A Novel Tram Stent Method in the Treatment of Coronary Bifurcation Lesions – Finite Element Study

A novel stent was designed for the treatment of coronary bifurcation lesion, and it was investigated for its performance by finite element analysis. This study was performed in search of a novel method of treatment of bifurcation lesion with provisional stenting. A bifurcation model was created with the proximal vessel of 3.2 mm diameter, and the distal vessel after the side branch (2.3 mm) was 2.7 mm. A novel stent was designed with connection links that had a profile of a tram. Laser cutting and shape setting of the stent was performed, and thereafter it was crimped and deployed over a balloon. The contact pressure, stresses on the arterial wall, stresses on the stent, the maximal principal log strain of the main artery and the side-branch were studied. The study was performed in Abaqus, Simulia. The stresses on the main branch and the distal branch were minimally increased after deployment of this novel stent. The side branch was preserved, and the stresses on the side branch were lesser; and at the confluence of bifurcation on either side of the side branch origin the von-Mises stress was marginally increased. The stresses and strain at the bifurcation were significantly lesser than the stresses and strain of the currently existing techniques used in the treatment of bifurcation lesions though the study was primarily focused only on the utility of the new technology. There is a potential for a novel Tram-stent method in the treatment of coronary bifurcation lesions.     

Ultrafast vascular strain compounding using plane wave transmission

Deformations of the atherosclerotic vascular wall induced by the pulsating blood can be estimated using ultrasound strain imaging. Because these deformations indirectly provide information on mechanical plaque composition, strain imaging is a promising technique for differentiating between stable and vulnerable atherosclerotic plaques. This paper first explains 1-D radial strain estimation as applied intravascularly in coronary arteries. Next, recent methods for noninvasive vascular strain estimation in a transverse imaging plane are discussed. Finally, a compounding technique that our group recently developed is explained. This technique combines motion estimates of subsequently acquired focused ultrasound images obtained at various insonification angles. However, because the artery moves and deforms during the multi-angle acquisition, errors are introduced when compounding. Recent advances in computational power have enabled plane wave ultrasound acquisition, which allows 100 times faster image acquisition and thus might resolve the motion artifacts. In this paper the performance of strain imaging using plane wave compounding is investigated using simulations of an artery with a vulnerable plaque and experimental data of a two-layered vessel phantom. The results show that plane wave compounding outperforms 0° focused strain imaging. For the simulations, the root mean squared error reduced by 66% and 50% for radial and circumferential strain, respectively. For the experiments, the elastographic signal-to-noise and contrast-to-noise ratio (SNR_e and CNR_e) increased with 2.1 dB and 3.7 dB radially, and 5.6 dB and 16.2 dB circumferentially. Because of the high frame rate, the plane wave compounding technique can even be further optimized and extended to 3D in future.     

Computer simulation of growth of anastomosing microvascular networks

Stochastic growth of polygonal microvascular networks was simulated on computer by dichotomous terminal branching and bridging (anastomosing with an existing segment). The model was applied to describe microvascular growth into a rectangular plane from the sides when vessels bifurcate in a probabilistic manner. The angle of bifurcation was drawn from a normal distribution, the mean of which was varied between 40 degrees and 80 degrees. The resulting networks contained an average of 88-104 nodes of which 30-38% were due to bridging. Number of nodes, number of branches, number of vascular polygons and a fractal dimension representing the density of nodes were calculated for each simulated network. Capillary density increased when mean angle of bifurcation was increased between 40 degrees and 80 degrees. Distributions of normalized vessel lengths and polygon shapes were compared with those of a mesenteric vascular network. The distributions were not found to be significantly different (p less than 0.05) for most values of the mean angle of bifurcation, matching best for the mean bifurcation angle of 50 degrees. Vascular polygons had an average shape between pentagonal and hexagonal for the mesenteric network as well as for all values of the mean bifurcation angle used in this study.     

Bifurcation of orbits and synchrony in inferior olive neurons

Inferior olive neurons (IONs) have rich dynamics and can exhibit stable, unstable, periodic, and even chaotic trajectories. This paper presents an analysis of bifurcation of periodic orbits of an ION when its two key parameters (a, μ) are varied in a two-dimensional plane. The parameter a describes the shape of the parabolic nonlinearity in the model and μ is the extracellular stimulus. The four-dimensional ION model considered here is a cascade connection of two subsystems (S(a) and S(b)). The parameter plane (a - μ) is delineated into several subregions. The ION has distinct orbit structure and stability property in each subregion. It is shown that the subsystem S(a) or S(b) undergoes supercritical Poincare-Andronov-Hopf (PAH) bifurcation at a critical value μ(c)(a) of the extracellular stimulus and periodic orbits of the neuron are born. Based on the center manifold theory, the existence of periodic orbits in the asymptotically stable S(a), when the subsystem S(b) undergoes PAH bifurcation, is established. In such a case, both subsystems exhibit periodic orbits. Interestingly when S(b) is under PAH bifurcation and S(a) is unstable, the trajectory of S(a) exhibits periodic bursting, interrupted by periods of quiescence. The bifurcation analysis is followed by the design of (i) a linear first-order filter and (ii) a nonlinear control system for the synchronization of IONs. The first controller uses a single output of each ION, but the nonlinear control system uses two state variables for feedback. The open-loop and closed-loop responses are presented which show bifurcation of orbits and synchronization of oscillating neurons.     

