Correlation of thrombosis growth rate to pathological wall shear rate during platelet accumulation

Local hemodynamics may strongly influence atherothrombosis, which can lead to acute myocardial infarction and stroke. The relationship between hemodynamics and thrombosis during platelet accumulation was studied through an in vitro flow system consisting of a stenosis. Specifically, wall shear rates (WSR) ranging from 0 to 100,000 s^?1 were ascertained through computations and compared with thrombus growth rates found by image analysis for over 5,000 individual observation points per experiment. A positive correlation (P < 0.0001) was found between thrombus accumulation rates and WSR up to 6,000 s^?1, with a decrease in growth rates at WSR >6,000 s^?1 (P < 0.0001). Furthermore, growth rates at pathological shear rates were found to be two to four times greater than for physiological arterial shear rates below 400 s^?1. Platelets did not accumulate for the first minute of perfusion. The initial lag time, before discernible thrombus growth could be found, diminished with shear (P < 0.0001). These studies show the quantitative increase in thrombus growth rates with very high shear rates in stenoses onto a collagen substrate. Biotechnol. Bioeng. 2012; 109: 2642–2650. © 2012 Wiley Periodicals, Inc.     

Shear rate dependence of free energy barrier height for phenyl ring rotations in polystyrene based on non-equilibrium molecular dynamics simulations

Polystyrene properties are influenced by ring motions in side groups. The main chain conformation and interaction with the surroundings dominate the ring rotations. It is known that shear flow affects linear chain conformation and molecular distribution. However, shear-induced variations in the ring rotations have yet to be studied. This study presents a shear flow system of polystyrene via non-equilibrium molecular dynamics simulations. The free energy barrier of the phenyl ring rotations was obtained from the distribution of angle χ between the ring and main chain based on the Boltzmann distribution law. The results showed that the barrier height approaches a constant value at a shear rate less than 10¹⁰ s^? 1, but decreases with an increase in shear rate higher than 10^10.5 s^? 1. Furthermore, the radial distribution function and potential energies were compared. Remarkably, the shear flow reduced the bond vibrations of the phenyl rings, but increased the separation between intermolecular particles. Hence, a smaller cavity is necessary for the rings to rotate once but more volume is occupied by the rings. The smaller volume obtained via main chain motions needed to construct the cavity lowers the energy barrier height at shear rate higher than 10^10.5 s^? 1.     

Adhesion study of silicone coatings: the interaction of thickness,modulus and shear rate on adhesion force

Abstract

Interactions between coating thickness, modulus and shear rate on pseudobarnacle adhesion to a platinum-cured silicone coating were studied using a statistical experimental design. A combined design method was used for two mixture components and two process variables. The two mixture components, vinyl end-terminated polydimethylsiloxanes (V21: MW = 6 kg mole^?1 and V35: MW = 4 9.5 kg mole^?1, Gelest Inc.) were mixed at five different levels to vary the modulus. The dry coating thickness was varied from 160 – 740 μm and shear tests were performed at four different shear rates (2, 7, 12, and 22 μm s^?1). The results of the statistical analysis showed that the mixture components were significant factors on shear stress, showing an interaction with the process variable. For the soft silicone coating based on the high molecular weight polydimethylsiloxane (E = 0.08 MPa), shear stress significantly increased as coating thickness decreased, while shear rate slightly impacted shear force especially at 160 μm coating thickness. As the modulus was increased (E = 1.3 MPa), more force was required to detach the pseudobarnacle from the coatings, but thickness and rate dependence on shear stress became less important.     

