Multi-scale interaction of particulate flow and the artery wall.

We discuss, from the perspective of basic science, the physical and biological processes which underlie atherosclerotic (plaque) initiation at the vascular endothelium, identifying the widely separated spatial and temporal scales which participate. We draw on current, related models of vessel wall evolution, paying particular attention to the role of particulate flow (blood is not a continuum fluid), and proceed to propose, then validate all the key components in a multiply-coupled, multi-scale modeling strategy (in qualitative terms only, note). Eventually, this strategy should lead to a quantitative, patient-specific understanding of the coupling between particulate flow and the endothelial state.

Adaptation and development of software simulation methodologies for cardiovascular engineering: present and future challenges from an end-user perspective.

This paper describes the use of diverse software tools in cardiovascular applications. These tools were primarily developed in the field of engineering and the applications presented push the boundaries of the software to address events related to venous and arterial valve closure, exploration of dynamic boundary conditions or the inclusion of multi-scale boundary conditions from protein to organ levels. The future of cardiovascular research and the challenges that modellers and clinicians face from validation to clinical uptake are discussed from an end-user perspective.

A validated model of calf compression and deep vessel collapse during external cuff inflation.

This paper presents a validated model of calf compression with an external pressure cuff as used for deep vein thrombosis. Magnetic resonance (MR) images of calf geometry were used to generate subject-specific finite-element (FE) models of the calf cross section. Ultrasound images of deep vessel collapse obtained through a water-filled cuff were used to validate model behavior. Calf/cuff pressure interface measurements were applied to the FE model and the resulting tissue deformation was compared with MR image in normal volunteers (three females, four males, age range 20-55) using two distinct cuffs. MR observations and the model results showed good qualitative agreement. A similar reduction in cross-sectional area of the posterior tibial veins was obtained under both symmetric compression (89%) and asymmetric compression (81%), but greater compression of the anterior tibial veins was achieved with symmetric compression. The need to account for the effective compressibility of the calf tissue suggests that external measurements of the calf tissue deformation will not accurately predict deep vessel collapse. These results have implications for the modification of venous haemodynamics by such systems and could help to improve cuff design.

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.

The application of multiscale modelling to the process of development and prevention of stenosis in a stented coronary artery.

The inherent complexity of biomedical systems is well recognized; they are multiscale, multiscience systems, bridging a wide range of temporal and spatial scales. While the importance of multiscale modelling in this context is increasingly recognized, there is little underpinning literature on the methodology and generic description of the process. The COAST (complex autonoma simulation technique) project aims to address this by developing a multiscale, multiscience framework, coined complex autonoma (CxA), based on a hierarchical aggregation of coupled cellular automata (CA) and agent-based models (ABMs). The key tenet of COAST is that a multiscale system can be decomposed into N single-scale CA or ABMs that mutually interact across the scales. Decomposition is facilitated by building a scale separation map on which each single-scale system is represented according to its spatial and temporal characteristics. Processes having well-separated scales are thus easily identified as the components of the multiscale model. This paper focuses on methodology, introduces the concept of the CxA and demonstrates its use in the generation of a multiscale model of the physical and biological processes implicated in a challenging and clinically relevant problem, namely coronary artery in-stent restenosis.

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.

Mechanistic hypothesis for eye injury in infant shaking : An experimental and computational study.

The terms abusive head injury and shaken baby syndrome are used to describe a unique pattern of nonaccidental traumatic injuries occurring in children that many clinicians and researchers have good reason to believe is caused by violent shaking. Typical injuries include severe brain injury, with intracranial and retinal hemorrhages, but the pathogenesis of injuries is poorly understood. A major paradox in head trauma in infants is that the injuries induced by a shaking event are much more severe than those caused by even very violent single-impact head trauma, despite the relatively low accelerations in shaking.We have developed a finite element computer model of the eye, orbit, and orbital bone and used it to simulate the effects of single-impact and oscillatory motion inputs. The model was informed by data from semiquantitative in vitro anatomical traction experiments on in situ rabbit eyes. The new results reported here strongly suggest that suction between the eye and its surrounding fat dominates the dynamical stability of the system composed of the eye, its socket, and the components and material supporting the eye. Computer simulations incorporating this functional anatomical relationship show that deceleration of the head generates pressure gradients inside and outside the eye; these could cause damaging shear stresses in structures such as the retina and blood vessels. Simulations also show that oscillating the bone of the orbit causes the eye to move anteriorly and posteriorly with an increasing amplitude, building up the stresses within the eye over time. This is the first time that any biomechanical mechanism has been identified that might explain the disproportionally severe injuries caused by an oscillatory mechanism such as violent shaking of an abused infant. However, further study is required and this conclusion is therefore preliminary and provisional.

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.

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.

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.

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.

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.

Development of an ex vivo model to investigate the effects of altered haemodynamics on human bypass grafts.

The insertion of vein grafts into the arterial circulation may contribute to vessel wall thickening and accelerated atherosclerosis, a common feature of late vein graft failure. We aimed to develop a model suitable for investigation of the effects of altered haemodynamics on human saphenous vein following its implantation into the arterial circulation. Segments of human saphenous vein obtained from patients undergoing coronary artery bypass surgery were sutured at each end to PTFE and placed into a flow system. Pressure and flow rates to stimulate the arterial and venous systems were achieved. A theoretical model of the flow chamber was created and computational fluid dynamics software (FLOTRAN, Swanson Analysis Systems) was used to determine the flow profile within the model. In summary, a flow model has been developed to investigate the effect of altered haemodynamics on the molecular and pathological changes that occur in vein grafts incorporated into the arterial circulation.

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.

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.

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.

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.