Evaluation of an aortic valve prosthesis: Fluid-structure interaction or structural simulation?

Bio-inspired polymeric heart valves (PHVs) are excellent candidates to mimic the structural and the fluid dynamic features of the native valve. PHVs can be implanted as prosthetic alternative to currently clinically used mechanical and biological valves or as potential candidate for a minimally invasive treatment, like the transcatheter aortic valve implantation. Nevertheless, PHVs are not currently used for clinical applications due to their lack of reliability. In order to investigate the main features of this new class of prostheses, pulsatile tests in an in-house pulse duplicator were carried out and reproduced in silico with both structural Finite-Element (FE) and Fluid-Structure interaction (FSI) analyses. Valve kinematics and geometric orifice area (GOA) were evaluated to compare the in vitro and the in silico tests. Numerical results showed better similarity with experiments for the FSI than for the FE simulations. The maximum difference between experimental and FSI GOA at maximum opening time was only 5%, as compared to the 46.5% between experimental and structural FE GOA. The stress distribution on the valve leaflets clearly reflected the difference in valve kinematics. Higher stress values were found in the FSI simulations with respect to those obtained in the FE simulation. This study demonstrates that FSI simulations are more appropriate than FE simulations to describe the actual behaviour of PHVs as they can replicate the valve-fluid interaction while providing realistic fluid dynamic results.     

Pressure and flow in the umbilical cord

A fluid dynamic study of blood flow within the umbilical vessels of the human maternal-fetal circulatory system is considered. It is found that the umbilical coiling index (UCI) is unable to distinguish between cords of significantly varying pressure and flow characteristics, which are typically determined by the vessel curvature, torsion and length. Larger scale geometric non-uniformities superposed over the inherent coiling, including cords exhibiting width and/or local UCI variations as well as loose true knots, typically produce a small effect on the total pressure drop. Crucially, this implies that a helical geometry of mean coiling may be used to determine the steady vessel pressure drop through a more complex cord. The presence of vessel constriction, however, drastically increases the steady pressure drop and alters the flow profile. For pulsatile-flow within the arteries, the steady pressure approximates the time-averaged value with high accuracy over a wide range of cords. Furthermore, the relative peak systolic pressure measured over the period is virtually constant and approximately 25% below the equivalent straight-pipe value for a large range of non-straight vessels. Interestingly, this suggests that the presence of vessel helicity dampens extreme pressures within the arterial cycle and may provide another possible evolutionary benefit to the coiled structure of the cord.     

Hydrodynamic and Longitudinal Impedance Analysis of Cerebrospinal Fluid Dynamics at the Craniovertebral Junction in Type I Chiari Malformation

Elevated or reduced velocity of cerebrospinal fluid (CSF) at the craniovertebral junction (CVJ) has been associated with type I Chiari malformation (CMI). Thus, quantification of hydrodynamic parameters that describe the CSF dynamics could help assess disease severity and surgical outcome. In this study, we describe the methodology to quantify CSF hydrodynamic parameters near the CVJ and upper cervical spine utilizing subject-specific computational fluid dynamics (CFD) simulations based on in vivo MRI measurements of flow and geometry. Hydrodynamic parameters were computed for a healthy subject and two CMI patients both pre- and post-decompression surgery to determine the differences between cases. For the first time, we present the methods to quantify longitudinal impedance (LI) to CSF motion, a subject-specific hydrodynamic parameter that may have value to help quantify the CSF flow blockage severity in CMI. In addition, the following hydrodynamic parameters were quantified for each case: maximum velocity in systole and diastole, Reynolds and Womersley number, and peak pressure drop during the CSF cardiac flow cycle. The following geometric parameters were quantified: cross-sectional area and hydraulic diameter of the spinal subarachnoid space (SAS). The mean values of the geometric parameters increased post-surgically for the CMI models, but remained smaller than the healthy volunteer. All hydrodynamic parameters, except pressure drop, decreased post-surgically for the CMI patients, but remained greater than in the healthy case. Peak pressure drop alterations were mixed. To our knowledge this study represents the first subject-specific CFD simulation of CMI decompression surgery and quantification of LI in the CSF space. Further study in a larger patient and control group is needed to determine if the presented geometric and/or hydrodynamic parameters are helpful for surgical planning.     