Inhibition of Hb Binding to GP1bα Abrogates Hb-Mediated Thrombus Formation on Immobilized VWF and Collagen under Physiological Shear Stress

BackgroundReports including our own describe that intravascular hemolysis increases the risk of thrombosis in hemolytic disorders. Our recent study shows that plasma Hb concentrations correlate directly with platelet activation in patients with paroxysmal nocturnal hemoglobinuria (PNH). The binding of Hb to glycoprotein1bα (GP1bα) increases platelet activation. A peptide AA1-50, designed from N-terminal amino acid sequence of GP1bα significantly inhibits the Hb binding to GP1bα as well as Hb-induced platelet activation. This study further examined if the Hb-mediated platelet activation plays any significant role in thrombus formation on subendothelium matrix under physiological flow shear stresses and the inhibition of Hb-platelet interaction can abrogate the above effects of Hb.

Methods and Results

Study performed thrombus formation assay in vitro by perfusing whole blood over immobilized VWF or collagen type I in presence of Hb under shear stresses simulating arterial or venous flow. The Hb concentrations ranging from 5 to 10 μM, commonly observed level in plasma of the hemolytic patients including PNH, dose-dependently increased thrombus formation on immobilized VWF under higher shear stress of 25 dyne/cm², but not at 5 dyne/cm². The above Hb concentrations also increased thrombus formation on immobilized collagen under both shear stresses of 5 and 25 dyne/cm². The peptide AA1-50 abrogated invariably the above effects of Hb on thrombus formation.

Conclusions and Significance

This study therefore indicates that the Hb-induced platelet activation plays a crucial role in thrombus formation on immobilized VWF or collagen under physiological flow shear stresses. Thus suggesting a probable role of this mechanism in facilitating thrombosis under hemolytic conditions.     

Investigation of human platelet adhesion under low shear conditions in a rotational flow chamber

Even though blood pumps have come into clinical usage, thrombo-embolic complications still pose a major problem, and they have not yet been clarified and quantified. However, it is known that the basis of thrombus formation is platelet adhesion, which is thought to be closely associated with the shear rate. Therefore, our current interest focuses on the effect of shear conditions on platelet adhesion. We have designed and carried out an experimental setup allowing fluorescent microscopy of whole blood within a rotational viscometer under controllable shear conditions. A small area of the bottom plate was coated with type I collagen, which provided a model of the injured vessel as a target for platelet adhesion. Using this setup, the time course of platelet adhesion under several different shear rates, ranging from 127 to 723 s^?1, was studied. Platelet adhesion increased along with shear rates up to 283 s^?1, followed by a gradual decrease when the shear rate exceeded 346 s^?1. The adhesion amounts were statistically significant between 283 and 173 s^?1 (p = 0.02), 173 and 127 s^?1 (p = 0.035), and 283 and 503 s^?1 (p = 0.03), respectively. This result suggests that there is an optimal shear condition around 300 s^?1 for platelet adhesion to type I collagen.     

Improving the Shear Strength of Quartz Sand using the Microbial Method

An increase in urban population and the reduced number of suitable lands for construction projects have necessitated the need for ground improvement methods with no environmentally detrimental effects. Microbial-induced calcite precipitation (MICP) is a relatively environmentally friendly method for soil regeneration. In the present paper, X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses were performed to investigate the type and method of cement formation in loose quartz sand with different densities stabilized using bacteria. The results showed that the highest content of calcium carbonate cement was produced in the sample with the lowest density. Moreover, after microbial stabilization, the shear strength measured in the direct shear test was increased in the specimen with a lower density. We observed an increase in shear strength from 0.63 kg/cm² before injection for loose sand (γ = 1.5 g/cm³) to 3.92 kg/cm² after injection. In addition, the effect of injection time was investigated and found that shear strength in the two-stage injection per day is greater than that in one- and three-stage injections per day. With prolonging the injection time from one to five days, shear strength was significantly increased from 2.07 to 4.54 kg/cm². Furthermore, prolonging the bacterial treatment period led to a significant increase in the produced carbonate cement and, consequently, enhanced soil shear strength.     

