Attenuation of reflected waves in man during retrograde propagation from femoral artery to proximal aorta.

BACKGROUND: Wave reflection may be an important influence on blood pressure, but the extent to which reflections undergo attenuation during retrograde propagation has not been studied. We quantified retrograde transmission of a reflected wave created by occlusion of the left femoral artery in man. METHODS: 20 subjects (age 31-83 years; 14 male) underwent invasive measurement of pressure and flow velocity with a sensor-tipped intra-arterial wire at multiple locations distal to the proximal aorta before, during and following occlusion of the left femoral artery by thigh cuff inflation. A numerical model of the circulation was also used to predict reflected wave transmission. Wave reflection was measured as the ratio of backward to forward wave energy (WRI) and the ratio of peak backward to forward pressure (Pb/Pf). RESULTS: Cuff inflation caused a marked reflection which was largest at 5-10 cm from the cuff (change (Δ) in WRI=0.50 (95% CI 0.38, 0.62); p<0.001, ΔPb/Pf=0.23 (0.18-0.29); p<0.001). The magnitude of the cuff-induced reflection decreased progressively at more proximal locations and was barely discernible at sites>40 cm from the cuff including in the proximal aorta. Numerical modelling gave similar predictions to those observed experimentally. CONCLUSIONS: Reflections due to femoral artery occlusion are markedly attenuated by the time they reach the proximal aorta. This is due to impedance mismatches of bifurcations traversed in the backward direction. This degree of attenuation is inconsistent with the idea of a large discrete reflected wave arising from the lower limb and propagating back into the aorta.

A novel curve fitting method for AV optimisation of biventricular pacemakers.

In this study, we designed and tested a new algorithm, which we call the 'restricted parabola', to identify the optimum atrioventricular (AV) delay in patients with biventricular pacemakers. This algorithm automatically restricts the hemodynamic data used for curve fitting to the parabolic zone in order to avoid inadvertently selecting an AV optimum that is too long.We used R, a programming language and software environment for statistical computing, to create an algorithm which applies multiple different cut-offs to partition curve fitting of a dataset into a parabolic and a plateau region and then selects the best cut-off using a least squares method. In 82 patients, AV delay was adjusted and beat-to-beat systolic blood pressure (SBP) was measured non-invasively using our multiple-repetition protocol. The novel algorithm was compared to fitting a parabola across the whole dataset to identify how many patients had a plateau region, and whether a higher hemodynamic response was achieved with one method.In 9/82 patients, the restricted parabola algorithm detected that the pattern was not parabolic at longer AV delays. For these patients, the optimal AV delay predicted by the restricted parabola algorithm increased SBP by 1.36 mmHg above that predicted by the conventional parabolic algorithm (95% confidence interval: 0.65 to 2.07 mmHg, p-value = 0.002).AV optima selected using our novel restricted parabola algorithm give a greater improvement in acute hemodynamics than fitting a parabola across all tested AV delays. Such an algorithm may assist the development of automated methods for biventricular pacemaker optimisation.

Phakic iris-fixated intraocular lens placement in the anterior chamber: effects on aqueous flow.

PURPOSE: Phakic intraocular lenses (pIOLs) are used for correcting vision; in this paper we investigate the fluid dynamical effects of an iris-fixated lens in the anterior chamber. In particular, we focus on changes in the wall shear stress (WSS) on the cornea and iris, which could be responsible for endothelial and pigment cell loss, respectively, and also on the possible increase of the intraocular pressure, which is known to correlate with the incidence of secondary glaucoma. METHODS: We use a mathematical model to study fluid flow in the anterior chamber in the presence of a pIOL. The governing equations are solved numerically using the open source software OpenFOAM. We use an idealized standard geometry for the anterior chamber and a realistic geometric description of the pIOL. RESULTS: We consider separately the main mechanisms that produce fluid flow in the anterior chamber. The numerical simulations allow us to obtain a detailed description of the velocity and pressure distribution in the anterior chamber, and indicated that implantation of the pIOL significantly modifies the fluid dynamics in the anterior chamber. However, lens implantation has negligible influence on the intraocular pressure and does not produce a significant increase of the shear stress on the cornea, while the shear stress on the iris, although increased, is not enough to cause detachment of cells. CONCLUSIONS: We conclude that alterations in the fluid dynamics in the anterior chamber as a result of lens implantation are unlikely to be the cause of medical complications associated with its use.

Automated fiducial point selection for reducing registration error in the co-localisation of left atrium electroanatomic and imaging data.

