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Johnson, M. R., P. L. Manning, L. Margetss, P. J. Withers y P. M. Mummery. "Virtual repair of fossil CT scan data". Geological Curator 9, n.º 3 (septiembre de 2010): 193–98. http://dx.doi.org/10.55468/gc228.
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X-ray micro-tomography (XMT) and 3D image-based modelling software has unlocked the ability to digitally repair distorted or broken fossil specimens, thus permitting interpretation of previously unusable finds in finite element analyses (FEA). A fossilized terminal ungual phalanx from the manus of the dromaeosaur Velociraptor mongoliensis (Manchester Museum, University of Manchester, specimen LL.12392) was scanned at the Henry Moseley X-ray Imaging Facility. Inspection of radiographs revealed the Velociraptor manual ungual was broken in several places, previously going unnoticed due to cement repair of the fossil. After conducting a high resolution scan of the ungual the increased sensitivity of the apparatus enabled separation of areas of differing density, in this case the fossilized bone and cement. Image-based modelling software produced by Simpleware (Simpleware Ltd, Rennes Drive, Exeter, EX4 4RN, UK.) allowed slice-by-slice repair in three planes, resulting in a complete, fully stitched 3D digital model of the ungual, whilst maintaining internal cavities and the micron resolution reconstruction of trabecular bone architecture. This software also has the capability to digitally re-inflate specimens that have been compressed during fossilization, restoring skeletons to their original shape and dimension. 3D dissections on geometrically precise reconstructions allow the interpretation of previously unusable specimens and reinterpretation of already described fossils. Further, use of Simpleware software to convert repaired fossils into microstructurally-faithful finite element meshes enable the biomechanical testing of these repaired structures. Testing of fossil structure and function is already underway at the University of Manchester and is adding to our knowledge of the mechanical behaviour of extinct animal biomaterials.
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Pettersen, Fred-Johan y Jan Olav Høgetveit. "From 3D tissue data to impedance using Simpleware ScanFE+IP and COMSOL Multiphysics – a tutorial". Journal of Electrical Bioimpedance 2, n.º 1 (23 de julio de 2019): 13–32. http://dx.doi.org/10.5617/jeb.173.
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Abstract Tools such as Simpleware ScanIP+FE and COMSOL Multiphysics allow us to gain a better understanding of bioimpedance measurements without actually doing the measurements. This tutorial will cover the steps needed to go from a 3D voxel data set to a model that can be used to simulate a transfer impedance measurement. Geometrical input data used in this tutorial are from MRI scan of a human thigh, which are converted to a mesh using Simpleware ScanIP+FE. The mesh is merged with electrical properties for the relevant tissues, and a simulation is done in COMSOL Multiphysics. Available numerical output data are transfer impedance, contribution from different tissues to final transfer impedance, and voltages at electrodes. Available volume output data are normal and reciprocal current densities, potential, sensitivity, and volume impedance sensitivity. The output data are presented as both numbers and graphs. The tutorial will be useful even if data from other sources such as VOXEL-MAN or CT scans are used.
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Kalluri, Lohitha, Bernard Seale, Megha Satpathy, Josephine F. Esquivel-Upshaw y Yuanyuan Duan. "Three-Dimensional Finite Element Analysis of the Veneer—Framework Thickness in an All-Ceramic Implant Supported Fixed Partial Denture". Ceramics 4, n.º 2 (28 de abril de 2021): 199–207. http://dx.doi.org/10.3390/ceramics4020015.
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This study was performed as an adjunct to an existing clinical study to validate the effect of veneer: framework thickness ratio on stress distribution in an implant-supported all-ceramic fixed partial denture. Two commercially available titanium dental implants with corresponding customized abutments and a patient-retrieved all-ceramic fixed partial denture were scanned using a high-resolution micro-CT scanner. Reconstructed 3D objects, along with a simulated bone surface, were incorporated into a non-manifold assembly and meshed simultaneously using Simpleware software (Synopsys Simpleware ScanIP Version P-2019.09; Mountain View, CA). Three such volume meshes (Model A, Model B, Model C) corresponding to veneer: framework thickness ratios of 3:1, 1:1, and 1:3 respectively were created, and exported to a finite element analysis software (ABAQUS). An axial load of 110 N was applied uniformly on the occlusal surfaces to calculate the static stresses and contour plots were generated in the post-processing module. From the data obtained, we observed optimum stress distribution in Model B. Also, the tensile stresses were concentrated in the posterior connector region of the prosthesis in all three models tested. Within the limitations of this study, we can conclude that equal thickness of veneer and framework layers would aid in better stress distribution.
