Systematic review and meta-analysis of Murray's law in the coronary arterial circulation.

Murray's law has been viewed as a fundamental law of physiology. Relating blood flow ([Formula: see text]) to vessel diameter (D) ([Formula: see text]·âˆ·D3), it dictates minimum lumen area (MLA) targets for coronary bifurcation percutaneous coronary intervention (PCI). The cubic exponent (3.0), however, has long been disputed, with alternative theoretical derivations, arguing this should be closer to 2.33 (7/3). The aim of this meta-analysis was to quantify the optimum flow-diameter exponent in human and mammalian coronary arteries. We conducted a systematic review and meta-analysis of all articles quantifying an optimum flow-diameter exponent for mammalian coronary arteries within the Cochrane library, PubMed Medline, Scopus, and Embase databases on 20 March 2023. A random-effects meta-analysis was used to determine a pooled flow-diameter exponent. Risk of bias was assessed with the National Institutes of Health (NIH) quality assessment tool, funnel plots, and Egger regression. From a total of 4,772 articles, 18 were suitable for meta-analysis. Studies included data from 1,070 unique coronary trees, taken from 372 humans and 112 animals. The pooled flow diameter exponent across both epicardial and transmural arteries was 2.39 (95% confidence interval: 2.24-2.54; I2 = 99%). The pooled exponent of 2.39 showed very close agreement with the theoretical exponent of 2.33 (7/3) reported by Kassab and colleagues. This exponent may provide a more accurate description of coronary morphometric scaling in human and mammalian coronary arteries, as compared with Murray's original law. This has important implications for the assessment, diagnosis, and interventional treatment of coronary artery disease.

Measuring three-dimensional strain distribution in tendon.

Tendons are tough fibrous tissues that facilitate skeletal movement by transferring muscular force to bone. Studies into the effects of mechanical stress on tendons have shown that these can either accelerate healing or cause tendon injuries depending on the load applied. It is known that local strain magnitude and direction play an important role in tendon remodelling and also failure, and different techniques to study strain distribution have been proposed. Image registration and processing techniques are among the recently employed methods. In this study, a novel three-dimensional image processing technique using the Sheffield Image Registration Toolkit is introduced to study local strain and displacement distribution in tendon. The results show that the local normal strain values in the loading axis are smaller than the global applied load, and fibre sliding was detected as a dominant mechanism for transferring the applied load within tendon. However, results from different samples suggest three distinct modes of deformation during loading, as some show only parallel sliding of fibres in respect to the loading axis, whereas others are twisted or deflected in directions transverse to the loading axis. The proposed 3D image registration method is essential for analysing this out-of-plane movement, which cannot be detected using a standard 2D method.

Validation of a novel numerical model to predict regionalized blood flow in the coronary arteries.

Aims: Ischaemic heart disease results from insufficient coronary blood flow. Direct measurement of absolute flow (mL/min) is feasible, but has not entered routine clinical practice in most catheterization laboratories. Interventional cardiologists, therefore, rely on surrogate markers of flow. Recently, we described a computational fluid dynamics (CFD) method for predicting flow that differentiates inlet, side branch, and outlet flows during angiography. In the current study, we evaluate a new method that regionalizes flow along the length of the artery. Methods and results: Three-dimensional coronary anatomy was reconstructed from angiograms from 20 patients with chronic coronary syndrome. All flows were computed using CFD by applying the pressure gradient to the reconstructed geometry. Side branch flow was modelled as a porous wall boundary. Side branch flow magnitude was based on morphometric scaling laws with two models: a homogeneous model with flow loss along the entire arterial length; and a regionalized model with flow proportional to local taper. Flow results were validated against invasive measurements of flow by continuous infusion thermodilution (Coroventis™, Abbott). Both methods quantified flow relative to the invasive measures: homogeneous (r 0.47, P 0.006; zero bias; 95% CI -168 to +168 mL/min); regionalized method (r 0.43, P 0.013; zero bias; 95% CI -175 to +175 mL/min). Conclusion: During angiography and pressure wire assessment, coronary flow can now be regionalized and differentiated at the inlet, outlet, and side branches. The effect of epicardial disease on agreement suggests the model may be best targeted at cases with a stenosis close to side branches.

The EurValve model execution environment.

The goal of this paper is to present a dedicated high-performance computing (HPC) infrastructure which is used in the development of a so-called reduced-order model (ROM) for simulating the outcomes of interventional procedures which are contemplated in the treatment of valvular heart conditions. Following a brief introduction to the problem, the paper presents the design of a model execution environment, in which representative cases can be simulated and the parameters of the ROM fine-tuned to enable subsequent deployment of a decision support system without further need for HPC. The presentation of the system is followed by information concerning its use in processing specific patient cases in the context of the EurValve international collaboration.

Automated tracking of migrating cells in phase-contrast video microscopy sequences using image registration.