Assimilate transport in phloem sets conditions for leaf gas exchange

Carbon uptake and transpiration in plant leaves occurs through stomata that open and close. Stomatal action is usually considered a response to environmental driving factors. Here we show that leaf gas exchange is more strongly related to whole tree level transport of assimilates than previously thought, and that transport of assimilates is a restriction of stomatal opening comparable with hydraulic limitation. Assimilate transport in the phloem requires that osmotic pressure at phloem loading sites in leaves exceeds the drop in hydrostatic pressure that is due to transpiration. Assimilate transport thus competes with transpiration for water. Excess sugar loading, however, may block the assimilate transport because of viscosity build‐up in phloem sap. Therefore, for given conditions, there is a stomatal opening that maximizes phloem transport if we assume that sugar loading is proportional to photosynthetic rate. Here we show that such opening produces the observed behaviour of leaf gas exchange. Our approach connects stomatal regulation directly with sink activity, plant structure and soil water availability as they all influence assimilate transport. It produces similar behaviour as the optimal stomatal control approach, but does not require determination of marginal cost of water parameter.     

An analytical model of the hydraulic aspects of stomatal dynamics

An analytical model of the hydraulic aspects of stomatal dynamics is formulated in this paper. The model consists of a coupled system of non-linear, ordinary differential equations, written in terms of water potentials, hydrostatic pressures, osmotic potentials, water vapor resistances and water fluxes. The model is validated by comparisons with the experimental literature. Numerical solutions of the model show qualitative agreement with most known stomatal responses.Stomatal opening in the model is dependent on the interaction of the guard and subsidiary cells in the following manner. Pore opening is initiated by a rise in the guard cell hydrostatic pressure. As the stomate opens, transpiration increases, causing the cell wall water potential to drop. The drop in cell wall water potential then causes the subsidiary cell pressure to drop, opening is accelerated, and the stomate literally “pops” open. Simulated opening proceeds in two distinct phases: a stress phase and a motor phase. During the stress phase, guard cell pressure rises but the pore remains closed. The motor phase commences when the guard cell pressure has risen sufficiently to initiate pore opening, beyond which point opening progresses rapidly.Hydropassive stomatal movements are found to be insufficient to regulate water loss at low leaf water potentials. Stable, hydraulically-based oscillations in stomatal aperture are shown in the model by the existence of a stable limit cycle. The period of these oscillations is strongly influenced by the cell membrane hydraulic conductivity. An increased conductivity results in a shorter period oscillation. Environmental conditions promoting oscillatory behavior are in qualitative agreement with the experimental literature.     

Systolic fluid–structure interaction model of the congenitally bicuspid aortic valve: assessment of modelling requirements

A transient fluid–structure interaction (FSI) model of a congenitally bicuspid aortic valve has been developed which allows simultaneous calculation of fluid flow and structural deformation. The valve is modelled during the systolic phase (the stage when blood pressure is elevated within the heart to pump blood to the body). The geometry was simplified to represent the bicuspid aortic valve in two dimensions. A congenital bicuspid valve is compared within the aortic root only and within the aortic arch. Symmetric and asymmetric cusps were simulated, along with differences in mechanical properties. A moving arbitrary Lagrange–Euler mesh was used to allow FSI. The FSI model requires blood flow to induce valve opening and induced strains in the region of 10%. It was determined that bicuspid aortic valve simulations required the inclusion of the ascending aorta and aortic arch. The flow patterns developed were sensitive to cusp asymmetry and differences in mechanical properties. Stiffening of the valve amplified peak velocities, and recirculation which developed in the ascending aorta. Model predictions demonstrate the need to take into account the category, including any existing cusp asymmetry, of a congenital bicuspid aortic valve when simulating its fluid flow and mechanics.     