Three-dimensional macro-scale assessment of regional and temporal wall shear stress characteristics on aortic valve leaflets

The aortic valve (AV) achieves unidirectional blood flow between the left ventricle and the aorta. Although hemodynamic stresses have been shown to regulate valvular biology, the native wall shear stress (WSS) experienced by AV leaflets remains largely unknown. The objective of this study was to quantify computationally the macro-scale leaflet WSS environment using fluid–structure interaction modeling. An arbitrary Lagrangian–Eulerian approach was implemented to predict valvular flow and leaflet dynamics in a three-dimensional AV geometry subjected to physiologic transvalvular pressure. Local WSS characteristics were quantified in terms of temporal shear magnitude (TSM), oscillatory shear index (OSI) and temporal shear gradient (TSG). The dominant radial WSS predicted on the leaflets exhibited high amplitude and unidirectionality on the ventricularis (TSM>7.50 dyn/cm², OSI < 0.17, TSG>325.54 dyn/cm² s) but low amplitude and bidirectionality on the fibrosa (TSM < 2.73 dyn/cm², OSI>0.38, TSG < 191.17 dyn/cm² s). The radial WSS component computed in the leaflet base, belly and tip demonstrated strong regional variability (ventricularis TSM: 7.50–22.32 dyn/cm², fibrosa TSM: 1.26–2.73 dyn/cm²). While the circumferential WSS exhibited similar spatially dependent magnitude (ventricularis TSM: 1.41–3.40 dyn/cm², fibrosa TSM: 0.42–0.76 dyn/cm²) and side-specific amplitude (ventricularis TSG: 101.73–184.43 dyn/cm² s, fibrosa TSG: 41.92–54.10 dyn/cm² s), its temporal variations were consistently bidirectional (OSI>0.25). This study provides new insights into the role played by leaflet–blood flow interactions in valvular function and critical hemodynamic stress data for the assessment of the hemodynamic theory of AV disease.     

Albumin permeability across endothelial monolayers under pulsatile shear stress

Recent studies suggest that the temporal gradient of shear stress that is generated by blood flow plays an important role in the pathology of arteriosclerosis. We focused on the temporal gradient of shear stress and measured the permeability of albumin under steady or pulsatile shear stress conditions. Porcine aortic endothelial cells were seeded on a membrane filter and subjected to steady or pulsatile shear stress (1 Hz) at 1 Pa for 48 h, and the permeability of albumin was measured over time. The permeability increased gradually under steady flow but increased acutely under pulsatile shear stress. In particular, the maximum permeability of albumin differed under these conditions. The value was 4.2 × 10^?5 cm/s at 18 h under pulsatile shear stress and 2.8 × 10^?5 cm/s at 48 h under steady shear stress. The permeable route of albumin was examined using isoproterenol, which decreases junctional permeability. The increase in albumin permeability with pulsatile shear stress was decreased by isoproterenol. These results suggest that the increased permeability of albumin with pulsatile shear stress was related to trafficking through paracellular junctions. Thus, pulsation may promote a mechanotransduction process that differs from that of steady shear stress, and these pulsation effects likely play an important role in the permeability of macromolecules.     

Influence of flow rate variation on the development of Escherichia coli biofilms

This work investigates the effect of flow rate variation on mass transfer and on the development of Escherichia coli biofilms on a flow cell reactor under turbulent flow conditions. Computational fluid dynamics (CFD) was used to assess the applicability of this reactor for the simulation of industrial and biomedical biofilms and the numerical results were validated by streak photography. Two flow rates of 374 and 242 L h^?1 (corresponding to Reynolds numbers of 6,720 and 4,350) were tested and wall shear stresses between 0.183 and 0.511 Pa were predicted in the flow cell reactor. External mass transfer coefficients of 1.38 × 10^?5 and 9.64 × 10^?6 m s^?1 were obtained for the higher and lower flow rates, respectively. Biofilm formation was favored at the lowest flow rate because shear stress effects were more important than mass transfer limitations. This flow cell reactor generates wall shear stresses that are similar to those found in some industrial and biomedical settings, thus it is likely that the results obtained on this work can be used in the development of biofilm control strategies in both scenarios.     