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Cotton, R. T., C. W. Pearce, P. G. Young, N. Kota, A. C. Leung, A. Bagchi y S. M. Qidwai. "Development of a geometrically accurate and adaptable finite element head model for impact simulation: the Naval Research Laboratory–Simpleware Head Model". Computer Methods in Biomechanics and Biomedical Engineering 19, n.º 1 (7 de enero de 2015): 101–13. http://dx.doi.org/10.1080/10255842.2014.994118.
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Romeed, Shihab A., Raheel Malik y Stephen M. Dunne. "Stress Analysis of Occlusal Forces in Canine Teeth and Their Role in the Development of Non-Carious Cervical Lesions: Abfraction". International Journal of Dentistry 2012 (2012): 1–7. http://dx.doi.org/10.1155/2012/234845.
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Non-carious cervical tooth lesions for many decades were attributed to the effects of abrasion and erosion mainly through toothbrush trauma, abrasive toothpaste, and erosive acids. However, though the above may be involved, more recently a biomechanical theory for the formation of these lesions has arisen, and the term abfraction was coined. The aim of this study was to investigate the biomechanics of abfraction lesions in upper canine teeth under axial and lateral loading conditions using a three-dimensional finite element analysis. An extracted human upper canine tooth was scanned byμCT machine (Skyscan, Belgium). TheseμCT scans were segmented, reconstructed, and meshed using ScanIP (Simpleware, Exeter, UK) to create a three-dimensional finite element model. A 100 N load was applied axially at the incisal edge and laterally at 45° midpalatally to the long axis of the canine tooth. Separately, 200 N axial and non-axial loads were applied simultaneously to the tooth. It was found that stresses were concentrated at the CEJ in all scenarios. Lateral loading produced maximum stresses greater than axial loading, and pulp tissues, however, experienced minimum levels of stresses. This study has contributed towards the understanding of the aetiology of non-carious cervical lesions which is a key in their clinical management.
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Mansell, Doyin S., Evelyn G. Frank, Nathaniel S. Kelly, Bruno Agostinho-Hernandez, James Fletcher, Vito D. Bruno, Eva Sammut et al. "Comparison of the within-reader and inter-vendor agreement of left ventricular circumferential strains and volume indices derived from cardiovascular magnetic resonance imaging". PLOS ONE 15, n.º 12 (15 de diciembre de 2020): e0242908. http://dx.doi.org/10.1371/journal.pone.0242908.
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Purpose Volume indices and left ventricular ejection fraction (LVEF) are routinely used to assess cardiac function. Ventricular strain values may provide additional diagnostic information, but their reproducibility is unclear. This study therefore compares the repeatability and reproducibility of volumes, volume fraction, and regional ventricular strains, derived from cardiovascular magnetic resonance (CMR) imaging, across three software packages and between readers. Methods Seven readers analysed 16 short-axis CMR stacks of a porcine heart. Endocardial contours were manually drawn using OsiriX and Simpleware ScanIP and repeated in both softwares. The images were also contoured automatically in Circle CVI42. Endocardial global, apical, mid-ventricular, and basal circumferential strains, as well as end-diastolic and end-systolic volume and LVEF were compared. Results Bland-Altman analysis found systematic biases in contour length between software packages. Compared to OsiriX, contour lengths were shorter in both ScanIP (-1.9 cm) and CVI42 (-0.6 cm), causing statistically significant differences in end-diastolic and end-systolic volumes, and apical circumferential strain (all p<0.006). No differences were found for mid-ventricular, basal or global strains, or left ventricular ejection fraction (all p<0.007). All CVI42 results lay within the ranges of the OsiriX results. Intra-software differences were found to be lower than inter-software differences. Conclusion OsiriX and CVI42 gave consistent results for all strain and volume metrics, with no statistical differences found between OsiriX and ScanIP for mid-ventricular, global or basal strains, or left ventricular ejection fraction. However, volumes were influenced by the choice of contouring software, suggesting care should be taken when comparing volumes across different software.