Relative contribution of articular cartilage’s constitutive components to load support depending on strain rate

Cartilage is considered a biphasic material in which the solid is composed of proteoglycans and collagen. In biphasic tissue, the hydraulic pressure is believed to bear most of the load under higher strain rates and its dissipation due to fluid flow determines creep and relaxation behavior. In equilibrium, hydraulic pressure is zero and load bearing is transferred to the solid matrix. The viscoelasticity of the collagen network also contributes to its time-dependent behavior, and the osmotic pressure to load bearing in equilibrium. The aim of the present study was to determine the relative contributions of hydraulic pressure, viscoelastic collagen stress, solid matrix stiffness and osmotic pressure to load carriage in cartilage under transient and equilibrium conditions. Unconfined compression experiments were simulated using a fibril-reinforced poroviscoelastic model of articular cartilage, including water, fibrillar viscoelastic collagen and non-fibrillar charged glycosaminoglycans. The relative contributions of hydraulic and osmotic pressures and stresses in the fibrillar and non-fibrillar network were evaluated in the superficial, middle and deep zone of cartilage under five different strain rates and after relaxation. Initially upon loading, the hydraulic pressure carried most of the load in all three zones. The osmotic swelling pressure carried most of the equilibrium load. In the surface zone, where the fibers were loaded in tension, the collagen network carried 20 % of the load for all strain rates. The importance of these fibers was illustrated by artificially modifying the fiber architecture, which reduced the overall stiffness of cartilage in all conditions. In conclusion, although hydraulic pressure dominates the transient behavior during cartilage loading, due to its viscoelastic nature the superficial zone collagen fibers carry a substantial part of the load under transient conditions. This becomes increasingly important with higher strain rates. The interesting and striking new insight from this study suggests that under equilibrium conditions, the swelling pressure generated by the combination of proteoglycans and collagen reinforcement accounts cartilage stiffness for more than 90 % of the loads carried by articular cartilage. This finding is different from the common thought that load is transferred from fluid to solid and is carried by the aggregate modulus of the solid. Rather, it is transformed from hydraulic to osmotic swelling pressure. These results show the importance of considering both (viscoelastic) collagen fibers as well as swelling pressure in studies of the (transient) mechanical behavior of cartilage.     

Incorporating measured valve properties into a numerical model of a lymphatic vessel

An existing lumped-parameter model of multiple lymphangions (lymphatic vascular segments) in series is adapted for the incorporation of recent physiological measurements of lymphatic vascular properties. The new data show very marked nonlinearity of the passive pressure–diameter relation during distension, relative to comparable blood vessels, and complex valve behaviour. Since lymph is transported as a result of either the active contraction or the passive squeezing of vascular segments situated between two one-way valves, the performance of these valves is of primary importance. The valves display hysteresis (the opening and closing pressure drop thresholds differ), a bias to staying open (both state changes occur when the trans-valve pressure drop is adverse) and pressure-drop threshold dependence on transmural pressure. These properties, in combination with the strong nonlinearity that valve operation represents, have in turn caused intriguing numerical problems in the model, and we describe numerical stratagems by which we have overcome the problems. The principal problem is also generalised into a relatively simple mathematical example, for which solution detail is provided using two different solvers.     

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.

     

Mathematica numerical simulation of peristaltic biophysical transport of a fractional viscoelastic fluid through an inclined cylindrical tube

This paper studies the peristaltic transport of a viscoelastic fluid (with the fractional second-grade model) through an inclined cylindrical tube. The wall of the tube is modelled as a sinusoidal wave. The flow analysis is presented under the assumptions of long wave length and low Reynolds number. Caputo's definition of fractional derivative is used to formulate the fractional differentiation. Analytical solutions are developed for the normalized momentum equations. Expressions are also derived for the pressure, frictional force, and the relationship between the flow rate and pressure gradient. Mathematica numerical computations are then performed. The results are plotted and analysed for different values of fractional parameter, material constant, inclination angle, Reynolds number, Froude number and peristaltic wave amplitude. It is found that fractional parameter and Froude number resist the flow pattern while material constant, Reynolds number, inclination of angle and amplitude aid the peristaltic flow. Furthermore, frictional force and pressure demonstrate the opposite behaviour under the influence of the relevant parameters emerging in the equations of motion. The study has applications in uretral biophysics, and also potential use in peristaltic pumping of petroleum viscoelastic bio-surfactants in chemical engineering and astronautical applications involving conveyance of non-Newtonian fluids (e.g. lubricants) against gravity and in conduits with deformable walls.     

