Diurnal changes in volume and solute transport coefficients of phaseolus roots

Volume (J_v) and solute (J_s) fluxes through Phaseolus root systems were observed over a 24-hour period. The volume flux was varied in a pressure chamber by altering the hydrostatic pressure in 10 steps, from 0 to 0.41 megapascals. All root systems showed strong diurnal peaks in volume flux. The five transport coefficients (σ, ω, J_s^*, L_p, and π^*) were estimated from a nonlinear least squares algorithm. Analysis of the data revealed that all the coefficients exhibited a diurnal rhythm. When the total differential of the volume flux was considered it was possible to show that the diurnal changes in volume flux were due to a complex interaction between the diurnally shifting coefficients with the role of each highly dependent on the level of volume flux. At low volume fluxes, ω, J_s^*, and π^* accounted for nearly all the diurnal change in volume flux. At high volume fluxes, however, the major influence shifted to L_p and π^*, while ω and J_s^* became relatively unimportant. Thus, π^* was the only coefficient of interest across the entire range of J_v and appeared to be the single most important one in determining the diurnal rhythm of J_v under conditions of a constant applied pressure.     

Development of a three-dimensional finite element model of a human tibia using experimental modal analysis.

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.     

A molecular framework for coupling cellular volume and osmotic solute transport control

Eukaryotic cells expand using vesicle traffic to increase membrane surface area. Expansion in walled eukaryotes is driven by turgor pressure which depends fundamentally on the uptake and accumulation of inorganic ions. Thus, ion uptake and vesicle traffic must be controlled coordinately for growth. How this coordination is achieved is still poorly understood, yet is so elemental to life that resolving the underlying mechanisms will have profound implications for our understanding of cell proliferation, development, and pathogenesis, and will find applications in addressing the mineral and water use by plants in the face of global environmental change. Recent discoveries of interactions between trafficking and ion transport proteins now open the door to an entirely new approach to understanding this coordination. Some of the advances to date in identifying key protein partners in the model plant Arabidopsis and in yeast at membranes vital for cell volume and turgor control are outlined here. Additionally, new evidence is provided of a wider participation among Arabidopsis Kv-like K(+) channels in selective interaction with the vesicle-trafficking protein SYP121. These advances suggest some common paradigms that will help guide further exploration of the underlying connection between ion transport and membrane traffic and should transform our understanding of cellular homeostasis in eukaryotes.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

A three-dimensional finite element model for arterial clamping

Clamp induced injuries of the arterial wall may determine the outcome of surgical procedures. Thus, it is important to investigate the underlying mechanical effects. We present a three-dimensional finite element model, which allows the study of the mechanical response of an artery-treated as a two-layer tube-during arterial clamping. The important residual stresses, which are associated with the load-free configuration of the artery, are also considered. In particular, the finite element analysis of the deformation process of a clamped artery and the associated stress distribution is presented. Within the clamping area a zone of axial tensile peak-stresses was identified, which (may) cause intimal and medial injury. This is an additional injury mechanism, which clearly differs from the commonly assumed wall damage occurring due to compression between the jaws of the clamp. The proposed numerical model provides essential insights into the mechanics of the clamping procedure and the associated injury mechanisms. It allows detailed parameter studies on a virtual clamped artery, which can not be performed with other methodologies. This approach has the potential to identify the most appropriate clamps for certain types of arteries and to guide optimal clamp design.     

Variability of a three-dimensional finite element model constructed using magnetic resonance images of a knee for joint contact stress analysis