Analysis of in vitro cell motility is a useful tool for assessing cellular response to a range of factors. However, the majority of cell-tracking systems available are designed primarily for use with fluorescently labelled images. In this paper, five commonly used tracking systems are examined for their performance compared with the use of a novel in-house cell-tracking system based on the principles of image registration and optical flow. Image registration is a tool commonly used in medical imaging to correct for the effects of patient motion during imaging procedures and works well on low-contrast images, such as those found in bright-field and phase-contrast microscopy. The five cell-tracking systems examined were Retrac, a manual tracking system used as the gold standard; CellTrack, a recently released freely downloadable software system that uses a combination of tracking methods; ImageJ, which is a freely available piece of software with a plug-in for automated tracking (MTrack2) and Imaris and Volocity, both commercially available automated tracking systems. All systems were used to track migration of human epithelial cells over ten frames of a phase-contrast time-lapse microscopy sequence. This showed that the in-house image-registration system was the most effective of those tested when tracking non-dividing epithelial cells in low-contrast images, with a successful tracking rate of 95%. The performance of the tracking systems was also evaluated by tracking fluorescently labelled epithelial cells imaged with both phase-contrast and confocal microscopy techniques. The results showed that using fluorescence microscopy instead of phase contrast does improve the tracking efficiency for each of the tested systems. For the in-house software, this improvement was relatively small (<5% difference in tracking success rate), whereas much greater improvements in performance were seen when using fluorescence microscopy with Volocity and ImageJ.

Estimation of valvular resistance of segmented aortic valves using computational fluid dynamics.

Aortic valve stenosis is associated with an elevated left ventricular pressure and transaortic pressure drop. Clinicians routinely use Doppler ultrasound to quantify aortic valve stenosis severity by estimating this pressure drop from blood velocity. However, this method approximates the peak pressure drop, and is unable to quantify the partial pressure recovery distal to the valve. As pressure drops are flow dependent, it remains difficult to assess the true significance of a stenosis for low-flow low-gradient patients. Recent advances in segmentation techniques enable patient-specific Computational Fluid Dynamics (CFD) simulations of flow through the aortic valve. In this work a simulation framework is presented and used to analyze data of 18 patients. The ventricle and valve are reconstructed from 4D Computed Tomography imaging data. Ventricular motion is extracted from the medical images and used to model ventricular contraction and corresponding blood flow through the valve. Simplifications of the framework are assessed by introducing two simplified CFD models: a truncated time-dependent and a steady-state model. Model simplifications are justified for cases where the simulated pressure drop is above 10 mmHg. Furthermore, we propose a valve resistance index to quantify stenosis severity from simulation results. This index is compared to established metrics for clinical decision making, i.e. blood velocity and valve area. It is found that velocity measurements alone do not adequately reflect stenosis severity. This work demonstrates that combining 4D imaging data and CFD has the potential to provide a physiologically relevant diagnostic metric to quantify aortic valve stenosis severity.

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.

Reproducibility of haemodynamical simulations in a subject-specific stented aneurysm model--a report on the Virtual Intracranial Stenting Challenge 2007.

This paper presents the results of the Virtual Intracranial Stenting Challenge (VISC) 2007, an international initiative whose aim was to establish the reproducibility of state-of-the-art haemodynamical simulation techniques in subject-specific stented models of intracranial aneurysms (IAs). IAs are pathological dilatations of the cerebral artery walls, which are associated with high mortality and morbidity rates due to subarachnoid haemorrhage following rupture. The deployment of a stent as flow diverter has recently been indicated as a promising treatment option, which has the potential to protect the aneurysm by reducing the action of haemodynamical forces and facilitating aneurysm thrombosis. The direct assessment of changes in aneurysm haemodynamics after stent deployment is hampered by limitations in existing imaging techniques and currently requires resorting to numerical simulations. Numerical simulations also have the potential to assist in the personalized selection of an optimal stent design prior to intervention. However, from the current literature it is difficult to assess the level of technological advancement and the reproducibility of haemodynamical predictions in stented patient-specific models. The VISC 2007 initiative engaged in the development of a multicentre-controlled benchmark to analyse differences induced by diverse grid generation and computational fluid dynamics (CFD) technologies. The challenge also represented an opportunity to provide a survey of available technologies currently adopted by international teams from both academic and industrial institutions for constructing computational models of stented aneurysms. The results demonstrate the ability of current strategies in consistently quantifying the performance of three commercial intracranial stents, and contribute to reinforce the confidence in haemodynamical simulation, thus taking a step forward towards the introduction of simulation tools to support diagnostics and interventional planning.

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%.

Efficient computational fluid dynamics mesh generation by image registration.