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Swain, L., D. Shillabeer, H. Wyatt, I. Jonkers, C. Holt y D. Williams. "IN VIVO PILOT STUDY OF TIBIOFEMORAL KINEMATICS DURING LOADED DYNAMIC ACTIVITIES". Orthopaedic Proceedings 105-B, SUPP_8 (11 de abril de 2023): 12. http://dx.doi.org/10.1302/1358-992x.2023.8.012.
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Biplane video X-ray (BVX) – with models segmented from magnetic resonance imaging (MRI) – is used to directly track bones during dynamic activities. Investigating tibiofemoral kinematics helps to understand effects of disease, injury, and possible interventions.Develop a protocol and compare in-vivo kinematics during loaded dynamic activities using BVX and MRI.BVX (60 FPS) was captured whilst three healthy volunteers performed three repeats of lunge, stair ascent and gait. MRI scans were performed (Magnetom 3T Prisma, Siemens). 3D bone models of the tibia and femur were segmented (Simpleware Scan IP, Synopsis). Bone poses were obtained by manually matching bone models to X-rays (DSX Suite, C-Motion Inc.). Mean range of motion (ROM) of the contact points on the medial and lateral tibial plateau were calculated using custom MATLAB code (MathWorks). Results were filtered using an adaptive low pass Butterworth filter (Frequency range: 5-29Hz).Gait and Stair ascent activities from one participant's data showed increased ROM for medial-lateral (ML) translation in the medial compartment but decreased ROM in anterior-posterior (AP) translation when comparing against the same translations on the lateral compartment of the tibial plateau. Lunge activity showed increased ROM for both ML and AP translation in the medial compartment when compared with the lateral compartment.These results highlight the variability in condylar translations between different activities. Understanding healthy in-vivo kinematics across different activities allows the determination of suitable activities to best investigate the kinematic changes due to disease or injury and assess the efficacy of different interventions.Acknowledgements: This research was supported by the Engineering and Physical Sciences Research Council (EPSRC) doctoral training grant (EP/T517951/1).
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Williams, D., G. Chapman, L. Esquivel y C. Brockett. "DEVELOPMENT OF AN IN VIVO ANKLE AND HINDFOOT KINEMATIC PROTOCOL TO INVESTIGATE ACTIVITIES OF DAILY LIVING". Orthopaedic Proceedings 105-B, SUPP_8 (11 de abril de 2023): 98. http://dx.doi.org/10.1302/1358-992x.2023.8.098.
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To be able to assess the biomechanical and functional effects of ankle injury and disease it is necessary to characterise healthy ankle kinematics. Due to the anatomical complexity of the ankle, it is difficult to accurately measure the Tibiotalar and Subtalar joint angles using traditional marker-based motion capture techniques. Biplane Video X-ray (BVX) is an imaging technique that allows direct measurement of individual bones using high-speed, dynamic X-rays.The objective is to develop an in-vivo protocol for the hindfoot looking at the tibiotalar and subtalar joint during different activities of living.A bespoke raised walkway was manufactured to position the foot and ankle inside the field of view of the BVX system. Three healthy volunteers performed three gait and step-down trials while capturing Biplane Video X-Ray (125Hz, 1.25ms, 80kVp and 160 mA) and underwent MR imaging (Magnetom 3T Prisma, Siemens) which were manually segmented into 3D bone models (Simpleware Scan IP, Synopsis). Bone position and orientation for the Talus, Calcaneus and Tibia were calculated by manual matching of 3D Bone models to X-Rays (DSX Suite, C-Motion, Inc.). Kinematics were calculated using MATLAB (MathWorks, Inc. USA).Pilot results showed that for the subtalar joint there was greater range of motion (ROM) for Inversion and Dorsiflexion angles during stance phase of gait and reduced ROM for Internal Rotation compared with step down. For the tibiotalar joint, Gait had greater inversion and internal rotation ROM and reduced dorsiflexion ROM when compared with step down.The developed protocol successfully calculated the in-vivo kinematics of the tibiotalar and subtalar joints for different dynamic activities of daily living. These pilot results show the different kinematic profiles between two different activities of daily living. Future work will investigate translation kinematics of the two joints to fully characterise healthy kinematics.
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Rodrigues, Nadja Da Nóbrega y Naylla Vieira de Almeida Estrela. "SimpleWay process: parceria entre academia e indústria através de engenharia de software aplicada a projetos reais". Revista Principia - Divulgação Científica e Tecnológica do IFPB 1, n.º 23 (21 de junio de 2013): 95. http://dx.doi.org/10.18265/2447-9187a2013id7784.
