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.

Evaluation of models of sequestration flow in coronary arteries-Physiology versus anatomy?

BACKGROUND: Myocardial ischaemia results from insufficient coronary blood flow. Computed virtual fractional flow reserve (vFFR) allows quantification of proportional flow loss without the need for invasive pressure-wire testing. In the current study, we describe a novel, conductivity model of side branch flow, referred to as 'leak'. This leak model is a function of taper and local pressure, the latter of which may change radically when focal disease is present. This builds upon previous techniques, which either ignore side branch flow, or rely purely on anatomical factors. This study aimed to describe a new, conductivity model of side branch flow and compare this with established anatomical models. METHODS AND RESULTS: The novel technique was used to quantify vFFR, distal absolute flow (Qd) and microvascular resistance (CMVR) in 325 idealised 1D models of coronary arteries, modelled from invasive clinical data. Outputs were compared to an established anatomical model of flow. The conductivity model correlated and agreed with the reference model for vFFR (r = 0.895, p < 0.0001; ＋0.02, 95% CI 0.00 to ＋ 0.22), Qd (r = 0.959, p < 0.0001; -5.2 mL/min, 95% CI -52.2 to ＋13.0) and CMVR (r = 0.624, p < 0.0001; ＋50 Woods Units, 95% CI -325 to ＋2549). CONCLUSION: Agreement between the two techniques was closest for vFFR, with greater proportional differences seen for Qd and CMVR. The conductivity function assumes vessel taper was optimised for the healthy state and that CMVR was not affected by local disease. The latter may be addressed with further refinement of the technique or inferred from complementary image data. The conductivity technique may represent a refinement of current techniques for modelling coronary side-branch flow. Further work is needed to validate the technique against invasive clinical data.

Cardiac MR modelling of systolic and diastolic blood pressure.

AIMS: Blood pressure (BP) is a crucial factor in cardiovascular health and can affect cardiac imaging assessments. However, standard outpatient cardiovascular MR (CMR) imaging procedures do not typically include BP measurements prior to image acquisition. This study proposes that brachial systolic BP (SBP) and diastolic BP (DBP) can be modelled using patient characteristics and CMR data. METHODS: In this multicentre study, 57 patients from the PREFER-CMR registry and 163 patients from other registries were used as the derivation cohort. All subjects had their brachial SBP and DBP measured using a sphygmomanometer. Multivariate linear regression analysis was applied to predict brachial BP. The model was subsequently validated in a cohort of 169 healthy individuals. RESULTS: Age and left ventricular ejection fraction were associated with SBP. Aortic forward flow, body surface area and left ventricular mass index were associated with DBP. When applied to the validation cohort, the correlation coefficient between CMR-derived SBP and brachial SBP was (r=0.16, 95% CI 0.011 to 0.305, p=0.03), and CMR-derived DBP and brachial DBP was (r=0.27, 95% CI 0.122 to 0.403, p=0.0004). The area under the curve (AUC) for CMR-derived SBP to predict SBP>120 mmHg was 0.59, p=0.038. Moreover, CMR-derived DBP to predict DBP>80 mmHg had an AUC of 0.64, p=0.002. CONCLUSION: CMR-derived SBP and DBP models can estimate brachial SBP and DBP. Such models may allow efficient prospective collection, as well as retrospective estimation of BP, which should be incorporated into assessments due to its critical effect on load-dependent parameters.

Rapid virtual fractional flow reserve using 3D computational fluid dynamics.

