting of nanoparticles to cells for biomedical applications.

Thermal Annealing Triggers Collapse of Biphasic Supported Lipid Bilayers into Multilayer Islands

The collapse of phase-separating single, supported lipid bilayers, consisting of mixtures of a zwitterionic phospholipid (POPC) and an anionic lipid (DPPA) upon thermal annealing in the presence of ions is examined using a combination of scanning probe, epifluorescence, and ellipsometric microscopies. We find that thermal annealing in the presence of ions in the bathing medium induces an irreversible transition from domain-textured, single supported bilayers to one comprising islands of multibilayer stacks, whose lateral area decays with lamellarity, producing pyramidal staircase "mesa" topography. The higher order lamellae are almost invariably localized above the anionic-lipid rich, gel-phase domains in the parent bilayer and depends on the ions in the bathing medium. The collapse mechanism appears to involve synergistic influences of two independent mechanisms: (1) stabilization of the incipient headgroup-headgroup interface in the emergent multibilayer configuration facilitated by ions in the bath and (2) domain-boundary templated folding. This collapse mechanism is consistent with previous theoretical predictions of topography-induced rippling instability in collapsing lipid monolayers and suggests the role of the mismatch in height and/or spontaneous curvature at domain boundaries in the collapse of phase-separated single supported bilayers.

Experimental measurement of coil-rod-coil block copolymer tracer diffusion through entangled coil homopolymers.

The diffusion of coil-rod-coil triblock copolymers in entangled coil homopolymers is experimentally measured and demonstrated to be significantly slower than rod or coil homopolymers of the same molecular weight. A model coil-rod-coil triblock was prepared by expressing rodlike alanine-rich α-helical polypeptides in E. coli and conjugating coillike poly(ethylene oxide) (PEO) to both ends to form coil-rod-coil triblock copolymers. Tracer diffusion through entangled PEO homopolymer melts was measured using forced Rayleigh scattering at various rod lengths, coil molecular weights, and coil homopolymer concentrations. For rod lengths, L, that are close to the entanglementh length, a, the ratio between triblock diffusivity and coil homopolymer diffusivity decreases monotonically and is only a function of L/a, in quantitative agreement with previous simulation results. For large rod lengths, diffusion follows an arm retraction scaling, which is also consistent with previous theoretical predictions. These experimental results support the key predictions of theory and simulation, suggesting that the mismatch in curvature between rod and coil entanglement tubes leads to the observed diffusional slowing.

Improved interfacial stress analysis of a plated beam

A plated beam is strengthened by bonding a thin plate to the tension face; it often fails because of premature debonding of the thin plate from the original beam in a brittle manner. A sound understanding of the mechanism of such debonding failure is very important for the effective use of this strengthening technique. This paper presents an improved analytical solution for interfacial stresses that incorporates multiple loading conditions simultaneously, including prestress, mechanical and thermal loads, and the effects of adherend shear deformations and curvature mismatches between the beam and the plate. Simply supported beams bonded with a thin prestressing plate and subjected to both mechanical and thermal loading were considered in the present work. The effects of the curvature mismatch and adherend shear deformations of the beam and plate were investigated and compared. The main mechanisms affecting the distribution of interfacial stresses were analyzed. Both the normal and shear stresses were found to be significantly influenced by the coupled effects of the elastic moduli with the ratios <TEX>$E_a/E_b$</TEX> and <TEX>$E_a/E_p$</TEX>.

The transport along membrane nanotubes driven by the spontaneous curvature of membrane components

Intercellular membrane nanotubes (ICNs) serve as a very specific transport system between neighboring cells. The underlying mechanisms responsible for the transport of membrane components and vesicular dilations along the ICNs are not clearly understood. The present study investigated the spatial distribution of anisotropic membrane components of tubular shapes and isotropic membrane components of spherical shapes. Experimental results revealed the preferential distribution of CTB (cholera toxin B)–GM1 complexes mainly on the spherical cell membrane, and cholesterol–sphingomyelin at the membrane leading edge and ICNs. In agreement with previous studies, we here propose that the spatial distribution of CTB–GM1 complexes and cholesterol–sphingomyelin rafts were due to their isotropic and anisotropic shapes, respectively. To elucidate the relationship between a membrane component shape and its spatial distribution, a two-component computational model was constructed. The minimization of the membrane bending (free) energy revealed the enrichment of the anisotropic component along the ICN and the isotropic component in the parent cell membrane, which was due to the curvature mismatch between the ICN curvature and the spontaneous curvature of the isotropic component. The equations of motion, derived from the differentiation of the membrane free energy, revealed a curvature-dependent flux of the isotropic component and a curvature-dependent force exerted on a vesicular dilation along the ICN. Finally, the effects of possible changes in the orientational ordering of the anisotropic component attendant to the transport of the vesicular dilation were discussed with connection to the propagation of electrical and chemical signals.