Modelling the interaction of haemodynamics and the artery wall: current status and future prospects.

Clinical research has historically focused on the two main strategies of in vivo and in vitro experimentation. The concept of applying scientific theory to direct clinical applications is relatively recent. In this paper we focus on the interaction of wall shear stress with the endothelium and discuss how 'state of the art' computer modelling techniques can provide valuable data to aid understanding. Such data may be used to inform experiment and further, may help identify the key features of this complex system. Current emphasis is on coupling haemodynamics with models of biological phenomena to test hypotheses or predict the likely outcome of a disease or an intervention. New technologies to enable the integration of models of different types, levels of complexity and scales, are being developed. As will be discussed, the ultimate goal is the translation of this technology to the clinical arena.

Application and validation of the lattice Boltzmann method for modelling flow-related clotting.

The purpose of this paper is to present a simple clotting model, based on residence time and shear stress distribution, that can simulate the deposition over time of enzyme-activated milk in an in vitro system. Results for the model are compared with experiments exhibiting clot deposition in the region of a sharp-edged stenosis. The milk experiments have been shown to be a valuable analogue for the experimental representation of flow-induced blood clotting, particularly in the context of separation of hydrodynamic from biochemical factors. The facility to predict the flow-induced clotting of the blood analogue, in which the chemistry reduces to what is effectively a zeroth order reaction, gives confidence in this physics-based approach to simulation of the final part of the coagulation cascade. This type of study is a necessary precursor to the development of a complex, multi-factorial, biochemical model of the process of thrombosis. In addition to the clotting simulations, comparisons are reported between the computed flow patterns prior to clot deposition and flow visualisation studies. Excellent agreement of hydrodynamic parameters is reported for a Reynolds number of 100, and qualitative agreement is seen for the complex, disturbed flow occurring at a physiologically relevant Reynolds number of 550. The explicit, time-stepping lattice Boltzmann approach may have particular merit for the transitional flow at this higher Reynolds number.

Characterisation of the haemodynamics of the superior mesenteric artery.

In contrast to its prevalence in the surrounding vasculature, occurrence of primary atherosclerotic disease in the superior mesenteric artery (SMA) is rare (Glagov et al., 1988. Hemodynamics and atherosclerosis, Insights and perspectives gained from studies of human arteries. Archives of Pathology and Laboratory Medicine 112(10), 1018-1031; Hansen et al., 2004. Mesenteric artery disease in the elderly. Journal of Vascular Surgery 40(1), 45-52). We hypothesise that this sparing might be attributed to more favourable haemodynamic characteristics in the SMA than in other vessels locally. Dynamic magnetic resonance imaging (MRI) images established that the SMA is highly mobile (Jeays, 2006. Investigation of blood flow in the superior mesenteric artery and its potential influence on atheroma and gut ischaemia. Ph.D. Thesis, University of Sheffield), and thus that an analysis based on rigid geometry might be inappropriate. This paper describes an efficient methodology for the construction of a patient-specific, time-dependent model of an arterial segment and reports the results of a haemodynamic characterisation of the SMA for one individual. A transient computational fluid dynamic (CFD) model was constructed by morphing a parametric mesh constructed from simple geometric primitives. This process has the merit that it is easy to control the element size distribution mapped onto the original geometric primitives. It is robust in operation, and is ideally suited to the generation of dynamic CFD meshes of arterial systems that are free from major pathology. Flow boundary conditions were determined based on phase contrast MRI velocity measurements. Comparative studies with rigid walls and with moving walls, based on the transient data, indicated that, despite the significant motion of the SMA (radial dilation of the order of 10% and translation of the order of the radius), the maximum (spatially and temporally-resolved) wall shear stresses changed by no more than 21.6% of a global norm, and the average change was less than 2.1%.

Computer modelling study of the mechanism of optic nerve injury in blunt trauma.