Magnetic resonance (MR) imaging has been widely used to evaluate the thickness and volume of articular cartilage both in vivo and in vitro. While morphological information on the cartilage can be obtained using MR images, image processing for extracting geometric boundaries of the cartilage may introduce variations in the thickness of the cartilage. To evaluate the variability of using MR images to construct finite element (FE) knee cartilage models, five investigators independently digitized the same set of MR images of a human knee. The topology of cartilage thickness was determined using a minimal distance algorithm. Less than 8 percent variation in cartilage thickness was observed from the digitized data. The effect of changes in cartilage thickness on contact stress analysis was then investigated using five FE models of the knee. One FE model (average FE model) was constructed using the mean values of the digitized contours of the cartilage, and the other four were constructed by varying the thickness of the average FE model by +/- 5 percent and +/- 10 percent, respectively. The results demonstrated that under axial tibial compressive loading (up to 1,400 N), variations of cartilage thickness caused by digitization of MR images may result in a difference of approximately 10 percent in peak contact stresses (surface pressure, von Mises stress, and hydrostatic pressure) in the cartilage. A reduction of cartilage thickness caused increases of contact stresses, while an increase of cartilage thickness reduced contact stresses. Furthermore, the effect of variation of material properties of the cartilage on contact stress analysis was investigated. The peak contact stress increased almost linearly with the Young's modulus of the cartilage. The peak von Mises stress was dramatically reduced when the Poisson,s ratio was increased from 0.05 to 0.49 under an axial compressive load of 1,400 N, while peak hydrostatic pressure was dramatically increased. Peak surface pressure was also increased with the Poisson's ratio, but with a lower magnitude compared to von Mises stress and hydrostatic pressure. In conclusion, the imaging process may cause 10 percent variations in peak contact stress, and the predicted stress distribution is sensitive to the accuracy of the material properties of the cartilage model, especially to the variation of Poisson's ratio.     

Development of an accurate three-dimensional finite element knee model

This paper presents the development of a detailed articulating three-dimensional finite-element model of the human knee, derived from MRI scan images. The model utilises precise material models and many contact interfaces in order to produce a realistic kinematic response. The behaviour of the model was examined within two fields of biomechanical simulations: general life and car-crash. These simulations were performed with the non-linear explicit dynamic code PAM-SAFE trade mark. The knee model produced results that compared favourably with existing literature. Such a model (together with other joint models that could be constructed using the same techniques) would be a valuable tool for examining new designs of prosthesis and mechanisms of injury.     

Orbital volume measurements in enophthalmos using three-dimensional CT imaging

The purpose of this study was to investigate enophthalmos by measuring the volume of various orbital structures using off-line computer techniques on images generated by a CT scanner. Eleven patients with enophthalmos had CT scans of the orbits consisting of 30 to 40 adjacent 1.5-mm slices. The data from the scans were analyzed on a Nova 830 stand-alone computer system using software programs that allowed measurement of total bony orbital volume, total soft-tissue volume, globe volume, orbital fat volume, neuromuscular tissue volume, and apex-to-globe distance in the horizontal plane. These data were analyzed comparing the volumes in the normal eye with the volumes in the enophthalmic eye in each patient. The analysis demonstrated a statistically significant increase in bony orbital volume in the enophthalmic eye, but the total soft-tissue volume, fat volume, neuromuscular tissue volume, and globe volume were the same as in the normal eye. The apex-to-globe distance, a measure of the degree of enophthalmos, was less in the enophthalmic eye than in the normal eye. These results suggest that in the majority of patients, the cause of posttraumatic enophthalmos is increased bony orbital volume rather than by soft-tissue loss or fat necrosis. (Several patients showed no volume discrepancies, and it is likely that cicatricial contracture is responsible for the enophthalmos in these cases.) This study suggests that the objective of surgery for correction of enophthalmos in patients with a volume discrepancy should be to decrease the volume of the bony orbit and to increase the anterior projection of the globe.     

A finite element model for protein transport in vivo

Background  

Biological mass transport processes determine the behavior and function of cells, regulate interactions between synthetic agents and recipient targets, and are key elements in the design and use of biosensors. Accurately predicting the outcomes of such processes is crucial to both enhancing our understanding of how these systems function, enabling the design of effective strategies to control their function, and verifying that engineered solutions perform according to plan.     

