Surgical Planning and Additive Manufacturing of an Anatomical Model: A Case Study of a Spine Surgery

3D scanning technologies have promising solutions for medical needs such as anatomical models, biocompatible implants, and orthotic/prosthetic models. Although virtual presurgical planning offers more precise results, it may not be applied in every hospital because of the high costs. The aim of this study is to assess the accuracy of the suggested low-cost and effective surgical planning method by means of additive manufacturing to increase success rate of each surgery. In this study, a full spine model of a scoliosis patient was acquired and reconstructed in MIMICS software using different filters and parameters. Therefore, a comparison in terms of geometrical errors among each model was performed based on a reference model. Subsequently, patient-specific full spine model was manufactured using a three-dimensional printing method (fused deposition modeling) and utilized before the surgery. 3D surgical model reconstruction parameters such as wrap tool, binomial blur, and curvature flow filters produced high geometrical errors, while mean filter produced the lowest geometrical error. Furthermore, similarity results of the curvature flow and discrete Gaussian filters were close to mean filter. Smooth tool and mean filter produced almost the same volume of the reference model. Consequently, an ideal protocol for surgical planning of a spine surgery is defined with measurable accuracy. Thus, success rate of a spine surgery may be increased especially for the severe cases owing to the more accurate preoperative review: operability

On a coupled system of generalized hybrid pantograph equations involving fractional deformable derivatives

The goal of this work is to study the existence of a unique solution and the Ulam-Hyers stability of a coupled system of generalized hybrid pantograph equations with fractional deformable derivatives. Our main tool is Banach's contraction principle. The paper ends with an example to support our results

Solving a Boundary Value Problem via Fixed-Point Theorem on ®-Metric Space

In this paper, we prove the fixed-point theorem for rational contractive mapping on ®-metric space. Additionally, an Euclidean metric space with a binary relation example and an application to the first-order boundary value problem are given. Moreover, the obtained results generalize and extend some of the well-known results in the literature.The authors thank the Basque Government for its support of this work through Grant IT1207-19

Fixed-Point Theorems for Nonlinear Contraction in Fuzzy-Controlled Bipolar Metric Spaces

In this paper, we introduce the concept of fuzzy-controlled bipolar metric space and prove some fixed-point theorems in this space. Our results generalize and expand some of the literature’s well-known results. We also provide some applications of our main results to integral equations.The authors thank the Basque Government for its support of this study through grant IT1555-22

Digital fixed points, approximate fixed points, and universal functions

[EN] A. Rosenfeld introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approximate fixed points of digitally continuous functions. Among these are several results concerning the relationship between universal functions and the approximate fixed point property (AFPP).Boxer, L.; Ege, O.; Karaca, I.; Lopez, J.; Louwsma, J. (2016). Digital fixed points, approximate fixed points, and universal functions. Applied General Topology. 17(2):159-172. doi:10.4995/agt.2016.4704.SWORD15917217

Relative Homology Groups of Digital Images

Some properties of the Euler characteristics for digital images are given. We also present reduced homology groups for digital images. The main purpose is to obtain some differences between notions in digital topology and algebraic topology

Digital Co-Hopf Spaces

EGE, OZGUR/0000-0002-3877-2714WOS:000607561100018In this work, we deal with co-Hopf space structure of digital images. We prove that a pointed digital image having the same digital homotopy type as a digital co-Hopf space is itself a digital co-Hopf space. We conclude that a kappa-deformation retract of a digital co-Hopf space is a digital co-Hopf space. We also show that the digital equivalences are digital co-Hopf homomorphisms

Image restoration via Picard's and Mountain-pass Theorems

In this work, we present existence results for some problems which arise in image pro-cessing namely image restoration. Our essential tools are Picard's fixed point theorem for a strict contraction and Mountain-pass Theorem for critical point