AIM: The potential causes of the optic nerve injury as a result of blunt object trauma, were investigated using a computer model. METHODS: A finite element model of the eye, the optic nerve, and the orbit with its content was constructed to simulate blunt object trauma. We used a model of the first phalanx of the index finger to represent the blunt body. The trauma was simulated by impacting the blunt body at the surface between the globe and the orbital wall at velocities between 2-5 m/s, and allowing it to penetrate 4-10 mm below the orbital rim. RESULTS: The impact caused rotations of the globe of up to 5000 degrees /s, lateral velocities of up to 1 m/s, and intraocular pressures (IOP) of over 300 mm Hg. The main stress concentration was observed at the insertion of the nerve into the sclera, at the side opposite to the impact. CONCLUSIONS: The results suggest that the most likely mechanisms of injury are rapid rotation and lateral translation of the globe, as well as a dramatic rise in the IOP. The strains calculated in the study should be sufficiently high to cause axonal damage and even the avulsion of the nerve. Finite element computer modelling has therefore provided important insights into a clinical scenario that cannot be replicated in human or animal experiments.

A computational study of the passive mechanisms of eye restraint during head impact trauma.

A finite element model of the eye and the orbit was used to examine the hypothesis that the orbital fat provides an important mechanism of eye stability during head trauma. The model includes the globe, the orbital fat, the extra-ocular muscles, and the optic nerve. MRI images of an adult human orbit were used to generate an idealized geometry of the orbital space. The globe was approximated as a sphere 12 mm in radius. The optic nerve and the sclera were represented as thin shells, whereas the vitreous and the orbital fat were represented as nearly incompressible solids of low stiffness. The orbital bone was modelled as a rigid shell. Frontal head impact resulting from a fall onto a hard floor was simulated by prescribing to the orbital bone a triangular acceleration pulse of 200 g (1962 m/s(2)) peak for a duration of 4.5 ms. The results show that the fat provides the crucial passive mechanism of eye restraint. The mechanism is a consequence of the fact that the fat is incompressible and that its motion is restricted by the rigidity of the orbital walls. Thus, the acceleration loads of short duration cannot generate significant distortion of the fat. In contrast, the passive muscles provide little support to the globe. When the connection between the orbital fat and the eye is absent the eye is held mainly by the optic nerve. We discuss the possible role that this loss of contact may have in some cases of the evulsion of the eye and the optic nerve.

Pericardial heterografts: why do these valves fail?

Eighteen explanted pericardial heterografts were studied (16 standard Ionescu-Shiley, one Hancock, and one Mitroflow). Regurgitation was the reason given for explantation of all the Ionescu-Shiley valves. The other two valves were removed for technical reasons. All the Ionescu-Shiley valves had commissural tears and there was concomitant gross calcification in 10 of the 16 valves. In addition, an apparent increase in cusp area had caused "leaflet sagging". The explanted leaflets were thicker and stiffer than leaflets from an unimplanted valve. These features were confirmed directly with an animal model of subcutaneous implantation. Examination with an electron microscope revealed that these changes in mechanical properties seemed to be linked to fiber separation and infiltration by an amorphous proteinlike matrix. The durability of the glutaraldehyde-fixed pericardium depended on a number of factors. Early and midterm failure appeared to be stress induced. Predisposition to high mechanical stresses near the stent was exacerbated by the changes induced by the host environment. This problem was aggravated further in the Ionescu-Shiley valves by stress concentrations around the hole associated with the holding suture. In the long term, collagen disruption associated with leaflet flexure was followed by secondary calcification at the boundary between the intact and disrupted material.

Pericardial heterografts. Toward quality control of the mechanical properties of glutaraldehyde-fixed leaflets.

The mechanical properties of five different, equally distributed, and randomly oriented sites in natural and glutaraldehyde-fixed calf pericardial sacs were investigated. Identical sites in different sacs were obtained by placing a template over each sac and using the ligaments still attached to the pericardium as a reference frame. Mean maximum extension of the fixed tissue was statistically significantly greater than that of natural tissue at the same degree of stress. There was no significant difference in thickness from position to position within a sac, from sac to sac, or from the natural to fixed pericardium. However, the extensibility of one particular site was significantly greater than that of other positions in the pericardial sac. This position lay entirely in a well-defined sector that emanated radially from the pericardial ligaments. Light and electron microscopy showed no difference in collagen structure in the five positions studied. In contrast, both the content and ultrastructure of the tissue elastin differed in the region of high extensibility compared with those sites studied in the remainder of the sac. This region contained coarse condensed elastin whereas the other sites had fine elastin dispersed diffusely throughout the tissue. These results suggest that pericardial heterografts of uniform thickness may be harvested from any position in calf pericardium. However, unless the region of coarse condensed elastin is excluded, leaflets with significantly different mechanical properties may be produced.