Internal Flow Effects on Isotropic Confined Sand-Clay Mixtures

Under the effect of internal flows, a liner can undergo a washing out of particles, which modifies the particle size distribution and affects hydraulic, chemical and mechanical characteristics. This paper discusses the effects of internal flows on sand/kaolin mixture, in terms of rate of erosion and modification of the hydraulic conductivity. A parametric study is conducted with a specific device that consists of three modified triaxial cells. These cells allow isotropically consolidating and confining specimens, they prevent a parasitic flow and survey large deformations of specimen. The tests reveal that suffusion of clay is accompanied by a clogging in the specimen that induces a drop in hydraulic conductivity. For high gradients the erosion of clay is accompanied by the backward erosion of sand and finally the specimen collapses. The erosion rate then depends on the values of the different parameters considered (hydraulic gradient, clay content and filter pore opening size).     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Determinants of transpyloric fluid transport: a study using combined real-time ultrasound,manometry, and impedance recording

Intraluminal impedance recording has made it possible to record fluid transport across the pylorus during the interdigestive state without filling the stomach. During antral phase II, fluid transport occurs with and without manometrically detectable antral contraction. Our aim was to investigate the relationships between ultrasonographic patterns of antral contraction, manometric pressure waves, and transpyloric fluid transport during antral phase II. Antral wall movements were recorded by real-time ultrasound (US) in eight healthy volunteers (mean age 24 +/- 7 yr) during 17 +/- 5 min of antral phase II. Concomitantly, a catheter positioned across the pylorus, monitored by transmucosal potential difference measurement, recorded five impedance signals (1 antral, 1 pyloric, and 3 duodenal) and six manometric signals (2 antral, 1 pyloric, and 3 duodenal). Antral contractions detected by US at the level of the two antral impedance electrodes were classified according to their association with a pyloric opening or a duodenal contraction. Transpyloric liquid transport events (impedance drop of >40% of the baseline with an antegrade or retrograde propagation) and manometric pressure waves (amplitude and duration) were identified during the whole study and especially during each period of US antral contraction. A total of 110 antral contractions was detected by US. Of these, 79 were also recorded by manometry. Fluid transport across the pylorus was observed in 70.9% of the US-detected antral contractions. Pyloric opening was observed in 98.6% of the contractions associated with fluid transport compared with 50% in the absence of fluid transport (P < 0.05). Antral contractions associated with fluid transport were significantly (P < 0.05) more often propagated to the duodenum (92%) than those without fluid transport (53%). Pressure waves associated with fluid transport were of higher amplitude (208 mmHg, range 22-493) and longer duration (7 s, range 2.5-13.5 s) than those not associated with fluid transport (102 mmHg, range 18-329 mmHg, and 4.1 s, range 2-8.5 s; P < 0.05). The propagation of the antral contractions in the duodenum in US was always associated with a pyloric opening, whereas only 8 of the 25 contractions without duodenal propagation were associated with a pyloric opening (P < 0.05). The presence of duodenal contractile activity before the onset of an antral contraction in US was always accompanied by pyloric opening and with fluid transport in 93.3%, compared with 56.8% in its absence (P < 0.05). In antral phase II, US is the most sensitive technique to detect antral contractions. Transpyloric fluid transport observed in relation to antral contractions occurs mainly in association with contractions of high amplitude and long duration and is associated with pyloric opening and/or duodenal propagation.     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.     