Thrombotic risk stratification using computational modeling in patients with coronary artery aneurysms following Kawasaki disease

Kawasaki disease (KD) is the leading cause of acquired heart disease in children and can result in life-threatening coronary artery aneurysms in up to 25 % of patients. These aneurysms put patients at risk of thrombus formation, myocardial infarction, and sudden death. Clinicians must therefore decide which patients should be treated with anticoagulant medication, and/or surgical or percutaneous intervention. Current recommendations regarding initiation of anticoagulant therapy are based on anatomy alone with historical data suggesting that patients with aneurysms \(\ge \) 8 mm are at greatest risk of thrombosis. Given the multitude of variables that influence thrombus formation, we postulated that hemodynamic data derived from patient-specific simulations would more accurately predict risk of thrombosis than maximum diameter alone. Patient-specific blood flow simulations were performed on five KD patients with aneurysms and one KD patient with normal coronary arteries. Key hemodynamic and geometric parameters, including wall shear stress, particle residence time, and shape indices, were extracted from the models and simulations and compared with clinical outcomes. Preliminary fluid structure interaction simulations with radial expansion were performed, revealing modest differences in wall shear stress compared to the rigid wall case. Simulations provide compelling evidence that hemodynamic parameters may be a more accurate predictor of thrombotic risk than aneurysm diameter alone and motivate the need for follow-up studies with a larger cohort. These results suggest that a clinical index incorporating hemodynamic information be used in the future to select patients for anticoagulant therapy.     

A computational model for false lumen thrombosis in type B aortic dissection following thoracic endovascular repair

Thoracic endovascular repair (TEVAR) has recently been established as the preferred treatment option for complicated type B dissection. This procedure involves covering the primary entry tear to stimulate aortic remodelling and promote false lumen thrombosis thereby restoring true lumen flow. However, complications associated with incomplete false lumen thrombosis, such as aortic dilatation and stent graft induced new entry tears, can arise after TEVAR. This study presents the application and validation of a recently developed mathematical model for patient-specific prediction of thrombus formation and growth under physiologically realistic flow conditions. The model predicts thrombosis through the evaluation of shear rates, fluid residence time and platelet distribution, based on convection-diffusion-reaction transport equations. The model was applied to 3 type B aortic dissection patients: two TEVAR cases showing complete and incomplete false lumen thrombosis respectively, and one medically treated dissection with no signs of thrombosis. Predicted thrombus growth over time was validated against follow-up CT scans, showing good agreement with in vivo data in all cases with a maximum difference between predicted and measured false lumen reduction below 8%. Our results demonstrate that TEVAR-induced thrombus formation in type B aortic dissection can be predicted based on patient-specific anatomy and physiologically realistic boundary conditions. Our model can be used to identify anatomical or stent graft related factors that are associated with incomplete false lumen thrombosis following TEVAR, which may help clinicians develop personalised treatment plans for dissection patients in the future.     

Biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus: a patient-specific modelling study

Cerebral aneurysm is an irreversible dilatation causing intracranial haemorrhage with severe complications. It is assumed that the biomechanical factor plays a significant role in the development of cerebral aneurysm. However, reports on the correlations between the formation of intraluminal thrombus and the flow pattern, wall shear stress (WSS) distribution of the cerebral aneurysm as well as wall compliance are still limited. In this research, patient-specific numerical simulation was carried out for three cerebral aneurysms based on magnetic resonance imaging (MRI) data-sets. The interaction between pulsatile blood and aneurysm wall was taken into account. The biomechanical behaviour of cerebral aneurysm and its relation with the formation of intraluminal thrombus was studied systematically. The results of the numerical simulation indicated that the region of low blood flow velocity and the region of swirling recirculation were nearly coincident with each other. Besides, there was a significant correlation between the slow swirling flow and the location of thrombus deposition. Excessively low WSS was also found to have strong association with the regions of thrombus formation. Moreover, the relationship between cerebral aneurysm compliance and thrombus deposition was discovered. The patient-specific modelling study based on fluid–structure interaction) may provide a basis for future investigation on the prediction of thrombus formation in cerebral aneurysm.     