Aims: Over the last ten years, virtual Fractional Flow Reserve (vFFR) has improved the utility of Fractional Flow Reserve (FFR), a globally recommended assessment to guide coronary interventions. Although the speed of vFFR computation has accelerated, techniques utilising full 3D computational fluid dynamics (CFD) solutions rather than simplified analytical solutions still require significant time to compute. Methods and results: This study investigated the speed, accuracy and cost of a novel 3D-CFD software method based upon a graphic processing unit (GPU) computation, compared with the existing fastest central processing unit (CPU)-based 3D-CFD technique, on 40 angiographic cases. The novel GPU simulation was significantly faster than the CPU method (median 31.7 s (Interquartile Range (IQR) 24.0-44.4s) vs. 607.5 s (490-964 s), P < 0.0001). The novel GPU technique was 99.6% (IQR 99.3-99.9) accurate relative to the CPU method. The initial cost of the GPU hardware was greater than the CPU (£4080 vs. £2876), but the median energy consumption per case was significantly less using the GPU method (8.44 (6.80-13.39) Wh vs. 2.60 (2.16-3.12) Wh, P < 0.0001). Conclusion: This study demonstrates that vFFR can be computed using 3D-CFD with up to 28-fold acceleration than previous techniques with no clinically significant sacrifice in accuracy.

Sex differences in coronary microvascular resistance measured by a computational fluid dynamics model.

Background: Increased coronary microvascular resistance (CMVR) is associated with coronary microvascular dysfunction (CMD). Although CMD is more common in women, sex-specific differences in CMVR have not been demonstrated previously. Aim: To compare CMVR between men and women being investigated for chest pain. Methods and results: We used a computational fluid dynamics (CFD) model of human coronary physiology to calculate absolute CMVR based on invasive coronary angiographic images and pressures in 203 coronary arteries from 144 individual patients. CMVR was significantly higher in women than men (860 [650-1,205] vs. 680 [520-865] WU, Z = -2.24, p = 0.025). None of the other major subgroup comparisons yielded any differences in CMVR. Conclusion: CMVR was significantly higher in women compared with men. These sex-specific differences may help to explain the increased prevalence of CMD in women.

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.

Quantifying Myocardial Blood Flow and Resistance Using 4D-Flow Cardiac Magnetic Resonance Imaging.

Background: Ischaemia with nonobstructive coronary arteries is most commonly caused by coronary microvascular dysfunction but remains difficult to diagnose without invasive testing. Myocardial blood flow (MBF) can be quantified noninvasively on stress perfusion cardiac magnetic resonance (CMR) or positron emission tomography but neither is routinely used in clinical practice due to practical and technical constraints. Quantification of coronary sinus (CS) flow may represent a simpler method for CMR MBF quantification. 4D flow CMR offers comprehensive intracardiac and transvalvular flow quantification. However, it is feasibility to quantify MBF remains unknown. Methods: Patients with acute myocardial infarction (MI) and healthy volunteers underwent CMR. The CS contours were traced from the 2-chamber view. A reformatted phase contrast plane was generated through the CS, and flow was quantified using 4D flow CMR over the cardiac cycle and normalised for myocardial mass. MBF and resistance (MyoR) was determined in ten healthy volunteers, ten patients with myocardial infarction (MI) without microvascular obstruction (MVO), and ten with known MVO. Results: MBF was quantified in all 30 subjects. MBF was highest in healthy controls (123.8 ± 48.4 mL/min), significantly lower in those with MI (85.7 ± 30.5 mL/min), and even lower in those with MI and MVO (67.9 ± 29.2 mL/min/) (P < 0.01 for both differences). Compared with healthy controls, MyoR was higher in those with MI and even higher in those with MI and MVO (0.79 (±0.35) versus 1.10 (±0.50) versus 1.50 (±0.69), P=0.02). Conclusions: MBF and MyoR can be quantified from 4D flow CMR. Resting MBF was reduced in patients with MI and MVO.

Integrating particle tracking with computational fluid dynamics to assess haemodynamic perturbation by coronary artery stents.

AIMS: Coronary artery stents have profound effects on arterial function by altering fluid flow mass transport and wall shear stress. We developed a new integrated methodology to analyse the effects of stents on mass transport and shear stress to inform the design of haemodynamically-favourable stents. METHODS AND RESULTS: Stents were deployed in model vessels followed by tracking of fluorescent particles under flow. Parallel analyses involved high-resolution micro-computed tomography scanning followed by computational fluid dynamics simulations to assess wall shear stress distribution. Several stent designs were analysed to assess whether the workflow was robust for diverse strut geometries. Stents had striking effects on fluid flow streamlines, flow separation or funnelling, and the accumulation of particles at areas of complex geometry that were tightly coupled to stent shape. CFD analysis revealed that stents had a major influence on wall shear stress magnitude, direction and distribution and this was highly sensitive to geometry. CONCLUSIONS: Integration of particle tracking with CFD allows assessment of fluid flow and shear stress in stented arteries in unprecedented detail. Deleterious flow perturbations, such as accumulation of particles at struts and non-physiological shear stress, were highly sensitive to individual stent geometry. Novel designs for stents should be tested for mass transport and shear stress which are important effectors of vascular health and repair.