Effects of humidity on light-induced stomatal opening: evidence for hydraulic coupling among stomata

A mechanism for co-ordinating behaviour of stomata within an areole during patchy stomatal conductance has recently been proposed. This mechanism depends on hydraulic interactions among stomata that are mediated by transpiration-induced changes in epidermal turgor. One testable prediction that arises from this proposed mechanism is that the strength of hydraulic coupling among stomata should be proportional to evaporative demand and, therefore, inversely proportional to humidity. When a leaf is illuminated following a period of darkness, there is typically a period of time, termed the Spannungsphase, during which guard cell osmotic and turgor pressure are increasing, but the pore remains closed. If hydraulic coupling is proportional to evaporative demand, then variation among stomata in the duration of the Spannungsphase should be lower for leaves at low humidity than for leaves at high humidity. A similar prediction emerged from a computer model based on the proposed hydraulic mechanisms. These predictions were tested by measuring individual stomatal apertures on intact transpiring leaves at low and high humidity and on vacuum-infiltrated leaf pieces (to eliminate transpiration) as PFD was increased to high values from either darkness or a low value. Results showed that the range of Spannungsphasenamong stomata was reduced at low humidity compared to high humidities. Experiments that began at low PFD, rather than at darkness, showed no delay in stomatal opening. These results are discussed in the context of the proposed hydraulic coupling mechanisms.     

Modelling human eye under blast loading

Primary blast injury (PBI) is the general term that refers to injuries resulting from the mere interaction of a blast wave with the body. Although few instances of primary ocular blast injury, without a concomitant secondary blast injury from debris, are documented, some experimental studies demonstrate its occurrence. In order to investigate PBI to the eye, a finite element model of the human eye using simple constitutive models was developed. The material parameters were calibrated by a multi-objective optimisation performed on available eye impact test data. The behaviour of the human eye and the dynamics of mechanisms occurring under PBI loading conditions were modelled. For the generation of the blast waves, different combinations of explosive (trinitrotoluene) mass charge and distance from the eye were analysed. An interpretation of the resulting pressure, based on the propagation and reflection of the waves inside the eye bulb and orbit, is proposed. The peculiar geometry of the bony orbit (similar to a frustum cone) can induce a resonance cavity effect and generate a pressure standing wave potentially hurtful for eye tissues.     

Evaluation of functional severity of coronary artery disease and fluid dynamics' influence on hemodynamic parameters: A review

Coronary Artery Disease (CAD) is responsible for most of the deaths in patients with cardiovascular diseases. Diagnostic coronary angiography analysis offers an anatomical knowledge of the severity of the stenosis. The functional or physiological significance is more valuable than the anatomical significance of CAD. Clinicians assess the functional severity of the stenosis by resorting to an invasive measurement of the pressure drop and flow. Hemodynamic parameters, such as pressure wire assessment fractional flow reserve (FFR) or Doppler wire assessment coronary flow reserve (CFR) are well-proven techniques to evaluate the physiological significance of the coronary artery stenosis in the cardiac catheterization laboratory. Between the two techniques mentioned above, the FFR is seen as a very useful index. The presence of guide wire reduces the coronary flow which causes the underestimation of pressure drop across the stenosis which leads to dilemma for the clinicians in the assessment of moderate stenosis. In such condition, the fundamental fluid mechanics is useful in the development of new functional severity parameters such as pressure drop coefficient and lesion flow coefficient. Since the flow takes place in a narrowed artery, the blood behaves as a non-Newtonian fluid. Computational fluid dynamics (CFD) allows a complete coronary flow simulation to study the relationship between the pressure and flow. This paper aims at explaining (i) diagnostic modalities for the evaluation of the CAD and valuable insights regarding FFR in the evaluation of the functional severity of the CAD (ii) the role of fluid dynamics in measuring the severity of CAD.     

Flow-induced deformation from pressurized cavities in absorbing porous tissues

The behaviour of a cavity during an injection of fluid into biological tissue is considered. High cavity pressure drives fluid into the neighbouring tissue where it is absorbed by capillaries and lymphatics. The tissue is modelled as a nonlinear deformable porous medium with the injected fluid absorbed by the tissue at a rate proportional to the local pressure. A model with a spherical cavity in an infinite medium is used to find the pressure and displacement of the tissue as a function of time and radial distance. Analytical and numerical solutions for a step change in cavity pressure show that the flow induces a radial compression in the medium together with an annular expansion, the net result being an overall expansion of the medium. Thus any flow induced deformation of the material will aid in the absorption of fluid.