Modes of Mechanical Failure of Hollow, Septate Stems

Three general modes of mechanical failure were observed whenhollow, septate stem segments ofArundinaria técta(Poaceae)were axially compressed and caused to fail: (1) rupture of tissuesat the opposing ends of the nodal transverse diaphragm parallelto the plane of stem flexure; (2) localized catastrophic transverseinvagination of internodes (Brazier buckling); and (3) longitudinalrupture of internodal walls along the convex surface of stemflexure attended by nodal tissue shearing. The frequencies ofoccurrence of these three modes were not equivalent among the100 stem segments examined; stem failure was dominated by nodaltissue shearing (i.e. 67% of the nodes failed by shearing; 52%of the internodes longitudinally invaginated; 27% of the internodesfailed in Brazier buckling; 21% of the internodes failed byrupturing). Computer simulations of axially compressed stemsegments consisting of one node and one internode composed ofnon-linearly elastic, anisotropic materials (tissues) successfullypredicted observed strain patterns and revealed that the pathwayto stem failure contains a bifurcation point below which deformationpatterns coalesce on a single configuration, and above whichstem failure by Brazier buckling or nodal tissue shearing areessentially mutually exclusive responses to excessive stem flexure.The patterns of actual and simulated stem flexure were consistentwith the hypothesis that nodes store strain energy as stemsflex, and release this energy to restore stem shape when bendingforces abate (i.e. nodes operate as spring-like joints). However,strain energy ‘sinks’ identified by simulationswere also located in bending internodal walls which can storeelastic strain energy to do work. Nodal diaphragms and internodalwalls likely comprise a complex and global rather than a simpleand local elastic system for the recovery of stem shape.Copyright1998 Annals of Botany Company Stem flexure; mechanical failure; stem nodes; internodes; plants; biomechanics; finite element analyses; Brazier buckling.     

In vitro study of modifications of blood flow patterns induced by a bifurcation

Velocity profiles obtained with atheromatous and normal bifurcation castings in the presence of various types of flows are proposed. In the atheromatous bifurcation, with steady flow, we observe radial positive or negative velocities at distance to the wall smaller than 1 mm, which may be attributed to small local eddy motions. The maximum of velocity needs a larger distance from the apex than in the case of the "normal" bifurcation to be again located on the axes. With periodical flows, the effects are strongly damped. The wall velocity gradients on several geometries of tubings are investigated to separate the effects of the local rugosity of the wall from those incidental to the geometry of the bifurcation. The alterations caused by the atheroma do not seem to be induced by local modifications or rugosity, but by slow modifications of the local diameter. As a consequence, the variations of the velocity gradient caused by atheroma in the total bifurcation, are more likely due to distance effects of the geometry itself than to local effects of rugosity.     

Division plane placement in pleomorphic archaea is dynamically coupled to cell shape

One mechanism for achieving accurate placement of the cell division machinery is via Turing patterns, where nonlinear molecular interactions spontaneously produce spatiotemporal concentration gradients. The resulting patterns are dictated by cell shape. For example, the Min system of Escherichia coli shows spatiotemporal oscillation between cell poles, leaving a mid‐cell zone for division. The universality of pattern‐forming mechanisms in divisome placement is currently unclear. We examined the location of the division plane in two pleomorphic archaea, Haloferax volcanii and Haloarcula japonica, and showed that it correlates with the predictions of Turing patterning. Time‐lapse analysis of H. volcanii shows that divisome locations after successive rounds of division are dynamically determined by daughter cell shape. For H. volcanii, we show that the location of DNA does not influence division plane location, ruling out nucleoid occlusion. Triangular cells provide a stringent test for Turing patterning, where there is a bifurcation in division plane orientation. For the two archaea examined, most triangular cells divide as predicted by a Turing mechanism; however, in some cases multiple division planes are observed resulting in cells dividing into three viable progeny. Our results suggest that the division site placement is consistent with a Turing patterning system in these archaea.     

