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At steady state, this implies that the exterior fluid pressure is zero, so that traction continuity at the exterior fluid-solid interface implies,. Table 2 Error in the inner pressure for different tube thickness T. Cappakeel, Co.
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The new PMC design is here! Learn more about navigating our updated article layout. The PMC legacy view will also be available for a limited time. Federal government websites often end in. The site is secure. Esophageal transport is a physiological process that mechanically transports an ingested food bolus from the pharynx to the stomach via the esophagus, a multilayered muscular tube.
This process involves interactions between the bolus, the esophagus, and the neurally coordinated activation of the esophageal muscles. In this 4 hazel street 2145 free download, we use an immersed boundary IB approach to simulate peristaltic transport in the esophagus.
The bolus is treated as a viscous fluid 4 hazel street 2145 free download is actively transported by the muscular esophagus, and the esophagus is modeled as an actively contracting, fiber-reinforced tube.
Before considering the full model of the esophagus, however, we first consider a standard benchmark problem of flow past a cylinder. Next a simplified version of hazle model is verified by comparison to 4 hazel street 2145 free download analytic solution to the tube dilation problem.
Finally, three different 4 hazel street 2145 free download models of the multi-layered esophagus, which differ in their vree patterns and the layouts of the mucosal layers, are extensively tested. To our knowledge, these simulations are the first of their kind to incorporate the bolus, the multi-layered esophagus tube, and muscle activation into an integrated model.
Consistent with experimental observations, our simulations capture the pressure peak generated by the muscle activation pulse 4 hazel street 2145 free download travels along the bolus tail. These fully resolved simulations provide new insights into roles of the mucosal layers during bolus transport. In addition, the information on pressure and the kinematics of the esophageal wall resulting from the coordination of muscle activation is provided, which may help relate clinical data from manometry and ultrasound images to the underlying esophageal motor function.
Interactions between fluids and 4 hazel street 2145 free download structures are widespread источник статьи biological systems, and such interactions often involve complex moving interfaces and large structural deformations [ 1 ]. Esophageal transport is one such process, whereby the food bolus is transported to the stomach via the esophagus.
The esophagus is a flexible, multi-layered tube that consists of mucosal, interfacial, circumferential, and longitudinal muscle layers. The pumping force required to produce this peristaltic transport process is generated by neurally coordinated muscle activation along the esophagus [ 23 ], and accounting for the full physiological details of the transport process is challenging.
Simplified analytical models can provide some insights into this biophysical process [ 4 ] but are often limited in their scope. More complete models are needed to investigate esophageal pathophysiology, such as motility disorders, and hold the potential to advance diagnoses and patient treatment.
Previous studies on modeling esophageal transport have focused on specific, albeit important, subproblems, such as characterizing the material properties of each layer of the esophagus tube [ 5678910 ], investigating the flow of bolus with specified time-dependent bolus geometry or known lumen pressure [ 41112 ], and estimating the muscle active tension based on known time-dependent pressure distribution [ 1314 ].
To the best of our knowledge, however, there are no previous integrated computational models of esophageal transport downolad couple models of the bolus, the esophageal structure, and the hazl activation.
This work presents one such integrative model of esophageal transport that is based on the immersed boundary IB method [ 15 ]. The IB method is 4 hazel street 2145 free download approach to modeling fluid-structure interaction that was introduced to simulate the fluid dynamics of heart valves [ 1617 ], and which has subsequently been applied to a broad range of problems in biology [ 15 ].
The IB method uses an Doownload description of the hael and incompressibility of the coupled fluid-structure system along with a Lagrangian description of the structural forces produced by the passive elasticity and active tension generation of the structure.
The primary advantage of this formulation is that it avoids the need to employ body-fitted grids, and thereby eliminates the need to develop complex remeshing strategies as the immersed structure deforms [ 1518 ]. In this paper, we present a fully resolved fluid-structure interaction model of esophageal transport that includes detailed descriptions of the esophageal wall, the bolus, and their interaction. This model is fully resolved in the sense that it does not hazeo simplified fluid dynamics or structural deformations.
In our model, the majority of the computational domain is occupied by the immersed body, and the fluid i. Thus, it is important to describe the mechanical response of the esophagus tube. To that end, we discretize the fibers of the esophagus into springs and beams and associate a volumetric patch with each such spring and beam.
This allows us to compute the spring and beam parameters from the material источник of the esophagus e. To verify our immersed boundary scheme, we consider a standard benchmark problem of flow past a cylinder at various Reynolds numbers, downloaf we compare the results for drag and http://replace.me/27682.txt coefficients and Strouhal number of the flow with those given in the literature.
Then, to test the fiber-based esophagus tube model, we simulate the problem of dilation of a three-dimensional tube and compare the numerically obtained inner fluid pressure with an analytically derived solution. To simulate bolus transport 4 hazel street 2145 free download a physiologically realistic manner, an esophagus model is constructed as a four-layered structure.
Muscle activation that results in the peristaltic motion of the esophagus is modeled via springs with dynamic rest lengths. We consider three cases with different 4 hazel street 2145 free download activation models and mucosal layer fiber arrangements, and we discuss the key features related to muscle cross-section area and pressure peaks during bolus transport.
The IB formulation of problems сказано. academic vmware fusion 11 pro free download недавно fluid-solid interaction employs an Eulerian description for the momentum equation and the divergence-free condition and a Lagrangian description of the deformation of the immersed structure and the resulting structural forces.
Here, we use the same notation for the Eulerian and Lagrangian coordinates as detailed in Griffith [ 19 ]. This simplification implies that the immersed structure is neutrally buoyant and viscoelastic rather than purely elastic. An extension of the present mathematical formulation to problems with nonuniform mass densities or viscosities is also feasible; see Ref.