Outlet strut fracture of Björk-Shiley convexo-concave valves: can valve-manufacturing characteristics explain the risk?

BACKGROUND: Björk-Shiley 60 degrees convexo-concave prosthetic heart valves (Shiley, Inc, Irvine, Calif, a subsidiary of Pfizer, Inc) continue to be a concern for approximately 35,000 nonexplanted patients worldwide, with approximately 600 events reported to the manufacturer to date. Fractures of the outlet struts of the valves began to appear in the early 1980s and have continued to the present, but their causes are only partially understood. METHODS: A matched case-control study was conducted evaluating manufacturing records for 52 valves with outlet strut fractures and 248 control subjects matched for age at implantation, valve size, and valve position. RESULTS: In addition to the risk factors recognized as determinants of outlet strut fracture, the United Kingdom case-control study has observed 7- to 9-fold increased risk with performance of multiple hook deflection tests. This test was performed more than once, usually after rework on the valve. Six valves in this study underwent multiple hook deflection tests, of which 4 experienced an outlet strut fracture. Cracks and further rework were noted for these valves. Significant associations were also observed between outlet strut fracture and disc-to-strut gap measurements taken before the attachment of the sewing ring. CONCLUSIONS: It is our view that a combination of factors related to valve design, manufacturing process, and patient characteristics are responsible for outlet strut fractures of Björk-Shiley convexo-concave valves. Multiple hook deflection tests have emerged as a potential new risk factor for outlet strut fracture in both The Netherlands and the United Kingdom. This factor appears to be correlated with the presence of other abnormalities. A further study is needed to investigate the factors correlated with multiple hook deflection tests. On confirmation of risk, the presence of multiple hook deflection tests may be added to equations, quantifying the risk of outlet strut fracture for comparison against risk of mortality and serious morbidity from explant operations.

Acid hydrolyzable aldehydes in long-term stored commercial bioprosthetic heart valves implications for calcification.

There is evidence that glutaraldehyde used routinely in the fixation process of bioprosthetic heart valves may be a major factor in their subsequent calcification. A further complication is introduced by the use of a formaldehyde treatment step, whether for sterilization or storage. The effects of this second aldehyde on calcification is also unknown. The aim of the present work is to determine the degree of glutaraldehyde and formaldehyde incorporation into commercial valve leaflets and to establish whether there is a relationship between the aldehyde treatment and tissue calcification. Both pre- and post-implantation concentrations of aldehydes were estimated by high performance liquid chromatography of acid hydrolyzates of commercial valve tissue. Control samples were taken from freshly prepared porcine aortic valves and bovine pericardium fixed in glutaraldehyde. The degree of calcification was investigated using the rat subcutaneous implant model. Samples were retrieved after 56 days and calcium estimated by atomic absorption spectroscopy. The results indicated that storage of both porcine and pericardial valves for periods of 5 years or longer reduced calcification. A greater reduction in calcification was noted when tissue was treated sequentially with glutaraldehyde and formaldehyde rather than glutaraldehyde alone. From this work it can be concluded that bioprosthetic valves calcify less in the rat model when they are stored for extended periods of time in glutaraldehyde solution. This effect is enhanced when formaldehyde storage is employed.

Elective removal of convexo-concave Björk-Shiley valves.

Replacement has been an accepted method for treating advanced cardiac valvular disease for more than 25 years. However, the perfect prosthesis has yet to be developed, judging by the number of devices available. A prosthesis that initially appears promising may cause problems in due course, and indeed some devices have been modified or withdrawn from clinical use. A notable example of a prosthetic valve that has give problems is the Björk-Shiley convexo-concave prosthesis, some models of which have undergone mechanical failure due to strut fracture. We report the elective removal of such a valve and the subsequent examination of the prosthesis. The results of this examination suggest that a policy of elective removal is justified.

