Numerical simulation of noninvasive blood pressure measurement

In this paper, a simulation model based on the partially pressurized collapsible tube model for reproducing noninvasive blood pressure measurement is presented. The model consists of a collapsible tube, which models the pressurized part of the artery, rigid pipes connected to the collapsible tube, which model proximal and distal region far from the pressurized part, and the Windkessel model, which represents the capacitance and the resistance of the distal part of the circulation. The blood flow is simplified to a one-dimensional system. Collapse and expansion of the tube is represented by the change in the cross-sectional area of the tube considering the force balance acting on the tube membrane in the direction normal to the tube axis. They are solved using the Runge-Kutta method. This simple model can easily reproduce the oscillation of inner fluid and corresponding tube collapse typical for the Korotkoff sounds generated by the cuff pressure. The numerical result is compared with the experiment and shows good agreement.     

A mathematical model for adaptive transport network in path finding by true slime mold

We describe here a mathematical model of the adaptive dynamics of a transport network of the true slime mold Physarum polycephalum, an amoeboid organism that exhibits path-finding behavior in a maze. This organism possesses a network of tubular elements, by means of which nutrients and signals circulate through the plasmodium. When the organism is put in a maze, the network changes its shape to connect two exits by the shortest path. This process of path-finding is attributed to an underlying physiological mechanism: a tube thickens as the flux through it increases. The experimental evidence for this is, however, only qualitative. We constructed a mathematical model of the general form of the tube dynamics. Our model contains a key parameter corresponding to the extent of the feedback regulation between the thickness of a tube and the flux through it. We demonstrate the dependence of the behavior of the model on this parameter.     

Influence of a downstream narrowing on the flow profile in a tube

The distance over which the upstream flow conditions in a tube are disturbed by a stenosis downstream, i.e. the outlet length, was investigated for Reynolds numbers in the range 210-2900. Two methods were used, the Navier-Stokes equations were solved with a computer and a physical model was constructed and maximal velocities were measured with an ultrasound Doppler system. The computer model showed that Re number does not influence the outlet length, varying the stenosis area from 25% to 90% has an effect. However, the outlet length remained small, below 70% of the diameter of the tube. The physical model confirmed for a 75% stenosis that the outlet length is small, this method set the limit at not more than 1.2 times the tube diameter.     

One-dimensional steady continuum model of retraction of pseudopod in leukocytes

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.     

Spatial velocity distributions in pulse-wave propagation based on fluid–structure interaction

In this paper, spatial velocity distributions in pulse-wave propagation based on a fluid–structure interaction model are presented. The investigation is performed using the assumption of laminar flow and a linear-elastic wall. The fluid–structure interaction scheme is constructed using the finite element method. The results show that velocity distributions embody an obvious time delay in an elastic tube model. Further, the fully developed flow is delayed and the velocity values are increased in comparison with a rigid tube model. The increase in the wall thickness makes the time delay between the velocity peaks of different sites smaller while the time delay between the velocity minima is unchanged. Similarly, the time delay between the velocity bottoms is more easily found when decreasing the internal radius. The model gives valid results for spatial velocity distributions, which provide important information for wave propagation.     

Assessment of inhibitory effects of fluoride-coated tubes on biofilm formation by using the in vitro dental unit waterline biofilm model