Role of solute drag in intestinal transport

This study presents experiments related to the role of solvent drag and solute drag in the transmembrane movement of nonelectrolytes in a perfused rat intestine preparation. Conditions were chosen to simulate the effects of luminal hyperosmolarity on the permeability of tracer solutes. Data are presented on net water flux, transepithelial potentials, and lumen-to-blood and blood-to-lumen tracer solute movements during control electrolyte perfusion and after making the perfusate hyperosmotic. The results indicate that both solvent drag and solute drag can play significant roles in the transepithelial movement of solute and solute permeabilities in the rat ileum preparation. It is suggested that the potential roles of solvent drag and solute drag should be accounted for or considered during the characterization of the mechanisms of biological membrane function.     

Theoretical aspects of evaluation of the plasma membrane time constant in myocardial tissue using a model of three-dimensional RC-medium of finite thickness

An analytical solution of the differential equation describing the distribution of the electrotonic potential in the three-dimensional RC-medium of finite thickness when the current source is hemispheric was obtained. Computerized programs were developed, and families of curves of T1/2 (time during which the electrotonic potential reaches half of the stationary amplitude) dependence on the size of current electrode (R0), the distance between the current electrode and the potential recording site (R), and medium thickness (D) were established. It is shown that function T1/2 = f(R) is not linear in close vicinity of the current electrode, and the application of linear dependence T1/2 = R/2 + const for the determination of the plasmic membrane time constant (taum) in myocardial tissue would lead to errors of -70% / +20%.     

Prediction of total knee motion using a three-dimensional computer-graphics model

Twenty-three knees were sectioned, digitized, and standardized to determine the 'average' three-dimensional bony geometry and ligamentous attachments. Data on normal knee motion were obtained from a cadaveric study. An algorithm was written to simulate three-dimensional patella motion. Verification of the knee model was achieved by determining femoro-tibial and patello-femoral contact locations, as well as ligament length patterns, and comparing the results with published data. The criterion for maximum predicted knee motion with a prosthesis in place was the length of the posterior cruciate ligament. Three total knee replacement surfaces were mathematically generated: flat, laxity and conforming. A greater flexion angle was obtained with a flat tibial surface than for the laxity or conforming. Posterior tibial component displacement increased the range of motion, but only slightly. For all tibial surfaces, increased range of motion was achieved with a 10 degrees posterior tilt of the tibial tray. Anterior femoral component displacement increased motion due to reduction in posterior cruciate tension during flexion. The results are applicable to the design and surgical technique of total knee replacement.     

A three-dimensional nonlinear finite element model of lumbar intervertebral joint in torsion

Torsion as a cause of failure in the lumbar intervertebral joint was studied using a three-dimensional nonlinear finite element model. The role of facets and ligaments as well as the stress distributions in the posterior elements, the disk, the ligaments, and the vertebral body were examined. For physiological range of torsion, the facets carried 10 to 40 percent of the torque. The fiber stresses in the disk were the highest at the lateral margin of the outer layer of the annulus. Therefore, torsion itself is unlikely to cause posterior or posterolateral disk prolapse.     

The effect of cyclic deformation and solute binding on solute transport in cartilage

Diffusive transport must play an important role in transporting nutrients into cartilage due to its avascular nature. Recent theoretical studies generally support the idea that cyclic loading enhances large molecule transport through advection. However, to date, reactive transport, i.e. the effects of solute binding, has not yet been taken into consideration in cyclically deformed cartilage. In the present study, we develop a reactive transport model to describe the potential role of binding of solute within cyclically deformed cartilage. Our results show that binding does have a significant effect on transport, particularly for the low IGF-I concentrations typical of synovial fluid. A dynamic loading regime of high strain magnitudes (up to 10%) in combination with high frequencies (e.g. 1 Hz) was seen to produce the most dramatic results with enhanced total uptake ratio as high as 25% averaged over the first 5h of cyclic loading.     

Energy transduction and solute transport in streptococci

Metabolic energy in lactic streptococci can be generated by substrate level phosphorylation and by efflux of end-products in symport with protons. During growth on lactose or glucose Streptococcus cremoris maintains a high proton motive force and phosphate potential. Both energy intermediates dissipate rapidly when the energy supply stops. In the initial phase of starvation the internal phosphoenolpyruvate (PEP) pool increases rapidly and this enables the organism for a prolonged period during starvation to accumulate the energy source via a PEP-dependent uptake system.     