The Benefits of Physical Activity for People with Obesity, Independent of Weight Loss: A Systematic Review.

Purposeful weight loss continues to be the primary focus for treating obesity. However, this strategy appears to be inadequate as obesity rates continue to rise and a myriad of benefits of physical activity that affect multiple health outcomes related to obesity and associated comorbidities are not integrated into treatment strategies. There are emerging correlational data in individuals with obesity that demonstrate physical activity can be beneficial to many critical health markers, independent of weight loss or changes in BMI. This systematic review investigates interventional studies that examine health markers, independent of weight loss, in individuals with obesity. Fourteen studies were identified that utilized a variety of physical activity interventions with primary endpoints that included cellular, metabolic, systemic and brain health outcomes. The review of the literature demonstrates that for individuals with obesity, there are both small-scale and large-scale physiologic benefits that occur with increased physical activity of various modalities. Focusing on these benefits, rather than a narrow focus of weight loss alone, may increase physical activity behavior and health for individuals with obesity.

Refining Our Understanding of the Flow Through Coronary Artery Branches; Revisiting Murray's Law in Human Epicardial Coronary Arteries.

Background: Quantification of coronary blood flow is used to evaluate coronary artery disease, but our understanding of flow through branched systems is poor. Murray's law defines coronary morphometric scaling, the relationship between flow (Q) and vessel diameter (D) and is the basis for minimum lumen area targets when intervening on bifurcation lesions. Murray's original law (Q α DP) dictates that the exponent (P) is 3.0, whilst constant blood velocity throughout the system would suggest an exponent of 2.0. In human coronary arteries, the value of Murray's exponent remains unknown. Aim: To establish the exponent in Murray's power law relationship that best reproduces coronary blood flows (Q) and microvascular resistances (Rmicro) in a bifurcating coronary tree. Methods and Results: We screened 48 cases, and were able to evaluate inlet Q and Rmicro in 27 branched coronary arteries, taken from 20 patients, using a novel computational fluid dynamics (CFD) model which reconstructs 3D coronary anatomy from angiography and uses pressure-wire measurements to compute Q and Rmicro distribution in the main- and side-branches. Outputs were validated against invasive measurements using a Rayflow™ catheter. A Murray's power law exponent of 2.15 produced the strongest correlation and closest agreement with inlet Q (zero bias, r = 0.47, p = 0.006) and an exponent of 2.38 produced the strongest correlation and closest agreement with Rmicro (zero bias, r = 0.66, p = 0.0001). Conclusions: The optimal power law exponents for Q and Rmicro were not 3.0, as dictated by Murray's Law, but 2.15 and 2.38 respectively. These data will be useful in assessing patient-specific coronary physiology and tailoring revascularisation decisions.

Endothelial repair in stented arteries is accelerated by inhibition of Rho-associated protein kinase.