Most implementations of computational fluid dynamics (CFD) solutions require a discretisation or meshing of the solution domain. The production from a medical image of a computationally efficient mesh representing the structures of interest can be time consuming and labour-intensive, and remains a major bottleneck in the clinical application of CFD. This paper presents a method for deriving a patient-specific mesh from a medical image. The method uses volumetric registration of a pseudo-image, produced from an idealised template mesh, with the medical image. The registration algorithm used is robust and computationally efficient. The accuracy of the new algorithm is measured in terms of the distance between a registered surface and a known surface, for image data derived from casts of the lumen of two different vessels. The true surface is identified by laser profiling. The average distance between the surface points measured by the laser profiler and the surface of the mapped mesh is better than 0.2 mm. For the images analysed, the new algorithm is shown to be 2-3 times more accurate than a standard published algorithm based on maximising normalised mutual information. Computation times are approximately 18 times faster for the new algorithm than the standard algorithm. Examples of the use of the algorithm on two clinical examples are also given. The registration methodology lends itself immediately to the construction of dynamic mesh models in which vessel wall motion is obtained directly using registration.

A cell-based mechanical model of coronary artery tunica media.

A three-dimensional cell-based mechanical model of coronary artery tunica media is proposed. The model is composed of spherical cells forming a hexagonal close-packed lattice. Tissue anisotropy is taken into account by varying interaction forces with the direction of intercellular connection. Several cell-centre interaction potentials for repulsion and attraction are considered, including the Hertz contact model and its neo-Hookean extension, the Johnson-Kendall-Roberts model of adhesive contact, and a wormlike chain model. The model is validated against data from in vitro uni-axial tension tests performed on dissected strips of tunica media. The wormlike chain potential in combination with the neo-Hookean Hertz contact model produces stress-stretch curves which represent the experimental data very well.

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.

Outlook for grid service technologies within the @neurIST eHealth environment.

The aim of the @neurIST project is to create an IT infrastructure for the management of all processes linked to research, diagnosis and treatment development for complex and multi-factorial diseases. The IT infrastructure will be developed for one such disease, cerebral aneurysm and subarachnoid haemorrhage, but its core technologies will be transferable to meet the needs of other medical areas. Since the IT infrastructure for @neurIST will need to encompass data repositories, computational analysis services and information systems handling multi-scale, multi-modal information at distributed sites, the natural basis for the IT infrastructure is a Grid Service middleware. The project will adopt a service-oriented architecture because it aims to provide a system addressing the needs of medical researchers, clinicians and health care specialists (and their IT providers/systems) and medical supplier/consulting industries.

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.

Automatic segmentation of medical images using image registration: diagnostic and simulation applications.

Automatic identification of the boundaries of significant structure (segmentation) within a medical image is an are of ongoing research. Various approaches have been proposed but only two methods have achieved widespread use: manual delineation of boundaries and segmentation using intensity values. In this paper we describe an approach based on image registration. A reference image is prepared and segmented, by hand or otherwise. A patient image is registered to the reference image and the mapping then applied to ther reference segmentation to map it back to the patient image. In general a high-resolution nonlinear mapping is required to achieve accurate segmentation. This paper describes an algorithm that can efficiently generate such mappings, and outlines the uses of this tool in two relevant applications. An important feature of the approach described in this paper is that the algorithm is independent of the segmentation problem being addresses. All knowledge about the problem at hand is contained in files of reference data. A secondary benefit is that the continuous three-dimensional mapping generated is well suited to the generation of patient-specific numerical models (e.g. finite element meshes) from the library models. Smoothness constraints in the morphing algorithm tend to maintain the geometric quality of the reference mesh.

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.

The epitheliome: agent-based modelling of the social behaviour of cells.

We have developed a new computational modelling paradigm for predicting the emergent behaviour resulting from the interaction of cells in epithelial tissue. As proof-of-concept, an agent-based model, in which there is a one-to-one correspondence between biological cells and software agents, has been coupled to a simple physical model. Behaviour of the computational model is compared with the growth characteristics of epithelial cells in monolayer culture, using growth media with low and physiological calcium concentrations. Results show a qualitative fit between the growth characteristics produced by the simulation and the in vitro cell models.

Modelling of epithelial tissue impedance measured using three different designs of probe.

Impedance measurement is a promising technique for detecting pre-malignant changes in epithelial tissue. This paper considers how the design of the impedance probe affects the ability to discriminate between tissue types. To do this, finite element models of the electrical properties of squamous and glandular columnar epithelia have been used. The glandular tissue model is described here for the first time. Glandular mucosa is found in many regions of the gastrointestinal tract, such as the stomach and intestine, and has a large effective surface area. Firstly, the electrical properties of a small section of gland, with epithelial cells and supportive tissue, are determined. These properties are then used to build up a three-dimensional model of a whole section of mucosa containing many thousands of glands. Measurements using different types of impedance probe were simulated by applying different boundary conditions to the models. Transepithelial impedance, and tetrapolar measurement with a probe placed on the tissue surface have been modelled. In the latter case, the impedance can be affected by conductive fluid, such as mucus, on the tissue surface. This effect has been investigated, and a new design of probe, which uses a guard electrode to counteract this potential source of variability, is proposed.