A three-dimensional finite element model for the mechanics of cell-cell interactions

Technical challenges, including significant ones associated with cell rearrangement, have hampered the development of three-dimensional finite element models for the mechanics of embryonic cells. These challenges have been overcome by a new formulation in which the contents of each cell, assumed to have a viscosity mu, are modeled using a system of orthogonal dashpots. This approach overcomes a stiffening artifact that affects more traditional models, in which space-filling viscous elements are used to model the cytoplasm. Cells are assumed to be polyhedral in geometry, and each n-sided polygonal face is subdivided into n triangles with a common node at the face center so that it needs not remain flat. A constant tension gamma is assumed to act along each cell-cell interface, and cell rearrangements occur through one of two complementary topological transformations. The formulation predicts mechanical interactions between pairs of similar or dissimilar cells that are consistent with experiments, two-dimensional simulations, contact angle theory, and intracellular pressure calculations. Simulations of the partial engulfment of one tissue type by another show that the formulation is able to model aggregates of several hundred cells without difficulty. Simulations carried out using this formulation suggest new experimental approaches for measuring cell surface tensions and interfacial tensions. The formulation holds promise as a tool for gaining insight into the mechanics of isolated or aggregated embryonic cells and for the design and interpretation of experiments that involve them.     

Anatomically based three-dimensional model of airways to simulate flow and particle transport using computational fluid dynamics.

We have studied gas flow and particle deposition in a realistic three-dimensional (3D) model of the bronchial tree, extending from the trachea to the segmental bronchi (7th airway generation for the most distal ones) using computational fluid dynamics. The model is based on the morphometrical data of Horsfield et al. (Horsfield K, Dart G, Olson DE, Filley GF, and Cumming G. J Appl Physiol 31: 207-217, 1971) and on bronchoscopic and computerized tomography images, which give the spatial 3D orientation of the curved ducts. It incorporates realistic angles of successive branching planes. Steady inspiratory flow varying between 50 and 500 cm(3)/s was simulated, as well as deposition of spherical aerosol particles (1-7 microm diameter, 1 g/cm(3) density). Flow simulations indicated nonfully developed flows in the branches due to their relative short lengths. Velocity flow profiles in the segmental bronchi, taken one diameter downstream of the bifurcation, were distorted compared with the flow in a simple curved tube, and wide patterns of secondary flow fields were observed. Both were due to the asymmetrical 3D configuration of the bifurcating network. Viscous pressure drop in the model was compared with results obtained by Pedley et al. (Pedley TJ, Schroter RC, and Sudlow MF. Respir Physiol 9: 387-405, 1970), which are shown to be a good first approximation. Particle deposition increased with particle size and was minimal for approximately 200 cm(3)/s inspiratory flow, but it was highly heterogeneous for branches of the same generation.     

Dynamic compression augments interstitial transport of a glucose-like solute in articular cartilage

Solute transport through the extracellular matrix is essential for cellular activities in articular cartilage. Increased solute transport via fluid convection may be a mechanism by which dynamic compression stimulates chondrocyte metabolism. However, loading conditions that optimally augment transport likely vary for different solutes. To investigate effects of dynamic loading on transport of a bioactive solute, triangular mechanical loading waveforms were applied to cartilage explants disks while interstitial transport of a fluorescent glucose analog was monitored. Peak-to-peak compression amplitudes varied from 5-50% and frequencies varied from 0.0006-0.1 Hz to alter the spatial distribution and magnitude of oscillatory fluid flow. Solute transport was quantified by monitoring accumulation of fluorescence in a saline bath circulated around the explant. Individual explants were subjected to a series of compression protocols, so that effects of loading on solute desorption could be observed directly. Maximum increases in solute transport were obtained with 10-20% compression amplitudes at 0.1 Hz; similar loading protocols were previously found to stimulate chondrocyte metabolism in vitro. Results therefore support hypotheses relating to increased solute transport as a mediator of the cartilage biological response to dynamic compression, and may have application in mechanical conditioning of cartilage constructs for tissue engineering.