... Recurrence Formula 219 -- 5.5 Complex Arithmetic 225 -- 5.6 Quadratic and Cubic Equations 227 -- 5.7 Numerical ... ... 685 -- 13.9 Computing Fourier Integrals Using the FFT 692 -- 13.10 Wavelet Transforms 699 -- 13.11 Numerical ... ... Data with Errors in Both Coordinates 785 -- 15.4 General Linear Least Squares 788 -- 15.5 Nonlinear Models ... ... 799 -- 15.6 Confidence Limits on Estimated Model Parameters 807 -- 15.7 Robust Estimation 818 -- 15.8 ... ... and k-Means Clustering 842 -- 16.2 Viterbi Decoding 850 -- 16.3 Markov Models and Hidden Markov Modeling ...
3rd ed. xxi, 1235 s. : il. ; 27 cm + 1 CD-ROM
- MeSH
- Mathematical Computing MeSH
- Mathematics MeSH
- Numerical Analysis, Computer-Assisted * MeSH
- Publication type
- Monograph MeSH
- Conspectus
- Počítačová věda. Výpočetní technika. Informační technologie
- NML Fields
- přírodní vědy
- přírodní vědy
This work presents a way of parallel computation of the electromagnetic fi eld scattering and Specifi c Absorption Rate distribution. Th e parallel program used in the computation has been based on the parallel implementation of the FDTD (Finite- Diff erence Time-Domain) method. Th e computations were made in a cluster system with the use of the MPI (Message Passing Interface) standard. In the paper an example of a human head numerical model based on the MRI (Magnetic Resonance Image) is also presented.
- MeSH
- Algorithms MeSH
- Models, Anatomic MeSH
- Electromagnetic Fields MeSH
- Financing, Organized MeSH
- Head physiology MeSH
- Humans MeSH
- Magnetic Resonance Imaging methods utilization MeSH
- Models, Structural MeSH
- Numerical Analysis, Computer-Assisted instrumentation MeSH
- Image Processing, Computer-Assisted methods utilization MeSH
- Check Tag
- Humans MeSH
In this article, the results of numerical simulations using computational fluid dynamics (CFD) and a comparison with experiments performed with phase Doppler anemometry are presented. The simulations and experiments were conducted in a realistic model of the human airways, which comprised the throat, trachea and tracheobronchial tree up to the fourth generation. A full inspiration/expiration breathing cycle was used with tidal volumes 0.5 and 1 L, which correspond to a sedentary regime and deep breath, respectively. The length of the entire breathing cycle was 4 s, with inspiration and expiration each lasting 2 s. As a boundary condition for the CFD simulations, experimentally obtained flow rate distribution in 10 terminal airways was used with zero pressure resistance at the throat inlet. CCM+ CFD code (Adapco) was used with an SST k-ω low-Reynolds Number RANS model. The total number of polyhedral control volumes was 2.6 million with a time step of 0.001 s. Comparisons were made at several points in eight cross sections selected according to experiments in the trachea and the left and right bronchi. The results agree well with experiments involving the oscillation (temporal relocation) of flow structures in the majority of the cross sections and individual local positions. Velocity field simulation in several cross sections shows a very unstable flow field, which originates in the tracheal laryngeal jet and propagates far downstream with the formation of separation zones in both left and right airways. The RANS simulation agrees with the experiments in almost all the cross sections and shows unstable local flow structures and a quantitatively acceptable solution for the time-averaged flow field.
- MeSH
- Models, Biological * MeSH
- Biomechanical Phenomena MeSH
- Bronchi physiology MeSH
- Time Factors MeSH
- Respiration * MeSH
- Humans MeSH
- Numerical Analysis, Computer-Assisted * MeSH
- Pulmonary Ventilation physiology MeSH
- Trachea physiology MeSH
- Check Tag
- Humans MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
- Comparative Study MeSH
PURPOSE OF THE STUDY In developing new or modifying the existing surgical treatment methods of spine conditions an integral part of ex vivo experiments is the assessment of mechanical, kinematic and dynamic properties of created constructions. The aim of the study is to create an appropriately validated numerical model of canine cervical spine in order to obtain a tool for basic research to be applied in cervical spine surgeries. For this purpose, canine is a suitable model due to the occurrence of similar cervical spine conditions in some breeds of dogs and in humans. The obtained model can also be used in research and in clinical veterinary practice. MATERIAL AND METHODS In order to create a 3D spine model, the LightSpeed 16 (GE, Milwaukee, USA) multidetector computed tomography was used to scan the cervical spine of Doberman Pinscher. The data were transmitted to Mimics 12 software (Materialise HQ, Belgium), in which the individual vertebrae were segmented on CT scans by thresholding. The vertebral geometry was exported to Rhinoceros software (McNeel North America, USA) for modelling, and subsequently the specialised software Abaqus (Dassault Systemes, France) was used to analyse the response of the physiological spine model to external load by the finite element method (FEM). All the FEM based numerical simulations were considered as nonlinear contact statistic tasks. In FEM analyses, angles between individual spinal segments were monitored in dependence on ventroflexion/ /dorziflexion. The data were validated using the latero-lateral radiographs of cervical spine of large breed dogs with no evident clinical signs of cervical spine conditions. The radiographs within the cervical spine range of motion were taken at three different positions: in neutral position, in maximal ventroflexion and in maximal dorziflexion. On X-rays, vertebral inclination angles in monitored spine positions were measured and compared with the results obtain0ed from FEM analyses of the numerical model. RESULTS It is obvious from the results that the physiological spine model tested by the finite element method shows a very similar mechanical behaviour as the physiological canine spine. The biggest difference identified between the resulting values was reported in C6-C7 segment in dorsiflexion (Δφ = 5.95%), or in C4-C5 segment in ventroflexion (Δφ = -3.09%). CONCLUSIONS The comparisons between the mobility of cervical spine in ventroflexion/dorsiflexion on radiographs of the real models and the simulated numerical model by finite element method showed a high degree of results conformity with a minimal difference. Therefore, for future experiments the validated numerical model can be used as a tool of basic research on condition that the results of analyses carried out by finite element method will be affected only by an insignificant error. The computer model, on the other hand, is merely a simplified system and in comparison with the real situation cannot fully evaluate the dynamics of the action of forces in time, their variability, and also the individual effects of supportive skeletal tissues. Based on what has been said above, it is obvious that there is a need to exercise restraint in interpreting the obtained results. Key words: cervical spine, kinematics, numerical modelling, finite element method, canine.