Extracellular potential field of excited isolated frog muscle fibres immersed in a volume conductor

The extracellular potential field of isolated frog muscle fibres immersed in a volume conductor was studied at radial distances up to 3 mm during excitation. The shape of the field distant from both the point of the origin of the excitation and the end of the fibre as well as changes in the field when depolarization wave approached the fibre end were described. Different amplitude decrease rates in individual phases of the extracellular potential and the peak-to-peak amplitude at different temperatures were found. Extracellular potentials at long radial distances were recorded using an averaging technique. The shape of the extracellular potentials at long radial distances over the fibre and beyond its end were very similar to the shape of extraterritorial potentials of a single motor unit.     

Three-dimensional aspects of arterial branching

Arterial junctions give rise to different images when viewed from different directions. When a two-dimensional bifurcation is viewed in a direction other than normal to its branching plane, the branching angles will be distorted and the resulting picture will not be a true picture of that bifurcation. If the bifurcation is three-dimensional, some distortions will occur no matter which way the bifurcation is viewed. These distortions are analyzed for a wide range of situations and data is provided from which the corresponding errors can be estimated.     

Stereoscopically observed deformations of a compliant abdominal aortic aneurysm model

A new experimental setup has been implemented to precisely measure the deformations of an entire model abdominal aortic aneurysm (AAA). This setup addresses a gap between the computational and experimental models of AAA that have aimed at improving the limited understanding of aneurysm development and rupture. The experimental validation of the deformations from computational approaches has been limited by a lack of consideration of the large and varied deformations that AAAs undergo in response to physiologic flow and pressure. To address the issue of experimentally validating these calculated deformations, a stereoscopic imaging system utilizing two cameras was constructed to measure model aneurysm displacement in response to pressurization. The three model shapes, consisting of a healthy aorta, an AAA with bifurcation, and an AAA without bifurcation, were also evaluated with computational solid mechanical modeling using finite elements to assess the impact of differences between material properties and for comparison against the experimental inflations. The device demonstrated adequate accuracy (surface points were located to within 0.07?mm) for capturing local variation while allowing the full length of the aneurysm sac to be observed at once. The experimental model AAA demonstrated realistic aneurysm behavior by having cyclic strains consistent with reported clinical observations between pressures 80 and 120?mm Hg. These strains are 1-2%, and the local spatial variations in experimental strain were less than predicted by the computational models. The three different models demonstrated that the asymmetric bifurcation creates displacement differences but not cyclic strain differences within the aneurysm sac. The technique and device captured regional variations of strain that are unobservable with diameter measures alone. It also allowed the calculation of local strain and removed rigid body motion effects on the strain calculation. The results of the computations show that an asymmetric aortic bifurcation created displacement differences but not cyclic strain differences within the aneurysm sac.     

The effect of compliance on wall shear in casts of a human aortic bifurcation

Rigid and compliant casts of a human aortic bifurcation were subjected to physiologically realistic pulsatile fluid flows. At a number of sites near the wall in the approximate median plane of the bifurcation of these models, fluid velocity was measured with a laser Doppler velocimeter, and wall motion (in the case of the compliant cast) was determined with a Reticon linescan camera. The velocity and wall motion data were combined to estimate the instantaneous shear rates at the cast wall. Analysis showed that at the outer walls the cast compliance reduced shear rates, while at the walls of the flow divider the shear rate was increased.     

Infrared imaging of 2-D temperature distribution during cryogen spray cooling

Cryogen spray cooling (CSC) is used in conjunction with pulsed laser irradiation for treatment of dermatologic indications. The main goal of this study was to determine the radial temperature distribution created by CSC and evaluate the importance of radial temperature gradients upon the subsequent analysis of tissue cooling throughout the skin. Since direct measurement of surface temperatures during CSC are hindered by the formation of a liquid cryogen layer, temperature distributions were estimated using a thin, black aluminum sheet. An infrared focal plane array camera was used to determine the 2-D backside temperature distribution during a cryogen spurt, which preliminary measurements have shown is a good indicator of the front-side temperature distribution. The measured temperature distribution was approximately gaussian in shape. Next, the transient temperature distributions in skin were calculated for two cases: 1) the standard 1-D solution which assumes a uniform cooling temperature distribution, and 2) a 2-D solution using a nonuniform surface cooling temperature distribution based upon the back-side infrared temperature measurements. At the end of a 100-ms cryogen spurt, calculations showed that, for the two cases, large discrepancies in temperatures at the surface and at a 60-micron depth were found at radii greater than 2.5 mm. These results suggest that it is necessary to consider radial temperature gradients during cryogen spray cooling of tissue.     

Bifurcation structure of a model of bursting pancreatic cells

One- and two-dimensional bifurcation studies of a prototypic model of bursting oscillations in pancreatic beta-cells reveal a squid-formed area of chaotic dynamics in the parameter plane, with period-doubling bifurcations on one side of the arms and saddle-node bifurcations on the other. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling bifurcation and the emergence of type-III intermittency. The period-adding transition itself is not smooth but consists of a saddle-node bifurcation in which (n+1)-spike bursting behavior is born, slightly overlapping with a subcritical period-doubling bifurcation in which n-spike bursting behavior loses its stability.     