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<span>Entendendo a necessidade de integração entre academia e indústria, este artigo relata a estratégia de uso de recursos técnicos de uma Empresa Júnior (EJ) da Área de Ciência da Computação enquanto instrumentos para ensino e aprendizagem de Engenharia de Software aplicada. A metodologia associada ao estudo baseou-se no uso de um Processo de Desenvolvimento de Software (PDS) específico, desenvolvido para a EJ, e do ambiente criado para este PDS, como instrumentos na instanciação de projetos reais da EJ ou fictícios, em sala de aula. As principais contribuições do uso do PDS e do seu ambiente foram o aumento na qualidade dos projetos e o valor agregado aos alunos, através da utilização de boas práticas da indústria.</span>
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Šoja, Tijana. "OPTIMAL LEVEL OF FOREIGN RESERVES – EXAMPLE OF BOSNIA AND HERZEGOVINA". ЗБОРНИК РАДОВА ЕКОНОМСКОГ ФАКУЛТЕТА У ИСТОЧНОМ САРАЈЕВУ 1, n.º 9 (31 de diciembre de 2014): 107. http://dx.doi.org/10.7251/zrefis1409107s.
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The paper points to the conceptualdefinition of foreign exchange reserves, the role,importance and objectives for holding foreignexchange reserves as well as evaluating the requiredamount of foreign exchange reserves, or adequacy offoreign exchange reserves. Foreign exchangereserves are important assets in each country andthey are significantly affected by monetary policy,exchange rate policy or regulation and externalinstability and the impact of the crisis that may comefrom the environment. This paper presents a simpleway of estimates of adequacy and optimality offoreign exchange reserves, which are basis for theanalysis of foreign exchange reserves, as well as inthe construction of statistical and mathematicalmodels that detail the optimal level of internationalreserves. Special review was paid to the assessmentof the adequacy of foreign exchange reserves ofBosnia and Herzegovina, and the Central Bank ofBosnia and Herzegovina.
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Belvedere, Claudio, Maurizio Ortolani, Emanuela Marcelli, Barbara Bortolani, Katsiaryna Matsiushevich, Stefano Durante, Laura Cercenelli y Alberto Leardini. "Comparison of Bone Segmentation Software over Different Anatomical Parts". Applied Sciences 12, n.º 12 (15 de junio de 2022): 6097. http://dx.doi.org/10.3390/app12126097.
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Three-dimensional bone shape reconstruction is a fundamental step for any subject-specific musculo-skeletal model. Typically, medical images are processed to reconstruct bone surfaces via slice-by-slice contour identification. Freeware software packages are available, but commercial ones must be used for the necessary certification in clinics. The commercial software packages also imply expensive hardware and demanding training, but offer valuable tools. The aim of the present work is to report the performance of five commercial software packages (Mimics®, AmiraTM, D2PTM, SimplewareTM, and Segment 3D PrintTM), particularly the time to import and to create the model, the number of triangles of the mesh, and the STL file size. DICOM files of three different computed tomography scans from five different human anatomical areas were utilized for bone shape reconstruction by using each of these packages. The same operator and the same hosting hardware were used for these analyses. The computational time was found to be different between the packages analyzed, probably because of the pre-processing implied in this operation. The longer “time-to-import” observed in one software is likely due to the volume rendering during uploading. A similar number of triangles per megabyte (approximately 20 thousand) was observed for the five commercial packages. The present work showed the good performance of these software packages, with the main features being better than those analyzed previously in freeware packages.
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"Simpleware ScanIP Software". Biomedical Safety & Standards 51, n.º 19 (1 de noviembre de 2021): 147. http://dx.doi.org/10.1097/01.bmsas.0000797208.11456.fb.
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Roytman, Gregory R., Matan Cutler, Kenneth Milligan, Steven M. Tommasini y Daniel H. Wiznia. "An open-access plug-in program for 3D modelling distinct material properties of cortical and trabecular bone". BMC Biomedical Engineering 4, n.º 1 (24 de septiembre de 2022). http://dx.doi.org/10.1186/s42490-022-00065-z.