Formaldehyde replaces glutaraldehyde in porcine bioprosthetic heart valves.

BACKGROUND AND AIMS OF THE STUDY: In the production of porcine bioprostheses, the initial glutaraldehyde treatment is often followed by a short incubation in formaldehyde to ensure sterility of the valve. It is assumed that the glutaraldehyde cross links are stable and that the formaldehyde step does not alter the glutaraldehyde incorporated. The objective of this study was to determine whether the formaldehyde interacts with the tissue to cause changes in the glutaraldehyde composition. MATERIALS AND METHODS: Two methods of tissue treatment were investigated: (i) fresh porcine leaflet tissue was treated with glutaraldehyde, followed by storage in formaldehyde, (ii) tissue processed in glutaraldehyde and transferred to formaldehyde for six hours was returned to glutaraldehyde for storage. The content of the two aldehydes was estimated by high performance liquid chromatography (HPLC), using an adaptation of the method developed by Hughes et al, which measures the acid labile Schiff bases formed between the collagen and the aldehyde. RESULTS: The initial content of glutaraldehyde in the tissue declined from 63 +/- 10 nmol/mg dry weight to 21 +/- 4 nmol/mg dry weight when the leaflets were placed in formaldehyde for 24 hours. The initial uptake of formaldehyde was 800 +/- 144 nmol/mg dry weight after 24 hours and this declined to 370 +/- 33 nmol/mg dry weight over a 16 week period of storage in formaldehyde. By this stage, the level of glutaraldehyde had decreased to 2.4 +/- 0.2 nmol/mg dry weight. There was a sharp decline in the glutaraldehyde concentration from 89 +/- 6 nmol/mg dry weight to 14 +/- 1 nmol/mg dry weight when the tissue was placed in 4% formaldehyde solution for six hours. The formaldehyde uptake was 770 +/- 54 nmol/mg dry weight. After return to 0.625% glutaraldehyde solution the formaldehyde concentration declined whilst the glutaraldehyde concentration initially increased. CONCLUSIONS: These results show that the formaldehyde reacts with the epsilon amino groups of lysine which had not reacted with glutaraldehyde, probably for steric reasons; and that formaldehyde replaces some glutaraldehyde in the tissue by a mass action effect. The tissue concentration of both aldehydes subsequently declined over the study period.

In vitro heart valve testing: steady versus pulsatile flow.

The design of artificial heart valves has traditionally been based on the development of a prototype device which was then subjected to extensive laboratory testing in order to confirm its suitability for clinical use. In the past the in vitro assessment of a valve's performance was based principally on the measurement of parameters such as pressure difference, regurgitation and, more recently, energy losses. Such measurements can be defined as being at the 'macro' level and rarely show any clinically significant differences amongst currently available prostheses. The analytical approach to flow through heart valves has previously been hampered by difficulties experienced in solving the relevant equations of flow particularly in the case of pulsatile conditions. Computational techniques are now available which enable appropriate solutions to be obtained for these problems and consequently provide an opportunity for detailed examination of the 'micro' level of flow disturbances exhibited by the different valves. This present preliminary study is designed to illustrate the use of such an analytical approach to the flow through prosthetic valves. A single topic has been selected for this purpose which is the comparative value of steady versus pulsatile flow testing. A bileaflet valve was chosen for the analysis and a mathematical model of this valve in the aortic position of the Sheffield Pulse Duplicator was created. The theoretical analysis was carried out using a commercially available Computational Fluid Dynamics package, namely, FIDAP, on a SUN MICROSYSTEMS 10-30 workstation.(ABSTRACT TRUNCATED AT 250 WORDS)

The use of enzyme activated milk for in vitro simulation of prosthetic valve thrombosis.