This study aimed to establish an in vitro model to simulate biofilms formed in dental unit waterlines (DUWLs) and to investigate the ability of polyvinylidene fluoride (PVDF)-coated tubes to inhibit biofilm formation using this model. The water and biofilm samples were obtained from DUWLs which had been clinically used for 2.5 years, and the predominant bacteria were identified. A conventional polyurethane tube was incubated for 24 to 96 h in the mixed flora of isolated bacteria, and the optimal incubation conditions to simulate a clinically formed biofilm were determined by observation with a scanning electron microscope. Biofilm formation on a PVDF-coated tube was observed using this in vitro model, and the adherence of different bacterial species to conventional and PVDF-coated tubes was assessed. Sphingomonas paucimobilis, Acinetobacter haemolytics, and Methylobacterium mesophilicum were predominantly isolated from contaminated DUWLs. Incubation of the polyurethane tube with the mixed flora containing these three species for 96 h resulted in the formation of a mature biofilm similar to the one clinically observed. The PVDF-coated tube was significantly less adhesive to all three bacterial species than the polyurethane tube (P < 0.05 by the Mann-Whitney U test), and the attachment of small amounts of rods was observed even after incubation with the mixed flora for 96 h. In conclusion, an in vitro biofilm model was obtained by using a mixed flora of bacteria isolated from DUWLs, and the PVDF-coated tube was found to be effective in preventing biofilm formation using this model.     

Periodic flow of a viscous liquid in a thick-walled elastic tube

Arterial blood flow is analyzed on the basis of a realistic model consisting of a viscous liquid contained in a thick-walled viscoelastic tube. Approximate forms of the Navier-Stokes and continuity equations are derived for this model and solved in conjunction with the equations of motion of an elastic solid. Expressions are found for the displacement of the tube wall, velocity distribution, volume flow rate and phase velocity of the pressure wave. Changes in the shape of the pressure wave caused by damping and dispersion are determined, and the effect of viscoelasticity is assessed. Numerical results are presented which correspond to observed parameters of the circulatory systems of living animals.     

Structure and dynamics of model pore insertion into a membrane

A cylindrical transmembrane molecule is constructed by linking hydrophobic sites selected from a coarse grain model. The resulting hollow tube assembly serves as a representation of a transmembrane channel, pore, or a carbon nanotube. The interactions of a coarse grain di-myristoyl-phosphatidyl-choline hydrated bilayer with both a purely hydrophobic tube and a tube with hydrophilic caps are studied. The hydrophobic tube rotates in the membrane and becomes blocked by lipid tails after a few tens of nanoseconds. The hydrophilic sites of the capped tube stabilize it by anchoring the tube in the lipid headgroup/water interfacial region of each membrane leaflet. The capped tube remains free of lipid tails. The capped tube spontaneously conducts coarse grain water sites; the free-energy profile of this process is calculated using three different methods and is compared to the barrier for water permeation through the lipid bilayer. Spontaneous tube insertion into an undisturbed lipid bilayer is also studied, which we reported briefly in a previous publication. The hydrophobic tube submerges into the membrane core in a carpetlike manner. The capped tube laterally fuses with the closest leaflet, and then, after plunging into the membrane interior, rotates to assume a transbilayer orientation. Two lipids become trapped at the end of the tube as it penetrates the membrane. The hydrophilic headgroups of these lipids associate with the lower tube cap and assist the tube in crossing the interior of the membrane. When the rotation is complete these lipids detach from the tube caps and fuse with the lower leaflet lipids.     

The gp27-like Hub of VgrG Serves as Adaptor to Promote Hcp Tube Assembly

Contractile injection systems are multiprotein complexes that use a spring-like mechanism to deliver effectors into target cells. In addition to using a conserved mechanism, these complexes share a common core known as the tail. The tail comprises an inner tube tipped by a spike, wrapped by a contractile sheath, and assembled onto a baseplate. Here, using the type VI secretion system (T6SS) as a model of contractile injection systems, we provide molecular details on the interaction between the inner tube and the spike. Reconstitution into the Escherichia coli heterologous host in the absence of other T6SS components and in vitro experiments demonstrated that the Hcp tube component and the VgrG spike interact directly. VgrG deletion studies coupled to functional assays showed that the N-terminal domain of VgrG is sufficient to interact with Hcp, to initiate proper Hcp tube polymerization, and to promote sheath dynamics and Hcp release. The interaction interface between Hcp and VgrG was then mapped using docking simulations, mutagenesis, and cysteine-mediated cross-links. Based on these results, we propose a model in which the VgrG base serves as adaptor to recruit the first Hcp hexamer and initiates inner tube polymerization.     