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Abstract Background Finite element modelling the material behavior of bone in-silico is a powerful tool to predict the best suited surgical treatment for individual patients. Results We demonstrate the development and use of a pre-processing plug-in program with a 3D modelling image processing software suite (Synopsys Simpleware, ScanIP) to assist with identifying, isolating, and defining cortical and trabecular bone material properties from patient specific computed tomography scans. The workflow starts by calibrating grayscale values of each constituent element with a phantom – a standardized object with defined densities. Using an established power law equation, we convert the apparent density value per voxel to a Young’s Modulus. The resulting “calibrated” scan can be used for modeling and in-silico experimentation with Finite Element Analysis. Conclusions This process allows for the creation of realistic and personalized simulations to inform a surgeon’s decision-making. We have made this plug-in program open and accessible as a supplemental file.
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Ullah, Irfan. "CHARACTERIZATION OF THE NONLINEAR BEHAVIOR OF FLEXIBLE ROAD PAVEMENTS". JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES 15, n.º 12 (29 de diciembre de 2020). http://dx.doi.org/10.26782/jmcms.2020.12.00010.
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In this paper, the Asphalt Concrete is analyzed by finite element modeling in Abaqus. The nonlinear viscoelastic behavior of Asphalt Concrete is simulated in Finite Element Analysis (FEA). The X-Ray Computed Tomography scans of the laboratory specimen are converted to a 3D virtual model in image processing software (Simpleware Scan IP). The 3D model is used in FEA by applying boundary conditions and giving mechanical properties, considering the Asphalt Concrete as a viscoelastic material. The mechanical properties of the Asphalt Concrete were determined from the laboratory test performed on the same sample. Three different types of model were analyzed. The representative 3D meshed model and Abaqus meshed model were analyzed for recovery of stress under constant strain and compared. It was concluded that the analysis on a model without considering the actual geometry of the Asphalt Concrete, gives a similar pattern of results but differ by 18% than a laboratory test. The actual 3D geometry of Asphalt Concrete specimen can be obtained by converting 2D X-ray CT scans. It was also found that the nonlinear viscoelastic analysis on a 3D virtual model of Asphalt Concrete gives 96% similar results to the laboratory tests.
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Ullah, Irfan. "CHARACTERIZATION OF THE NONLINEAR BEHAVIOR OF FLEXIBLE ROAD PAVEMENTS". JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES 15, n.º 12 (29 de diciembre de 2020). http://dx.doi.org/10.26782/jmcms.2020.12.00010.
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In this paper, the Asphalt Concrete is analyzed by finite element modeling in Abaqus. The nonlinear viscoelastic behavior of Asphalt Concrete is simulated in Finite Element Analysis (FEA). The X-Ray Computed Tomography scans of the laboratory specimen are converted to a 3D virtual model in image processing software (Simpleware Scan IP). The 3D model is used in FEA by applying boundary conditions and giving mechanical properties, considering the Asphalt Concrete as a viscoelastic material. The mechanical properties of the Asphalt Concrete were determined from the laboratory test performed on the same sample. Three different types of model were analyzed. The representative 3D meshed model and Abaqus meshed model were analyzed for recovery of stress under constant strain and compared. It was concluded that the analysis on a model without considering the actual geometry of the Asphalt Concrete, gives a similar pattern of results but differ by 18% than a laboratory test. The actual 3D geometry of Asphalt Concrete specimen can be obtained by converting 2D X-ray CT scans. It was also found that the nonlinear viscoelastic analysis on a 3D virtual model of Asphalt Concrete gives 96% similar results to the laboratory tests.
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Genc, Kerim O., Paul Segars, Steve Cockram, Dane Thompson, Marc Horner, Ross Cotton y Philippe Young. "Workflow For Creating a Simulation Ready Virtual Population For Finite Element Modeling". Journal of Medical Devices 7, n.º 4 (1 de diciembre de 2013). http://dx.doi.org/10.1115/1.4025847.
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Three dimensional image-based meshing of multipart structures from medical scan data continues to reveal exciting new possibilities for the application of simulation techniques to a wide range of biomedical problems. However, significant challenges to creating a population of simulation compatible models still exist. These include: 1) dataset availability—due to privacy rules and cost, very few readily available dataset repositories of human phantoms exist; 2) segmentation difficulty—segmentation of scan datasets is extremely man-hour intensive. Effort is often measured by months to years for a single model; 3) clean CAD model extraction—the faceted volumetric meshes and CAD geometry must contain conformal face mapping between touching objects. Since traditional part-by-part meshing approaches risk gaps or overlap between adjacent parts, manual and time consuming repair may be required. This paper demonstrates a potential solution to these challenges through a fast and efficient workflow that begins with newly available anatomical geometries, and culminates in a solved multi-object computational simulation. Using the new series of 4D extended cardiac-torso (XCAT) phantoms created by Segars et al., we use ScanIP (Simpleware Ltd., Exeter, UK) to convert these datasets into multi-object simulation ready geometry files that are imported into HFSS (ANSYS Inc., Canonsburg, PA) for EM simulation and analysis.