BACKGROUND AND AIM OF THE STUDY: Thrombosis remains a serious risk for patients with artificial heart valves and may be attributed in part to adverse blood flow patterns. Although the final assessment of a valve must follow years of clinical experience, in vitro flow analyses give valuable information prior to implantation. Laser Doppler velocimetry and computational fluid dynamics enable quantitative flow analyses to be made in vitro. Whilst these techniques highlight features such as areas of stasis, turbulence and high shear which may predispose to thrombus formation, the complex and time varying nature of the flow through valves makes it difficult to predict accurately potential sites of thrombus deposition and accumulation. METHODS: A technique is described which uses enzyme activated milk as a coagulable blood analogue to indicate flow related clotting. Milk flowing past a test valve or object was activated to clot downstream of the test piece after a certain time period. Milk clot was deposited clot at sites determined by the local flow disturbances. Milk clotting patterns produced on and around standard objects were compared with the transient flow patterns predicted around identical configurations to test the validity of computational flow analyses for predicting flow disturbances leading to clotting. Milk clots on valves were compared with examples of thrombus found on explanted valves of the same design. RESULTS: The sites of deposition were consistent with the predicted flow patterns around the two configurations of flow obstruction studied. Milk clotting patterns on valves corresponded with the early stages of thrombus on explanted valves of the same design. CONCLUSIONS: Whilst a coagulable milk mixture may be used to evaluate the risk of flow induced clot adherence, care must be taken when extrapolating to the clinical situation as other factors such as material properties, blood chemistry and concomitant disease must also be considered.

Glutaraldehyde-induced cross-links: a study of model compounds and commercial bioprosthetic valves.

BACKGROUND AND AIM OF THE STUDY: The treatment of bioprosthetic tissue routinely involves the use of glutaraldehyde, although the specific chemistry of glutaraldehyde fixation is not fully understood. Descriptions of definitive work on this reaction using model compounds are limited. The aim of the present study was to increase our understanding of the chemistry involved in the treatment of collagen-rich tissue with glutaraldehyde. Initially, 6-aminohexanoic acid (6-AHA) was used to model the lysine/hydroxylysine molecules in collagen before studying the more complex chemistry of the tissue. METHODS: The reaction between 0.6% glutaraldehyde and 6-AHA was studied by positive ion electrospray-mass spectroscopy. Untreated, locally treated and commercially produced explanted and non-implanted tissue were hydrolyzed under various conditions and analyzed both directly and after derivatization with 4-chlorophenylhydrazine, 4-bromophenacyl bromide and dansyl chloride by reverse-phase-high performance liquid chromatography-mass spectrometry. RESULTS: The mass spectral data obtained from the reaction of glutaraldehyde with 6-AHA showed the presence of alpha,beta unsaturated aldehydes and their further condensation products involving Michael reactions of glutaraldehyde, Schiff base cross-links and various cyclization products incorporating pyridinium and dihydropyridine ring structures. The only stable cross-link detected was an 'anabilysine'-like compound. Similar structures were present in the tissue, and anabilysine was identified by tandem mass spectrometry. CONCLUSION: The results from the reaction of glutaraldehyde with 6-AHA agree with those published previously. The only detectable stable cross-link definitively identified in treated bioprosthetic tissue was anabilysine. No long-chain polymers of glutaraldehyde were detected.

An inexpensive sensor for measuring surface geometry.

A technique to measure surface geometry using a conductive ink sensor is described. In the human system distorted cylinders are common, and geometry can be reconstructed from local measures of curvature. An algorithm is presented to reconstruct the shape of a surface from a series of curvature measurements. The Abrams Gentile Entertainment patented bend sensor was evaluated as a curvature transducer. The sensor was tested at the extremes of the likely measurement range, from curvatures below 0.01 mm(-1) up to a curvature of 0.1 mm(-1). The upper curvature limit proved beyond the design specification of the sensor. The technique was applied at the lower curvature range to reconstruct one quadrant of the chest of a volunteer and record breathing movement. The bend sensor is inexpensive and can be applied to obtain an approximate reconstruction of surface geometry in the human system.

A thermal analogy for modelling drug elution from cardiovascular stents.