Role of bronchial basement membrane in airway collapse

Bronchial basement membrane is an elastic structure that has the potential to be load bearing and thus to contribute to the mechanical stiffness of the bronchus. To investigate this possible role, the membrane was modeled as a thin-walled linearly elastic tube surrounded by a uniform liquid on the outside and by air on the inside. When the external pressure on such a tube exceeds the internal pressure by a critical amount, the tube buckles reversibly into two or more folds. The critical buckling pressure varies as the square of the number of folds. The analysis was used to investigate the collapse behavior of the model tube into patterns ranging from 2 to 24 folds. This showed that the resistance to collapse increases rapidly as the number of folds increases. Data in the literature lead to the conclusion that the pressures involved in collapsing the tubes are probably in the physiological range. It is suggested, on the basis of the model results reported here, that bronchial hyperresponsiveness could be related to the number of folds into which the basement membrane buckles when the bronchial muscle contracts. A reduced number of folds would yield an increased response.     

Analytical model for managing hypotony after implantation surgery of a glaucoma drainage device

The main aim of glaucoma treatment is to reduce the intraocular pressure (IOP). One of the most common surgical treatments of glaucoma is the implantation of a glaucoma drainage device to drain the aqueous humor from the anterior chamber to a filtration bleb, where the aqueous humor is absorbed. In some cases, the excess of drainage causes ocular hypotony, which constitutes a sight-threatening complication. To prevent hypotony after this intervention, surgeons frequently introduce a suture into the device tube, which increases the hydraulic resistance of the tube and, therefore, the IOP. This study aims to provide an analytical model to correct hypotony following implantation surgery of a glaucoma drainage device, which may help glaucoma surgeons decide on hypotony treatment. The results indicate that the IOP after implanting a cylindrical tube around 300 μm in diameter is essentially the same as that built up in the filtering bleb and can hardly be controlled by introducing a straight suture unless the suture diameter is slightly lower than that of the tube. On the contrary, when the tube diameter is smaller than, for example, 100 μm, significant reductions of the IOP can be obtained by introducing a thin suture into the tube.

     

A model for shape generation by strain and cell-cell adhesion in the epithelium of an arthropod leg segment

We present a model for the energetic factors determining the most stable shape of a tubular epithelium such as the hypodermis of an arthropod leg segment. The model uses the analysis by Steinberg (1963) of rearrangement of cells in aggregates under the influence of differential adhesion, combining this analysis with the assumption that the epithelium behaves as an elastic sheet. The epithelium is assumed to consist of blocks of cells with different adhesive affinities, which remain unmixed in a quilt pattern. Rearrangement of cells within each block can adjust the shape of the tube by changing the shapes of the blocks. By means of such rearrangements the tube develops that shape which minimizes a free energy. The free energy is the difference between the energy of mechanical strain due to bending of the epithelium and the work of adhesion among cells. Minimization of the free energy for a cylindrical segment yields a scaling relation involving the length and radius of the segment. Leg segments of Drosophila conformed approximately to this relation, with deviations which suggest that a whole-limb pattern of adhesive affinities modulates the shaping effects of an adhesive pattern repeated in each leg segment. The model also predicts a transient deformation in an epithelium following a grafting operation. For example, deleting a slab of tissue from a tubular segment and reuniting the cut ends should produce a constriction of the tube at the host-graft junction. We propose that patterns of strain and adhesion can provide positional information which regulates subsequent development. Local increases in strain or adhesive disparity may stimulate mitoses; the resulting changes in distribution of cells will affect morphogenesis.     