Tortuosity triggers platelet activation and thrombus formation in microvessels

Tortuous blood vessels are often seen in humans in association with thrombosis, atherosclerosis, hypertension, and aging. Vessel tortuosity can cause high fluid shear stress, likely promoting thrombosis. However, the underlying physical mechanisms and microscale processes are poorly understood. Accordingly, the objectives of this study were to develop and use a new computational approach to determine the effects of venule tortuosity and fluid velocity on thrombus initiation. The transport, collision, shear-induced activation, and receptor-ligand adhesion of individual platelets in thrombus formation were simulated using discrete element method. The shear-induced activation model assumed that a platelet became activated if it experienced a shear stress above a relative critical shear stress or if it contacted an activated platelet. Venules of various levels of tortuosity were simulated for a mean flow velocity of 0.10?cm s(-1), and a tortuous arteriole was simulated for a mean velocity of 0.47?cm s(-1). Our results showed that thrombus was initiated at inner walls in curved regions due to platelet activation in agreement with experimental studies. Increased venule tortuosity modified fluid flow to hasten thrombus initiation. Compared to the same sized venule, flow in the arteriole generated a higher amount of mural thrombi and platelet activation rate. The results suggest that the extent of tortuosity is an important factor in thrombus initiation in microvessels.     

Fluid–structure interactions in micro-interlocked regions of the cement–bone interface

Experimental tests and computational modelling were used to explore the fluid dynamics at the trabeculae–cement interlock regions found in the tibial component of total knee replacements. A cement–bone construct of the proximal tibia was created to simulate the immediate post-operative condition. Gap distributions along nine trabeculae–cement regions ranged from 0 to 50.4 μm (mean = 12 μm). Micro-motions ranged from 0.56 to 4.7 μm with a 1 MPa compressive load to the cement. Fluid–structure analysis between the trabeculae and the cement used idealised models with parametric evaluation of loading direction, gap closing fraction (GCF), gap thickness, loading frequency and fluid viscosity. The highest fluid shear stresses (926 Pa) along the trabecular surface were found for conditions with very thin and large GCFs, much larger than reported physiological levels (～1–5 Pa). A second fluid–structure model was created with a provision for bone resorption using a constitutive model with resorption velocity proportional to fluid shear rate. A lower cut-off was used, below which bone resorption would not occur (50 s^? 1). Results showed that there was initially high shear rates (>1000 s^? 1) that diminished after initial trabecular resorption. Resorption continued in high shear rate regions, resulting in a final shape with bone left deep in the cement layer, and is consistent with morphology found in post-mortem retrievals. Small gaps between the trabecular surface and the cement in the immediate post-operative state produce fluid flow conditions that appear to be supra-physiologic; these may cause fluid-induced lysis of trabeculae in the micro-interlock regions.     

Microfluidic Thrombosis under Multiple Shear Rates and Antiplatelet Therapy Doses