AIMS: Stent deployment causes endothelial cells (EC) denudation, which promotes in-stent restenosis and thrombosis. Thus endothelial regrowth in stented arteries is an important therapeutic goal. Stent struts modify local hemodynamics, however the effects of flow perturbation on EC injury and repair are incompletely understood. By studying the effects of stent struts on flow and EC migration, we identified an intervention that promotes endothelial repair in stented arteries. METHODS AND RESULTS: In vitro and in vivo models were developed to monitor endothelialization under flow and the influence of stent struts. A 2D parallel-plate flow chamber with 100 µm ridges arranged perpendicular to the flow was used. Live cell imaging coupled to computational fluid dynamic simulations revealed that EC migrate in the direction of flow upstream from the ridges but subsequently accumulate downstream from ridges at sites of bidirectional flow. The mechanism of EC trapping by bidirectional flow involved reduced migratory polarity associated with altered actin dynamics. Inhibition of Rho-associated protein kinase (ROCK) enhanced endothelialization of ridged surfaces by promoting migratory polarity under bidirectional flow (P < 0.01). To more closely mimic the in vivo situation, we cultured EC on the inner surface of polydimethylsiloxane tubing containing Coroflex Blue stents (65 µm struts) and monitored migration. ROCK inhibition significantly enhanced EC accumulation downstream from struts under flow (P < 0.05). We investigated the effects of ROCK inhibition on re-endothelialization in vivo using a porcine model of EC denudation and stent placement. En face staining and confocal microscopy revealed that inhibition of ROCK using fasudil (30 mg/day via osmotic minipump) significantly increased re-endothelialization of stented carotid arteries (P < 0.05). CONCLUSIONS: Stent struts delay endothelial repair by generating localized bidirectional flow which traps migrating EC. ROCK inhibitors accelerate endothelial repair of stented arteries by enhancing EC polarity and migration through regions of bidirectional flow.

Heart rate reduction with ivabradine promotes shear stress-dependent anti-inflammatory mechanisms in arteries.

Blood flow generates wall shear stress (WSS) which alters endothelial cell (EC) function. Low WSS promotes vascular inflammation and atherosclerosis whereas high uniform WSS is protective. Ivabradine decreases heart rate leading to altered haemodynamics. Besides its cardio-protective effects, ivabradine protects arteries from inflammation and atherosclerosis via unknown mechanisms. We hypothesised that ivabradine protects arteries by increasing WSS to reduce vascular inflammation. Hypercholesterolaemic mice were treated with ivabradine for seven weeks in drinking water or remained untreated as a control. En face immunostaining demonstrated that treatment with ivabradine reduced the expression of pro-inflammatory VCAM-1 (p<0.01) and enhanced the expression of anti-inflammatory eNOS (p<0.01) at the inner curvature of the aorta. We concluded that ivabradine alters EC physiology indirectly via modulation of flow because treatment with ivabradine had no effect in ligated carotid arteries in vivo, and did not influence the basal or TNFα-induced expression of inflammatory (VCAM-1, MCP-1) or protective (eNOS, HMOX1, KLF2, KLF4) genes in cultured EC. We therefore considered whether ivabradine can alter WSS which is a regulator of EC inflammatory activation. Computational fluid dynamics demonstrated that ivabradine treatment reduced heart rate by 20 % and enhanced WSS in the aorta. In conclusion, ivabradine treatment altered haemodynamics in the murine aorta by increasing the magnitude of shear stress. This was accompanied by induction of eNOS and suppression of VCAM-1, whereas ivabradine did not alter EC that could not respond to flow. Thus ivabradine protects arteries by altering local mechanical conditions to trigger an anti-inflammatory response.

Modelling the glycocalyx-endothelium-erythrocyte interaction in the microcirculation: a computational study.

A novel, coarse-grained, single-framework 'Eulerian' model for blood flow in the microvascular circulation is presented and used to estimate the variations in flow properties that accrue from all of the following: (i) wall position variation, associated with the endothelial cells' (ECs) shape, (ii) glycocalyx layer (GL) effects and (iii) the particulate nature of blood. We stress that our new model is fully coupled and uses only a single Eulerian computational framework to recover complex effects, dispensing altogether with the need for, e.g. re-meshing and advected sets of Lagrangian points. Physically, blood is modelled as a two-component, incompressible fluid - the plasma and corpuscular elements dispersed in it. The latter are modelled as deformable liquid droplets of increased viscosity. Interfacial membrane effects are present to mimic key blood properties and to avoid droplets' coalescence. The model is encapsulated within a multi-component lattice Boltzmann method that uses a sub-lattice 'wavy wall' closure to represent the ECs. Between this boundary and the flow domain, the model incorporates a coarse-grained representation of the endothelial GL, which is known to cover microvessel walls. The endothelial glycocalyx is modelled as a medium of variable and adaptive porosity, with approaching droplets being subject to a repulsive elastic force. Numerical simulations are presented to show the combined and simultaneous influence on fundamental flow properties of the EC wall undulation, the glycocalyx compression and repulsion and the particulate nature of blood. Several characteristic hemodynamical features of microvessel flow are successfully reproduced, including the deformability of particulates and the Fahraeus-Lindqvist effect. Moreover, the importance of modelling the GL is manifest in the magnitude of and the temporal variations in the flow rate and wall shear stresses.