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Bozkurt, Selim, Alessandro Borghi, Lara S. van de Lande, N. U. Owase Jeelani, David J. Dunaway y Silvia Schievano. "Computational modelling of patient specific spring assisted lambdoid craniosynostosis correction". Scientific Reports 10, n.º 1 (29 de octubre de 2020). http://dx.doi.org/10.1038/s41598-020-75747-6.
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Abstract Lambdoid craniosynostosis (LC) is a rare non-syndromic craniosynostosis characterised by fusion of the lambdoid sutures at the back of the head. Surgical correction including the spring assisted cranioplasty is the only option to correct the asymmetry at the skull in LC. However, the aesthetic outcome from spring assisted cranioplasty may remain suboptimal. The aim of this study is to develop a parametric finite element (FE) model of the LC skulls that could be used in the future to optimise spring surgery. The skull geometries from three different LC patients who underwent spring correction were reconstructed from the pre-operative computed tomography (CT) in Simpleware ScanIP. Initially, the skull growth between the pre-operative CT imaging and surgical intervention was simulated using MSC Marc. The osteotomies and spring implantation were performed to simulate the skull expansion due to the spring forces and skull growth between surgery and post-operative CT imaging in MSC Marc. Surface deviation between the FE models and post-operative skull models reconstructed from CT images changed between ± 5 mm over the skull geometries. Replicating spring assisted cranioplasty in LC patients allow to tune the parameters for surgical planning, which may help to improve outcomes in LC surgeries in the future.
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Alharthi, Salman, Jude Meakin, Chris Wright y Jonathan Fulford. "The impact of altering participant MRI scanning position on back muscle volume measurements". BJR|Open 4, n.º 1 (enero de 2022). http://dx.doi.org/10.1259/bjro.20210051.
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Objectives: Muscle volume may reflect both strength and functional capability and hence is a parameter often measured to assess the effect of various interventions. The aim of the current study was to determine the sensitivity of muscle volume calculations on participant postural position and hence gauge possible errors that may arise in longitudinal studies, especially those where an intervention leads to large muscle changes and potentially the degree of spinal curvature. Methods: Twenty healthy participants (22–49 years, 10 male and 10 female), were recruited and MRI images acquired with them lying in four different positions; neutral spine (P1), decreased lordosis (P2), increased lordosis (P3) and neutral spine repeated (P4). Images were analysed in Simpleware ScanIP, and lumbar muscle volume and Cobb’s angle, as an indicator of spine curvature, determined. Results: After comparing volume determinations, no statistically significant differences were found for P1 - P2 and P1 - P4, whereas significant changes were determined for P2 - P3 and P1 - P3. P2 and P3 represent the two extremes of spinal curvature with a difference in Cobb’s angle of 17°. However, the mean difference between volume determinations was only 29 cm3. These results suggest the differences in muscle volume determinations are generally greater with increasing differences in curvature between measurements, but that overall the effects are small. Conclusions: Thus, generally, spinal muscle volume determinations are robust in terms of participant positioning. Advances in knowledge: Differences in muscle volume calculations appear to become larger the greater the difference in spinal curvature between positions. Thus, spinal curvature should not have a major impact on the results of spinal muscle volume determinations following interventions in longitudinal studies.
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Ramswroop, Jagdev Singh y Devendra Kumar. "Numerical computation of fractional Lotka-Volterra equation arising in biological systems". Nonlinear Engineering 4, n.º 2 (1 de enero de 2015). http://dx.doi.org/10.1515/nleng-2015-0012.
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AbstractIn this paper, we present the homotopy analysis transform method (HATM) to solve fractional Lotka- Volterra equation, which describes the long term servival of species. The HATM solutions, denotes less error compare with their respective exact solution for alpha = 1. In addition to non-proposed techniques, HATMis valid for both small and large parameters, it also provides us with a simpleway to adjust and control the parameter hbar and auxiliary function H(t), which play effective role for convergence solutions of fractional differential-difference equations (FDDEs).