The mainstay of treatment for thrombosis, the formation of occlusive platelet aggregates that often lead to heart attack and stroke, is antiplatelet therapy. Antiplatelet therapy dosing and resistance are poorly understood, leading to potential incorrect and ineffective dosing. Shear rate is also suspected to play a major role in thrombosis, but instrumentation to measure its influence has been limited by flow conditions, agonist use, and non-systematic and/or non-quantitative studies.In this work we measured occlusion times and thrombus detachment for a range of initial shear rates (500, 1500, 4000, and 10000 s⁻¹) and therapy concentrations (0–2.4 µM for eptifibatide, 0–2 mM for acetyl-salicylic acid (ASA), 3.5–40 Units/L for heparin) using a microfluidic device. We also measured complete blood counts (CBC) and platelet activity using whole blood impedance aggregometry. Effects of shear rate and dose were analyzed using general linear models, logistic regressions, and Cox proportional hazards models.Shear rates have significant effects on thrombosis/dose-response curves for all tested therapies. ASA has little effect on high shear occlusion times, even at very high doses (up to 20 times the recommended dose). Under ASA therapy, thrombi formed at high shear rates were 4 times more prone to detachment compared to those formed under control conditions. Eptifibatide reduced occlusion when controlling for shear rate and its efficacy increased with dose concentration. In contrast, the hazard of occlusion from ASA was several orders of magnitude higher than that of eptifibatide. Our results show similar dose efficacy to our low shear measurements using whole blood aggregometry. This quantitative and statistically validated study of the effects of a wide range of shear rate and antiplatelet therapy doses on occlusive thrombosis contributes to more accurate understanding of thrombosis and to models for optimizing patient treatment.     

An integrated fluid–structure interaction and thrombosis model for type B aortic dissection

False lumen thrombosis (FLT) in type B aortic dissection has been associated with the progression of dissection and treatment outcome. Existing computational models mostly assume rigid wall behavior which ignores the effect of flap motion on flow and thrombus formation within the FL. In this study, we have combined a fully coupled fluid–structure interaction (FSI) approach with a shear-driven thrombosis model described by a series of convection–diffusion reaction equations. The integrated FSI-thrombosis model has been applied to an idealized dissection geometry to investigate the interaction between vessel wall motion and growing thrombus. Our simulation results show that wall compliance and flap motion can influence the progression of FLT. The main difference between the rigid and FSI models is the continuous development of vortices near the tears caused by drastic flap motion up to 4.45 mm. Flap-induced high shear stress and shear rates around tears help to transport activated platelets further to the neighboring region, thus speeding up thrombus formation during the accelerated phase in the FSI models. Reducing flap mobility by increasing the Young’s modulus of the flap slows down the thrombus growth. Compared to the rigid model, the predicted thrombus volume is 25% larger using the FSI-thrombosis model with a relatively mobile flap. Furthermore, our FSI-thrombosis model can capture the gradual effect of thrombus growth on the flow field, leading to flow obstruction in the FL, increased blood viscosity and reduced flap motion. This model is a step closer toward simulating realistic thrombus growth in aortic dissection, by taking into account the effect of intimal flap and vessel wall motion.

     

Development of a flow-through system to create occluding thrombus

Occlusive thrombosis accounts for many heart attacks and strokes. These acute events are difficult to catch in patients and animal test methods may be misleading because anti-thrombotic therapeutics often do not cross-react with different species. This paper presents a new flow-through system that leads to rapid occlusive thrombosis in arterial flow conditions. Whole porcine blood is perfused through a tubular test section. The growing thrombus is visualized in real time from early platelet attachment, through accumulation, to occlusion. The progression of flow rate reduction provides a clear distinguishing parameter between thrombus formation and embolization. Thrombus growth rate is a linear function of very high shear rate beyond 40,000 s(-1). The histology of the thrombus reveals predominantly platelet accumulation and growth as a rough surface with tendrils. This flow-through system may be useful for the economic testing of new anti-thrombosis therapies.     

A three-dimensional multiscale model for the prediction of thrombus growth under flow with single-platelet resolution