Study of deformation and shape recovery of NiTi nanowires under torsion

The nanomechanical properties, deformation, and shape recovery mechanism of NiTi nanowires (NWs) under torsion are studied using molecular dynamics simulations. The effects of loading rate, aspect ratio of NWs, and NW shape are evaluated in terms of atomic trajectories, potential energy, torque required for deformation, stress, shear modulus, centro-symmetry parameter, and radial distribution function. Simulation results show that dislocation nucleation starts from the surface and then extends to the interior along the {110} close-packed plane. For a high loading rate, the occurrence of torsional buckling of a NW is faster, and the buckling gradually develops near the location of the applied external loading. The critical torsional angle and critical buckling angle increase with aspect ratio of the NWs. Square NWs have better mechanical strength than that of circular NWs due to the effect of shape. Shape recovery naturally occurs before buckling.     

A modified radial isochron clock with slow and fast dynamics as a model of pacemaker neurons

A simple mathematical model of living pacemaker neurons is proposed. The model has a unit circle limit cycle and radial isochrons, and the state point moves slowly in one region and fast in the remaining region; regions can correspond to the subthreshold activity and to the action potentials of pacemaker neurons, respectively. The global bifurcation structure when driven by periodic pulse trains was investigated using one-dimensional maps (PTC), two-dimensional bifurcation diagrams, and skeletons involving stimulus period and intensity. The existence of both the slow and the fast dynamics has a critical influence on the global bifurcation structure of the oscillator when stimulated periodically.Supported by Trent H. Wells Jr. Inc.     

A numerical study of the shape of the surface separating flow into branches in microvascular bifurcations.

The shape of the separating surface formed by the streamlines entering the branches of microvascular bifurcations plays a major role in determining the distribution of red blood cells and other blood constituents downstream from the bifurcation. Using the finite element method, we determined the shape of the surface through numerical solution of three dimensional Navier-Stokes equations for fluid flow at low Reynolds numbers in a T-type bifurcation of circular tubes. Calculations were done for a wide range of daughter branch to parent vessel diameter ratios and flow ratios. The effect of Reynolds number was also studied. Our numerical results are in good agreement with previously reported experimental data of Rong and Carr (Microvascular Research, Vol. 39, pp. 186-202, 1990). The numerical results of this study will be used to predict the concentration of blood constituents downstream from microvascular bifurcations providing that the inlet concentration profile is known.     

不同光环境下桂花幼苗的构型差异

通过对不同光照条件下桂花幼苗的冠形、分枝率、叶片在树冠中的空间分布等特征进行研究,结果表明桂花幼苗构型发生了明显的可塑性适应:其树冠对光照条件的变化有显著的可塑性响应。在林隙中的幼苗受光的间歇性影响,总体分枝率明显小于全光、林冠下的幼苗分枝率。全光的幼苗叶片集中于二级枝,叶片长度和叶片面积相对较小,对光照利用充分;而林隙中的幼苗叶片集中于一级枝,避免处于植冠内侧受到遮蔽,表现出较大的叶片长度和叶面积;林冠下的叶片较均匀分布在一、二级枝上,叶片总数量较少,枝条高生长较全光下明显。幼苗在总体分枝格局中表现出独自的特点,即强光环境下产生短枝和高分枝率,在适度庇荫条件下产生长枝及低分枝率,在强度庇荫条件下以较长枝和较高分枝率来同时满足高生长和横向生长的需求。     

Quantification of the spatial strain distribution of scoliosis using a thin-plate spline method

The objective of this study was to quantify the three-dimensional spatial strain distribution of a scoliotic spine by nonhomogeneous transformation without using a statistically averaged reference spine. The shape of the scoliotic spine was determined from computed tomography images from a female patient with adolescent idiopathic scoliosis. The shape of the scoliotic spine was enclosed in a rectangular grid, and symmetrized using a thin-plate spline method according to the node positions of the grid. The node positions of the grid were determined by numerical optimization to satisfy symmetry. The obtained symmetric spinal shape was enclosed within a new rectangular grid and distorted back to the original scoliotic shape using a thin-plate spline method. The distorted grid was compared to the rectangular grid that surrounded the symmetrical spine. Cobb's angle was reduced from 35° in the scoliotic spine to 7° in the symmetrized spine, and the scoliotic shape was almost fully symmetrized. The scoliotic spine showed a complex Green–Lagrange strain distribution in three dimensions. The vertical and transverse compressive/tensile strains in the frontal plane were consistent with the major scoliotic deformation. The compressive, tensile and shear strains on the convex side of the apical vertebra were opposite to those on the concave side. These results indicate that the proposed method can be used to quantify the three-dimensional spatial strain distribution of a scoliotic spine, and may be useful in quantifying the deformity of scoliosis.