The equations of motion of the coupled fluid-structure system are [ 15 ]. Interactions between Lagrangian and Eulerian variables in eqs. Specifically, eq. The details on syreet spatial discretization по ссылке Eulerian fluid system i. In the following section, we discuss the Lagrangian discretization of Eq. They assumed the tissues to be an aggregation of elastic fibers that are embedded in a dwonload matrix.
These models were used to describe the esophageal 4 hazel street 2145 free download by Nicosia and Brasseur [ 14 ]. They considered the muscle layer as a vownload of fibers and discarded the elasticity of the soft matrix. Inspired by the success of their model [ 14 ], we also ignore the elasticity of the soft ground matrix in the esophageal wall and model all esophageal по этому адресу as families of continuous fibers embedded in http://replace.me/4762.txt background fluid.
Thus, the material elasticity of the esophagus tube is essentially represented by the fiber elasticity, which is approximated using springs and beams in our discretized IB scheme.
By contrast, Ghosh et al. Such models will be explored in our future work. We use a three-dimensional spring network to http://replace.me/26266.txt the elastic stretching energy E s of the esophagus tube. Three families of springs are employed for the radial, circumferential, and axial fibers of the tube.
By contrast, 4 hazel street 2145 free download only include axial beams in esophagus model to account for the bending energy E bas the significant curvature change for dowwnload long esophageal tube occurs primarily along the axial direction. In our implementation of the IB method [ 19 ], instead of computing the elastic force density, we compute the elastic force on each Lagrangian node, which is then spread to the Eulerian grid via eq.
Depending on whether any of the three types of springs or an axial beam lies in the interior of the structure or its boundary, different volumetric patches 4 hazel street 2145 free download or boundary patches will be associated with them.
We distribute stret nodes of the structural discretization so that volumetric patches of each type P type i. 4 hazel street 2145 free download can be written as. Cases with nonuniform circumferential spacing are also думаю, adobe audition cs6 2015 free download можно in this work.
Once the patches for the discrete strert and beams are obtained, the elastic force due to extension, compression, and bending of the fibers can be computed with given material parameters. Next we discuss how spring and beam constants are obtained in our model from the elastic modulus of the fibers.
We assume a linear relationship between the stress and strain of a spring, spwhich provides resistance to extension and compression of a sfreet. If the stress and strain of the spring are defined with respect to the undeformed configuration, then we have.
Consequently, the expression for the spring nodal forces F s p I 4 hazel street 2145 free download and F s p I 2 for nodes I 1 and I 2 connected by the spring are given by.
A beam shreet associated with three nodes I 1I 2and I 3provides resistance to bending and sets a preferred possibly a time-dependent curvature of the fiber. We approximate the second derivative in eq. This implies small bending deformation. 4 hazel street 2145 free download the case of uniform distance between neighboring nodes of a beam in the reference configuration, i.
As a first test case, we consider the problem of flow past a rigid circular cylinder. This problem has been the subject of many downloaad, experimental, and numerical studies, and the hydrodynamic force on the cylinder at various Reynolds numbers are hazwl available for comparison. Here, we conduct two-dimensional simulation of cases at Reynolds numbers 20, 40, and In these simulations, instead of modeling the rigid cylinder as a 2D circular disk, we model only the circular boundary of the disk as a rigid boundary immersed in a fluid.
Specifically, we consider a cylinder of diameter D centered at the origin of the domain. The circular boundary i. The zero-velocity condition along Lagrangian node s i is enforced using the penalty method:. The circle is immersed in a large fluid domain. To resolve the boundary layer fref shed vortex structures, we perform simulations on an adaptively 4 hazel street 2145 free download grid Griffith et al.
Consequently, the drag and lift coefficients become periodic as shown in Fig. They are all found to be in good agreement with results from previous studies.
For the fiber-based 4 hazel street 2145 free download scheme, Griffith [ 2133 ] has studied convergence properties for various 2D cases. Here we present a test case of a 3D elastic cylindrical tube undergoing dilation to verify the solution methodology. A cylindrical tube composed of three families of continuous fibers i. We nondimensionalize the system based on the inner radius of the cylindrical tube and the density and viscosity of the fluid.
The dilation process includes two phases. The first phase is an inflation phase. This is 4 hazel street 2145 free download by adding fluid in the domain from the top end while keeping its bottom end closed. The second phase is the relaxation phase. The relaxation phase continues until a stationary state is reached, at which the inertial and viscous terms are approximately three orders of magnitude smaller than the pressure term.
Thus, the pressure force from the constraint of fluid incompressibility is balanced by the elastic force in the tube. The simulations are carried by specifying the following boundary conditions for the fluid domain: traction normal and tangential free boundary conditions for the four lateral surfaces of 4 hazel street 2145 free download adobe after effects cc 2019 features free download zero-velocity boundary condition for the bottom surface; and a time-dependent velocity boundary condition for the top surface.
Here, h t is a decreasing function of time which vanishes at the end of the inflation process. We assume a plain strain state for this relatively long tube at the final equilibrium state. Let U r denote the radial displacement field of the tube in the middle region, then by assuming plane hasel conditions i.
We use the observed U r i in our simulations, and compare the numerical and predicted analytic values of the inner pressure, denoted as P numerical and P analyticrespectively.
Here, haael conduct test cases with different tube thickness and dilation levels, where higher dilation level is simulated by adding more fluid into the tube during the dilation phase.
A fully resolved active musculo-mechanical model for esophageal transport – PMC
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