Failure of homocysteine to induce neural tube defects in a mouse model

BACKGROUND: Folate deficiencies have been associated with many adverse congenital abnormalities. It is not clear, however, whether these defects are due to a folate deficiency or to an increase in homocysteine. Homocysteine has been shown to be teratogenic in the chicken-embryo model and it has been suggested that homocysteine-induced defects are mediated by inhibiting the N-methyl-D-aspartate (NMDA) receptor on neural crest cells. The majority of the teratology studies have been carried out using the chicken embryo model. In an effort to develop a murine model of homocysteine-induced neural tube defects, several inbred mouse strains were treated with homocysteine or the NMDA inhibitor MK801 and the fetuses examined for any induced-NTD. METHODS: Several in-bred mouse strains were administered homocysteine once on gestational day (GD) E8.5 or once daily on GD 6.5-10.5. Additionally, because homocysteine was been reported to mediate its effects through the NMDA receptor, the effect of MK801, an antagonist of this receptor, was also investigated. RESULTS: Regardless of the mouse treatment time, homocysteine failed to induce neural tube defects in our in-bred mouse strains. Homocysteine also failed to increase the number of neural tube defects in the splotch strain, regardless of the genotype. CONCLUSIONS: Irrespective of the mouse strain or treatment, homocysteine failed to induce neural tube defects in our mouse models, which is in contrast to what has been reported in the chicken embryo models.     

Matricellular proteins in development: Perspectives from the Drosophila heart

The Drosophila model represents an attractive system in which to study the functional contribution of specific genes to organ development. Within the embryo, the heart tube serves as an informative developmental paradigm to analyze functional aspects of matricellular proteins. Here, we describe two essential extracellular matricellular proteins, Multiplexin (Mp) and Lonely heart (Loh). Each of these proteins contributes to the development and morphogenesis of the heart tube by regulating the activity/localization of essential extracellular proteins. Mp, which is secreted by heart cardioblasts and is specifically distributed in the lumen of the heart tube, binds to the signaling protein Slit, and facilitates its local signaling at the heart's luminal domain. Loh is an ADAMTS-like protein, which serves as an adapter protein to Pericardin (a collagen-like protein), promoting its specific localization at the abluminal domain of the heart tube. We also introduce the Drosophila orthologues of matricellular proteins present in mammals, including Thrombospondin, and SPARC, and discuss a possible role for Teneurins (Ten-A and Ten-M) in the heart. Understanding the role of these proteins provides a novel developmental perspective into the functional contribution of matricellular proteins to organ development.     

An incremental deformation model of arterial dissection

We develop a mathematical model for a small axisymmetric tear in a residually stressed and axially pre-stretched cylindrical tube. The residual stress is modelled by an opening angle when the load-free tube is sliced along a generator. This has application to the study of an aortic dissection, in which a tear develops in the wall of the artery. The artery is idealised as a single-layer thick-walled axisymmetric hyperelastic tube with collagen fibres using a Holzapfel–Gasser–Ogden strain-energy function, and the tear is treated as an incremental deformation of this tube. The lumen of the cylinder and the interior of the dissection are subject to the same constant (blood) pressure. The equilibrium equations for the incremental deformation are derived from the strain energy function. We develop numerical methods to study the opening of the tear for a range of material parameters and boundary conditions. We find that decreasing the fibre angle, decreasing the axial pre-stretch and increasing the opening angle all tend to widen the dissection, as does an incremental increase in lumen and dissection pressure.

     

Introducing mesoscopic information into constitutive equations for arterial walls

We propose a new elastic constitutive law for arterial tissue in which the limiting polymeric chain extensibility of both collagen and elastin fibres is accounted for. The elastic strain-energy function is separated additively into two parts: an isotropic contribution associated with the matrix (incorporating the elastin fibre network) and an anisotropic one associated with the collagen fibres. Information on the limiting extensibility in each case provides some mesoscopic input into the model. The (logarithm-based) model is compared with the Fung-Demiray exponential model and certain other recently proposed models. Some aspects of the elastic response under extension and inflation of a thin-walled circular cylindrical tube (the artery) are then examined and compared with the corresponding response of a rubber-like tube. We point out that our model, when both isotropic and anisotropic terms are included, can be developed to accommodate changing mechanical properties associated with degradation of the elastin and collagen by considering the material constants that define the limit of chain extensibility to evolve in time.     