Restriction of blood flow by the narrowing or occlusion of arteries is one of the most common presentations of cardiovascular disease. One treatment involves the introduction of a metal scaffold, or stent, designed to prevent recoil and to provide structural stability to the vessel. On the occasions that this treatment is ineffective, failure is usually associated with re-invasion of tissue. This can be prevented by local delivery of drugs which inhibit tissue growth. The drug might be delivered locally in a polymer coating on the stent. This paper develops and explores the use of a thermal analogue of the drug delivery process and the associated three-dimensional convection-diffusion equation to model the spatial and temporal distribution of drug concentration within the vessel wall. This allows the routine use of commercial finite element analysis software to investigate the dynamics of drug distribution, assist in the understanding of the treatment process and develop improved delivery systems. Two applications illustrate how the model might be used to investigate the effects of controllable or measurable parameters on the progression of the process. It is demonstrated that the geometric characteristics of the stent can have significant impact on the homogeneity of the dosing in the vessel wall.

Understanding valve/host interactions through explanted valve analysis.

It is essential that the factors leading to bioprosthetic valve dysfunction are fully understood if a more durable bioprosthesis is to be developed and the incidence of premature failure reduced. Studies of explanted bioprostheses yield important information on both the aetiology of valve failure and influence of valve/host interactions. Details are given of the Sheffield Explant Study which holds data on 570 explants and 34 different models. Advantages and disadvantages of this type of study are discussed.

Measurement of the symmetry of in vitro stent expansion: a stereo-photogrammetric approach.

Balloon-expandable stents are used routinely in the treatment of coronary artery disease. Their effectiveness is limited by the occurrence of restenosis. Previous studies have suggested that the level of restenosis may be related to the deployed stent geometry, and in particular to the symmetry of the deployment profile. It is suggested that the symmetry of deployment might be influenced by the folding pattern of the balloon on which the stent is delivered. This paper describes a stereo-photogrammetric system for the three-dimensional reconstruction of stent geometry during expansion, including appropriate specification and calibration procedures. Calibration testing of the system indicated an accuracy of +/-0.05 mm in the reconstruction of the position of a point on the stent surface. Methods for processing the 3D data are described, including a technique for quantitatively differentiating between results from two alternative balloon folding patterns. This study may aid future balloon and stent design with respect to the optimization of stent deployment characteristics.

The origin and significance of secondary flows in the aortic arch.

This paper comprises a study of the secondary flow patterns that can develop in the human aortic arch. Clinical evidence of these secondary flows has been obtained by Kilner et al. using magnetic resonance velocity mapping techniques. Some of their results are presented for comparison in this paper. Four difference parametric models of the aortic arch have been analysed using computational fluid dynamic techniques. Both steady and transient flow conditions have been considered and two different commercially available software packages were used, namely FIDAP and FLOTRAN. A satisfactory comparison of the theoretical analysis with the results, both in vivo and in vitro, obtained by Kilner et al. for their out-of-plane inlet model was found. The theoretical analysis can now be extended to analyse the effect of different configurations and orientations of artificial aortic valves on the resulting aortic arch flow patterns.

Fluid-solid interaction: benchmarking of an external coupling of ANSYS with CFX for cardiovascular applications.

Fluid-solid interaction is a primary feature of cardiovascular flows. There is increasing interest in the numerical solution of these systems as the extensive computational resource required for such studies becomes available. One form of coupling is an external weak coupling of separate solid and fluid mechanics codes. Information about the stress tensor and displacement vector at the wetted boundary is passed between the codes, and an iterative scheme is employed to move towards convergence of these parameters at each time step. This approach has the attraction that separate codes with the most extensive functionality for each of the separate phases can be selected, which might be important in the context of the complex rheology and contact mechanics that often feature in cardiovascular systems. Penrose and Staples describe a weak coupling of CFX for computational fluid mechanics to ANSYS for solid mechanics, based on a simple Jacobi iteration scheme. It is important to validate the coupled numerical solutions. An extensive analytical study of flow in elastic-walled tubes was carried out by Womersley in the late 1950s. This paper describes the performance of the coupling software for the straight elastic-walled tube, and compares the results with Womersley's analytical solutions. It also presents preliminary results demonstrating the application of the coupled software in the context of a stented vessel.