The effects of stenting on shear stress: relevance to endothelial injury and repair.

Stent deployment following balloon angioplasty is used routinely to treat coronary artery disease. These interventions cause damage and loss of endothelial cells (EC), and thus promote in-stent thrombosis and restenosis. Injured arteries are repaired (intrinsically) by locally derived EC and by circulating endothelial progenitor cells which migrate and proliferate to re-populate denuded regions. However, re-endothelialization is not always complete and often dysfunctional. Moreover, the molecular and biomechanical mechanisms that control EC repair and function in stented segments are poorly understood. Here, we propose that stents modify endothelial repair processes, in part, by altering fluid shear stress, a mechanical force that influences EC migration and proliferation. A more detailed understanding of the biomechanical processes that control endothelial healing would provide a platform for the development of novel therapeutic approaches to minimize damage and promote vascular repair in stented arteries.

Large scale surveys suggest limited mercury availability in tropical north Queensland (Australia).

Little is known about the threat of mercury (Hg) to consumers in food webs of Australia's wet-dry tropics. This is despite high concentrations in similar biomes elsewhere and a recent history of gold mining that could lead to a high degree of exposure for biota. We analysed Hg in water, sediments, invertebrates and fishes in rivers and estuaries of north Queensland, Australia to determine its availability and biomagnification in food webs. Concentrations in water and sediments were low relative to other regions of Hg concern, with only four of 138 water samples and five of 60 sediment samples above detection limits of 0.1µgL(-1) and 0.1µgg(-1), respectively. Concentrations of Hg in fishes and invertebrates from riverine and wetland food webs were well below international consumption guidelines, including those in piscivorous fishes, likely due to low baseline concentrations and limited rates of biomagnification (average slope of log Hg vs. δ(15)N=0.08). A large fish species of recreational, commercial, and cultural importance (the barramundi, Lates calcarifer), had low concentrations that were below consumption guidelines. Observed variation in Hg concentrations in this species was primarily explained by age and foraging location (floodplain vs. coastal), with floodplain feeders having higher Hg concentrations than those foraging at sea. These analyses suggest that there is a limited threat of Hg exposure for fish-eating consumers in this region.

Fish mediate high food web connectivity in the lower reaches of a tropical floodplain river.

High levels of hydrological connectivity during seasonal flooding provide significant opportunities for movements of fish between rivers and their floodplains, estuaries and the sea, possibly mediating food web subsidies among habitats. To determine the degree of utilisation of food sources from different habitats in a tropical river with a short floodplain inundation duration (~2 months), stable isotope ratios in fishes and their available food were measured from three habitats (inundated floodplain, dry season freshwater, coastal marine) in the lower reaches of the Mitchell River, Queensland (Australia). Floodplain food sources constituted the majority of the diet of large-bodied fishes (barramundi Lates calcarifer, catfish Neoarius graeffei) captured on the floodplain in the wet season and for gonadal tissues of a common herbivorous fish (gizzard shad Nematalosa come), the latter suggesting that critical reproductive phases are fuelled by floodplain production. Floodplain food sources also subsidised barramundi from the recreational fishery in adjacent coastal and estuarine areas, and the broader fish community from a freshwater lagoon. These findings highlight the importance of the floodplain in supporting the production of large fishes in spite of the episodic nature and relatively short duration of inundation compared to large river floodplains of humid tropical regions. They also illustrate the high degree of food web connectivity mediated by mobile fish in this system in the absence of human modification, and point to the potential consequences of water resource development that may reduce or eliminate hydrological connectivity between the river and its floodplain.