Computer modelling of neural tube defects

Neurulation, the curling of the neuroepithelium to form the neural tube, is an essential component of the development of animal embryos. Defects of neural tube formation, which occur with an overall frequency of one in 500 human births, are the cause of severe and distressing congenital abnormalities. However, despite the fact that there is increasing information from animal experiments about the mechanisms which effect neural tube formation, much less is known about the fundamental causes of neural tube defects (NTD). The use of computer models provides one way of gaining clues about the ways in which neurulation may be compromised. Here we employ one computer model to examine the robustness of different cellular mechanisms which are thought to contribute to neurulation. The model, modified from that of Odell et al (Odell, G.M., Oster, G., Alberch, P. and Burnside, B., (1981)) mimics neurulation by laterally propagating a wave of apical contraction along an active zone within a ring of cells. We link the results to experimental evidence gained from studies of embryos in which neurulation has been perturbed. The results indicate that alteration of one of the properties of non-neural tissue can delay or inhibit neurulation, supporting the idea, gained from observation of embryos bearing genes which predispose to NTD, that the tissue underlying the neuroepithelium may contribute to the elevation of the neural folds. The results also show that reduction of the contractile properties of a small proportion of the neuroepithelial cell population may have a profound effect on overall tissue profiling. The results suggest that the elevation of the neural folds, and hence successful neurulation, may be vulnerable to relatively minor deficiencies in cell properties.     

Modelling the subgenual organ of the honeybee, Apis mellifera

In a recent study on the honeybee (Apis mellifera), the subgenual organ was observed moving inside the leg during sinusoidal vibrations of the leg (Kilpinen and Storm 1997). The subgenual organ of the honeybee is suspended in a haemolymph channel in the tibia of each leg. When the leg accelerates, the inertia causes the haemolymph and the subgenual organ to lag behind the movement of the rest of the leg. To elucidate the biophysics of the subgenual organ system of the honeybee, two mathematical models to simulate the experimentally observed mechanical response are considered. The models are a classical mass-spring model and a newly developed tube model consisting of an open-ended, fluid-filled tube occluded by an elastic structure midway. Both models suggest that the subgenual organ included in the haemolymph channel resembles that of an overdamped system. In resembling the biophysics of the subgenual organ system in the honeybee, we consider the tube model to be the better of the two because it simulates a mechanical response which complies best with the experimental data, and the physical parameters in the model can be related to the␣constituent parts of the subgenual organ included in the haemolymph channel. Received: 25 July 1997 / Accepted in revised form: 8 December 1997     

Movement of the tube cell in the lily style in the absence of the pollen grain and the spent pollen tube

Our model proposes that pollen tube growth is a form of cell movement where the tube tip can be considered analogous to a migrating cell which leaves a trail of extracellular matrix (the spent pollen tube) behind. We demonstrate that the tube cell can convey the sperm cells to the ovule and effect fertilization even in the absence of the pollen grain and the spent pollen tube. Adhesion is an integral part of cell attachment and movement in animal systems. We show that in vivo-grown pollen tubes grow beneath the cuticle of the stylar transmitting tract epidermis and directly adhere to one another and the outer wall of the epidermal cells. A fibrous wall material is found to cover the tip of the pollen tube cell wall and the surface of the transmitting tract cells where the two adhere. Fixation methods to preserve adhesive compounds were used. The pollen-tubes grown in vivo, but not in vitro, show star-shaped clusters of F-actin microfilaments in the region back from the tip, as seen by rhodamine-phalloidin staining. These configurations are similar to focal adhesions seen in moving animal cells.