Registration of electroanatomic surfaces and segmented images for the co-localisation of structural and functional data typically requires the manual selection of fiducial points, which are used to initialise automated surface registration. The identification of equivalent points on geometric features by the human eye is heavily subjective, and error in their selection may lead to distortion of the transformed surface and subsequently limit the accuracy of data co-localisation. We propose that the manual trimming of the pulmonary veins through the region of greatest geometrical curvature, coupled with an automated angle-based fiducial-point selection algorithm, significantly reduces target registration error compared with direct manual selection of fiducial points.

A technique for visualising three-dimensional left atrial cardiac activation data in two dimensions with minimal distance distortion.

Electro-anatomic mapping and medical imaging systems, used during clinical procedures for treatment of atrial arrhythmias, frequently record and display measurements on an anatomical surface of the left atrium. As such, obtaining a complete picture of activation necessitates simultaneous views from multiple angles. In addition, post-processing of three-dimensional surface data is challenging, since algorithms are typically applicable to planar or volumetric data. We applied a surface flattening methodology to medical imaging data and electro-anatomic mapping data to generate a two-dimensional representation that best preserves distances, since the calculation of many clinically relevant metrics, including conduction velocity and rotor trajectory identification require an accurate representation of distance. Distance distortions were small and improved upon exclusion of the pulmonary veins. The technique is demonstrated using maps of local activation time, based on clinical data, and plotting rotor-core trajectories, using simulated data.

Arterial pressure: agreement between a brachial cuff-based device and radial tonometry.

OBJECTIVES: Aortic (central) blood pressure (BP) differs from brachial BP and may be a superior predictor of cardiovascular events. However, its measurement is currently restricted to research settings, owing to a moderate level of operator dependency. We tested a new noninvasive device in a large UK cohort. The device estimates central BP using measurements obtained with an upper arm cuff inflated to suprasystolic pressure. We compared these estimates with those obtained using radial tonometry as well as with invasively acquired measurements of aortic BP in a limited number of individuals. METHODS: Consecutive cuff-based and tonometry-based estimates of the pressure waveform and the central BP were obtained from 1107 individuals (70 ±â€Š6 years). Short-term and long-term reproducibility studies were performed on 28 individuals. Simultaneous cuff-based and invasively measured pressure traces were acquired and compared in an additional six individuals (65 ±â€Š20 years). RESULTS: Central systolic BP, as estimated by the cuff-based device, was found to be highly reproducible (coefficient of variation 4 and 8% for short and long-term reproducibility, respectively) and was comparable to that estimated by tonometry (average difference 3 ±â€Š6  mmHg, intraclass correlation coefficient = 0.91). The cuff-based pressure waveforms were similar to those acquired invasively (cross-correlation coefficient 0.93), and the difference in the estimated central systolic BP was -5 ±â€Š8  mmHg (P = 0.2). CONCLUSION: Cuff-based devices show promise to simplify the measurement of central BP, whilst maintaining a similar fidelity to tonometry. This could lead to improved adoption of estimates of central BP in clinical practice.

A 3D porous media liver lobule model: the importance of vascular septa and anisotropic permeability for homogeneous perfusion.

The hepatic blood circulation is complex, particularly at the microcirculatory level. Previously, 2D liver lobule models using porous media and a 3D model using real sinusoidal geometries have been developed. We extended these models to investigate the role of vascular septa (VS) and anisotropic permeability. The lobule was modelled as a hexagonal prism (with or without VS) and the tissue was treated as a porous medium (isotropic or anisotropic permeability). Models were solved using computational fluid dynamics. VS inclusion resulted in more spatially homogeneous perfusion. Anisotropic permeability resulted in a larger axial velocity component than isotropic permeability. A parameter study revealed that results are most sensitive to the lobule size and radial pressure drop. Our model provides insight into hepatic microhaemodynamics, and suggests that inclusion of VS in the model leads to perfusion patterns that are likely to reflect physiological reality. The model has potential for applications to unphysiological and pathological conditions.

Mathematical model of blood and interstitial flow and lymph production in the liver.