Modelling wall shear stress in small arteries using the Lattice Boltzmann method: influence of the endothelial wall profile.

In order to address the problem of blood flow over the endothelium in small arteries, the near-endothelial region is here studied in more detail. The method used is a finite-volume discretisation of a Lattice Boltzmann equation over unstructured grids, named unstructured Lattice Boltzmann equation (ULBE). It is a new scheme based on the idea of placing the unknown fields at the nodes of the mesh and evolving them based on the fluxes crossing the surfaces of the corresponding control volumes. The study shows a significant variation and a high sensitivity of wall shear stress to the height of the endothelium corrugation and the presence of erythrocytes. The latter were modelled as deformable, viscous particles within a fluid continuum.

A local lattice Boltzmann method for multiple immiscible fluids and dense suspensions of drops.

The lattice Boltzmann method (LBM) for computational fluid dynamics benefits from a simple, explicit, completely local computational algorithm making it highly efficient. We extend LBM to recover hydrodynamics of multi-component immiscible fluids, while retaining a completely local, explicit and simple algorithm. Hence, no computationally expensive lattice gradients, interaction potentials or curvatures, that use information from neighbouring lattice sites, need to be calculated, which makes the method highly scalable and suitable for high performance parallel computing. The method is analytical and is shown to recover correct continuum hydrodynamic equations of motion and interfacial boundary conditions. This LBM may be further extended to situations containing a high number (O(100)) of individually immiscible drops. We make comparisons of the emergent non-Newtonian behaviour with a power-law fluid model. We anticipate our method will have a range applications in engineering, industrial and biological sciences.

Modeling the flow of dense suspensions of deformable particles in three dimensions.

We describe here a rigorous and accurate model for the simulation of three-dimensional deformable particles (DPs). The method is very versatile, easily simulating various types of deformable particles such as vesicles, capsules, and biological cells. Each DP is resolved explicitly and advects within the surrounding Newtonian fluid. The DPs have a preferred rest shape (e.g., spherical for vesicles, or biconcave for red blood cells). The model uses a classic hybrid system: an Eulerian approach is used for the Navier-Stokes solver (the lattice Boltzmann method) and a Lagrangian approach for the evolution of the DP mesh. Coupling is accomplished through the lattice Boltzmann velocity field, which transmits force to the membranes of the DPs. The novelty of this method resides in its ability (by design) to simulate a large number of DPs within the bounds of current computational limitations: our simple and efficient approach is to (i) use the lattice Boltzmann method because of its acknowledged efficiency at low Reynolds number and its ease of parallelization, and (ii) model the DP dynamics using a coarse mesh (approximately 500 nodes) and a spring model constraining (if necessary) local area, total area, cell volume, local curvature, and local primary stresses. We show that this approach is comparable to the more common - yet numerically expensive - approach of membrane potential function, through a series of quantitative comparisons. To demonstrate the capabilities of the model, we simulate the flow of 200 densely packed red blood cells - a computationally challenging task. The model is very efficient, requiring of the order of minutes for a single DP in a 50 microm x 40 microm x 40 microm simulation domain and only hours for 200 DPs in 80 microm x 30 microm x 30 microm . Moreover, the model is highly scalable and efficient compared to other models of blood cells in flow, making it an ideal and unique tool for studying blood flow in microvessels or vesicle or capsule flow (or a mixture of different particles). In addition to directly predicting fluid dynamics in complex suspension in any geometry, the model allows determination of accurate, empirical rules which may improve existing macroscopic, continuum models.

Simulation of a microfluidic flow-focusing device.

We present a model of microfluidic flow of several completely immiscible fluids and use it to simulate a whole flow focusing device chamber. Our efficient, practical model supports a large parameter space, spanned by surface wetting, surface tension, liquid-liquid wetting, viscosity ratio, and inlet velocity. It is based upon an N-component lattice Boltzmann method with interrupted coalescence [Dupin, Philos. Trans. R. Soc. London, Ser. A 362, 1885 (2004)], here adapted for calculations at low capillary and Reynolds numbers, with wetting and significantly reduced spurious flow. Results over 2 orders of magnitude in Reynolds number are presented.