Modeling thrombus growth in pathological flows allows evaluation of risk under patient-specific pharmacological, hematological, and hemodynamical conditions. We have developed a 3D multiscale framework for the prediction of thrombus growth under flow on a spatially resolved surface presenting collagen and tissue factor (TF). The multiscale framework is composed of four coupled modules: a Neural Network (NN) that accounts for platelet signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. A reduced model of the coagulation cascade was embedded into the framework to account for TF-driven thrombin production. The 3D model was first tested against in vitro microfluidics experiments of whole blood perfusion with various antiplatelet agents targeting COX-1, P₂Y₁, or the IP receptor. The model was able to accurately capture the evolution and morphology of the growing thrombus. Certain problems of 2D models for thrombus growth (artifactual dendritic growth) were naturally avoided with realistic trajectories of platelets in 3D flow. The generalizability of the 3D multiscale solver enabled simulations of important clinical situations, such as cylindrical blood vessels and acute flow narrowing (stenosis). Enhanced platelet-platelet bonding at pathologically high shear rates (e.g., von Willebrand factor unfolding) was required for accurately describing thrombus growth in stenotic flows. Overall, the approach allows consideration of patient-specific platelet signaling and vascular geometry for the prediction of thrombotic episodes.     

A fluid dynamics study in a 50 cc pulsatile ventricular assist device: influence of heart rate variability

Although left ventricular assist devices (LVADs) have had success in supporting severe heart failure patients, thrombus formation within these devices still limits their long term use. Research has shown that thrombosis in the Penn State pulsatile LVAD, on a polyurethane blood sac, is largely a function of the underlying fluid mechanics and may be correlated to wall shear rates below 500 s(-1). Given the large range of heart rate and systolic durations employed, in vivo it is useful to study the fluid mechanics of pulsatile LVADs under these conditions. Particle image velocimetry (PIV) was used to capture planar flow in the pump body of a Penn State 50 cubic centimeters (cc) LVAD for heart rates of 75-150 bpm and respective systolic durations of 38-50%. Shear rates were calculated along the lower device wall with attention given to the uncertainty of the shear rate measurement as a function of pixel magnification. Spatial and temporal shear rate changes associated with data collection frequency were also investigated. The accuracy of the shear rate calculation improved by approximately 40% as the resolution increased from 35 to 12 μm/pixel. In addition, data collection in 10 ms, rather than 50 ms, intervals was found to be preferable. Increasing heart rate and systolic duration showed little change in wall shear rate patterns, with wall shear rate magnitude scaling by approximately the kinematic viscosity divided by the square of the average inlet velocity, which is essentially half the friction coefficient. Changes in in vivo operating conditions strongly influence wall shear rates within our device, and likely play a significant role in thrombus deposition. Refinement of PIV techniques at higher magnifications can be useful in moving towards better prediction of thrombosis in LVADs.     

Engineered bone culture in a perfusion bioreactor: a 2D computational study of stationary mass and momentum transport

Successful bone cell culture in large implants still is a challenge to biologists and requires a strict control of the physicochemical and mechanical environments. This study analyses from the transport phenomena viewpoint the limiting factors of a perfusion bioreactor for bone cell culture within fibrous and porous large implants (2.5 cm in length, a few cubic centimetres in volume, 250 μm in fibre diameter with approximately 60% porosity).

A two-dimensional mathematical model, based upon stationary mass and momentum transport in these implants is proposed and numerically solved. Cell oxygen consumption, in accordance theoretically with the Michaelis–Menten law, generates non linearity in the boundary conditions of the convection diffusion equation. Numerical solutions are obtained with a commercial code (Femlab® 3.1; Comsol AB, Stockholm, Sweden). Moreover, based on the simplification of transport equations, a simple formula is given for estimating the length of the oxygen penetration within the implant.

Results show that within a few hours of culture process and for a perfusion velocity of the order of 10^? 4 m s^? 1, the local oxygen concentration is everywhere sufficiently high to ensure a suitable cell metabolism. But shear stresses induced by the fluid flow with such a perfusion velocity are found to be locally too large (higher than 10^? 3 Pa). Suitable shear stresses are obtained by decreasing the velocity at the inlet to around 2 × 10^? 5 m s^? 1. But consequently hypoxic regions (low oxygen concentrations) appear at the downstream part of the implant.

Thus, it is suggested here that in the determination of the perfusion flow rate within a large implant, a compromise between oxygen supply and shear stress effects must be found in order to obtain a successful cell culture.