We present a mathematical model of blood and interstitial flow in the liver. The liver is treated as a lattice of hexagonal 'classic' lobules, which are assumed to be long enough that end effects may be neglected and a two-dimensional problem considered. Since sinusoids and lymphatic vessels are numerous and small compared to the lobule, we use a homogenized approach, describing the sinusoidal and interstitial spaces as porous media. We model plasma filtration from sinusoids to the interstitium, lymph uptake by lymphatic ducts, and lymph outflow from the liver surface. Our results show that the effect of the liver surface only penetrates a depth of a few lobules' thickness into the tissue. Thus, we separately consider a single lobule lying sufficiently far from all external boundaries that we may regard it as being in an infinite lattice, and also a model of the region near the liver surface. The model predicts that slightly more lymph is produced by interstitial fluid flowing through the liver surface than that taken up by the lymphatic vessels in the liver and that the non-peritonealized region of the surface of the liver results in the total lymph production (uptake by lymphatics plus fluid crossing surface) being about 5% more than if the entire surface were covered by the Glisson-peritoneal membrane. Estimates of lymph outflow through the surface of the liver are in good agreement with experimental data. We also study the effect of non-physiological values of the controlling parameters, particularly focusing on the conditions of portal hypertension and ascites. To our knowledge, this is the first attempt to model lymph production in the liver. The model provides clinically relevant information about lymph outflow pathways and predicts the systemic response to pathological variations.

An automated algorithm for determining conduction velocity, wavefront direction and origin of focal cardiac arrhythmias using a multipolar catheter.

Determining locations of focal arrhythmia sources and quantifying myocardial conduction velocity (CV) are two major challenges in clinical catheter ablation cases. CV, wave-front direction and focal source location can be estimated from multipolar catheter data, but currently available methods are time-consuming, limited to specific electrode configurations, and can be inaccurate. We developed automated algorithms to rapidly identify CV from multipolar catheter data with any arrangement of electrodes, whilst providing estimates of wavefront direction and focal source position, which can guide the catheter towards a focal arrhythmic source. We validated our methods using simulations on realistic human left atrial geometry. We subsequently applied them to clinically-acquired intracardiac electrogram data, where CV and wavefront direction were accurately determined in all cases, whilst focal source locations were correctly identified in 2/3 cases. Our novel automated algorithms can potentially be used to guide ablation of focal arrhythmias in real-time in cardiac catheter laboratories.

Investigation of the motion of a viscous fluid in the vitreous cavity induced by eye rotations and implications for drug delivery.

Intravitreal drug delivery is a commonly used treatment for several retinal diseases. The objective of this research is to characterize and quantify the role of the vitreous humor motion, induced by saccadic movements, on drug transport processes in the vitreous chamber. A Perspex model of the human vitreous chamber was created, and filled with a purely viscous fluid, representing eyes with a liquefied vitreous humor or those containing viscous tamponade fluids. Periodic movements were applied to the model and the resulting three-dimensional (3D) flow fields were measured. Drug delivery within the vitreous chamber was investigated by calculating particle trajectories using integration over time of the experimental velocity fields. The motion of the vitreous humor generated by saccadic eye movements is intrinsically 3D. Advective mass transport largely overcomes molecular diffusive transport and is significantly anisotropic, leading to a much faster drug dispersion than in the case of stationary vitreous humor. Disregarding the effects of vitreous humor motion due to eye movements when predicting the efficiency of drug delivery treatments leads to significant underestimation of the drug transport coefficients, and this, in turn, will lead to significantly erroneous predictions of the concentration levels on the retina.

Mathematical model of flow through the patent ductus arteriosus.

The ductus arteriosus is one of several shunts in the cardiovascular system. It is a small vessel connecting the aortic arch and pulmonary artery that allows blood to bypass the pulmonary circulation. It is open during foetal development because the foetal lungs cannot function and oxygenation of the blood occurs by exchange with the maternal blood in the placenta. Normally it closes a few days after birth; however, in a small number of people closure does not occur, leading to a condition known as patent ductus arteriosus. In this paper our aim is to investigate the resulting cardiovascular effects. We develop a mathematical model of the haemodynamics in three different idealised geometries by assuming that the entry flow is irrotational and remains so in the core until at least the shunt position. We argue that separation or diffusion of vorticity into the core flow is delayed due to the high frequency associated with the pulsatile component of the flow profile. The analysis uses complex potential theory, Schwarz-Christoffel transformations, conformal mappings and Fourier series. The main results are based on the assumption that the flow in patients with patent ductus arteriosus is similar to the flow in healthy adults, and we apply this assumption using boundary conditions that are representative of physiological values in healthy adults. The model suggests that the pressures in the aorta and pulmonary artery are likely to equalise, that the shear stress increases near the edges of the shunt and that backflow of large volumes may occur from the pulmonary artery into the aorta or towards the ventricles due to the presence of the patent shunt. Our results strongly suggest that an abnormal compensatory physiology develops in patients with patent ductus arteriosus.

Shape change of the vitreous chamber influences retinal detachment and reattachment processes: is mechanical stress during eye rotations a factor?