- MeSH
- Cervical Vertebrae diagnostic imaging physiology MeSH
- Tomography, X-Ray Computed MeSH
- Computer Simulation * MeSH
- Dogs MeSH
- Range of Motion, Articular * physiology MeSH
- Imaging, Three-Dimensional MeSH
- Animals MeSH
- Check Tag
- Dogs MeSH
- Animals MeSH
- Publication type
- Journal Article MeSH
- Comparative Study MeSH
Among morphological phenomena, cellular patterns in developing sensory epithelia have gained attention in recent years. Although physical models for cellular rearrangements are well-established thanks to a large bulk of experimental work, their computational implementation lacks solid mathematical background and involves experimentally unreachable parameters. Here we introduce a level set-based computational framework as a tool to rigorously investigate evolving cellular patterns, and study its mathematical and computational properties. We illustrate that a compelling feature of the method is its ability to correctly handle complex topology changes, including frequent cell intercalations. Combining this accurate numerical scheme with an established mathematical model, we show that the proposed framework features minimum possible number of parameters and is capable of reproducing a wide range of tissue morphological phenomena, such as cell sorting, engulfment or internalization. In particular, thanks to precise mathematical treatment of cellular intercalations, this method succeeds in simulating experimentally observed development of cellular mosaic patterns in sensory epithelia.
- MeSH
- Algorithms * MeSH
- Models, Biological * MeSH
- Epithelium MeSH
- Morphogenesis MeSH
- Software MeSH
- Publication type
- Journal Article MeSH
- Research Support, Non-U.S. Gov't MeSH
This study presents a combined experimental and numerical investigation of fiber transport and deposition in a realistic model of the female respiratory tract, extending to the seventh generation of branching. Numerical simulations were performed using the Euler-Lagrange Euler-Rotation (ELER) method, an efficient alternative to conventional Finite Volume Methods that benefits from explicit formulation and vast scalability, enabling fast parallelization on high-performance clusters. The ELER method was coupled with the Lattice Boltzmann Method (LBM) to simulate fiber dynamics under a realistic inspiratory flow profile. Experimental validation was conducted using an identical physical airway replica. The results demonstrated good agreement between simulations and experiments in the upper airways and trachea, with some discrepancies in the bifurcations, likely owing to the challenges of modeling complex turbulent flow with ELER. This method is more accurate than corresponding effective diameter simulations. Deposition patterns were analyzed as a function of fiber dimensions, revealing higher accuracy of the ELER method for smaller particles and confirming the tendency of higher aspect ratio fibers to penetrate deeper into the lungs. The orientation-dependent deposition mechanism was deployed, underscoring the importance of solving the actual orientations of the fibers. While advancing our understanding of fiber transport in female airways, the findings also reveal limitations in current numerical techniques, particularly in bifurcations. This study emphasizes the distinct behavior of fibrous versus spherical particles, with fibers exhibiting a greater propensity to reach deeper lung regions, which has significant implications for inhalation toxicology and drug delivery.
- MeSH
- Administration, Inhalation MeSH
- Models, Biological * MeSH
- Respiratory System * MeSH
- Humans MeSH
- Lung MeSH
- Computer Simulation MeSH
- Trachea * physiology MeSH
- Check Tag
- Humans MeSH
- Female MeSH
- Publication type
- Journal Article MeSH
sv.
- MeSH
- Biomedical Engineering * methods MeSH
- Mathematical Computing MeSH
- Models, Theoretical MeSH
- Publication type
- Periodical MeSH
- Conspectus
- *Technika, technologie, inženýrství
- NML Fields
- biomedicínské inženýrství