PURPOSE: We aim to understand how mechanical causation influences retinal detachment and reattachment processes. In particular, myopes suffer retinal detachment more frequently than emmetropes, and following a retinal detachment, scleral buckling promotes retinal reattachment. We test the hypothesis that stresses arising from saccadic eye rotations are involved in the processes, and that the alteration in the stress due to the change in the vitreous chamber geometry is sufficient to explain the phenomena. METHODS: The vitreous chamber of the eye has an approximately spherical shape and it is filled with vitreous humor. We developed a mathematical model, treating the vitreous chamber in emmetropic and myopic eyes as a spheroid and in eyes subjected to scleral buckling as a sphere with a circumferential indentation. We assume that the eye performs prescribed small-amplitude, periodic, torsional rotations and we solve semi-analytically for the fluid pressure, velocity, and stress distributions. RESULTS: The shape of the vitreous chamber has a large effect on the retinal stress. The vitreous and the retina of a highly myopic eye continuously experience shear stresses significantly higher than those of an emmetropic eye. An eye fitted with a scleral buckle experiences large stress levels localized around the buckle. CONCLUSIONS: Our results provide a mechanical explanation for the more frequent occurrence of posterior vitreous detachment and retinal detachment in myopic eyes. To understand how the stress distribution in a buckled eye facilitates reattachment, an additional model of the details of the reattachment process should be coupled to this model.

Mathematical modeling of the circulation in the liver lobule.

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.

Mixing processes in the vitreous chamber induced by eye rotations.

In this paper, we study a model of flow in the vitreous humour in the posterior chamber of the human eye, induced by saccadic eye rotations. We concentrate on the effect of the shape of the chamber upon the mixing properties of the induced flows. We make particle image velocimetry measurements of the fluid velocity in a transparent plastic (Perspex) model of the posterior chamber during sinusoidal torsional oscillations about a vertical axis. We use a Newtonian fluid to model the vitreous humour, which is most realistic when either the vitreous humour is liquefied or has been replaced by purely viscous tamponade fluids. The model of the posterior chamber is a sphere with an indentation, representing the effect of the lens. In spite of the purely periodic forcing, a steady streaming flow is generated, which plays a fundamental role in the mixing processes in the domain. The streaming flow differs markedly from that in a perfect sphere, and its topological characteristics change substantially as the frequency of oscillation varies. We discuss the flow characteristics in detail and show that, for physiological parameter values, the Péclet number (based on a suitable measure of the steady streaming velocity) is large, suggesting that advection strongly dominates over diffusion for mass transport phenomena. We also compute particle trajectories based on the streaming velocity and use these to investigate the stirring properties of the flow.

Intracellular flow in optic nerve axons: a mechanism for cell death in glaucoma.

PURPOSE: In glaucoma, elevated intraocular pressure causes a progressive loss of retinal ganglion cells and results in optic neuropathy. The authors propose a potential mechanism for cell death, whereby elevated intraocular pressure causes fluid to permeate axonal membranes, creating a passive intracellular fluid flow within the axons. It is hypothesized that this intracellular flow locally depletes the adenosine triphosphate (ATP) concentration, disrupting axonal transport and leading to cell death. METHODS: A mathematical model was developed that takes into account the biomechanical principles underpinning the proposed hypothesis, and was solved to determine the implications of the mechanism. RESULTS: The model suggests that the raised intraocular pressures present in glaucoma are adequate to produce significant intracellular fluid flow. In the periphery of the optic nerve head, this flow may be sufficient to disrupt the diffusion of ATP and hence interrupt active axonal transport. CONCLUSIONS: The mathematical model demonstrates that it is physically plausible that a passive intracellular fluid flow could significantly contribute to the pathophysiology of the retinal ganglion cell axon in glaucoma.

Flow dynamics in a stented ureter.

Vesicorenal reflux is a major side effect associated with ureteric stent placement. In a stented upper urinary tract when the bladder pressure rises, such as during bladder spasms (due to irritation caused by the stent) or voiding of the bladder, it drives urine reflux up the ureter, which, in turn, may be a contributory factor for infections in the renal pelvis. We develop a mathematical model to examine urine flow in a stented ureter, assuming that it remains axisymmetric and treating the wall as a non-linear elastic membrane. The stent is modelled as a rigid, permeable, hollow, circular cylinder lying coaxially inside the ureter. The renal pelvis is treated as an elastic bag, whose volume increases in response to an increased internal pressure. Fluid enters the renal pelvis from the kidney with a prescribed flux. The stent, ureter and renal pelvis are filled with urine, and the bladder pressure is prescribed. We use the model to calculate the total volume of reflux generated during rises in bladder pressure and investigate how it is affected by the stent and ureter properties.