Red Blood Cell Flow Research Articles

Numerical Simulation of Capillary Convection with Encapsulated Phase-Change Particles

This study presents preliminary numerical simulations of forced convection with encapsulated phase-change material (EPCM) particles suspended in water, flowing through a square cross-section duct with top and bottom isoflux surfaces. The EPCM particles fit snugly in the channel, mimicking the flow of red blood cells and plasma in alveolar capillaries. Results for particles of different diameters show the snug fitting to yield enhanced heat transfer. The numerical results also seem to indicate the existence of an optimum number of particles for maximum heat transfer coefficient, a result of the interplay of flow circulation and heat transfer competition as the number of particles is changed in the channel.

Abnormal blood flow in the sublingual microcirculation at high altitude.

We report the first direct observations of deranged microcirculatory blood flow at high altitude, using sidestream dark-field imaging. Images of the sublingual microcirculation were obtained from a group of 12 volunteers during a climbing expedition to Cho Oyu (8,201 m) in the Himalayas. Microcirculatory flow index (MFI) was calculated from the moving images of microcirculatory red blood cell flow, and comparison was made between the baseline and high altitude measurements. Peripheral oxygen saturation (SpO2) and Lake Louise scores (LLS) were recorded along with MFI. Our data demonstrate that there was a significant reduction in MFI from baseline to 4,900 m in small (less than 25 μm) and medium (26–50 μm) sized blood vessels (P = 0.025 and P = 0.046, respectively). There was no significant correlation between MFI and SpO2 or MFI and LLS. Disruption of blood flow within microcirculatory may explain persistent abnormal oxygen flux to tissues following the normalisation of systemic oxygen delivery that accompanies acclimatisation to high altitude.

Erythrocyte flow in choriocapillaris of normal and diabetic rats

The choriocapillaris is a unique capillary bed that provides nutrients to the retinal photoreceptors. It changes anatomically in diabetes, but the impact of these changes on blood flow is unknown. In this study hemodynamic parameters in individual choriocapillaris vessels were compared in normal and diabetic rats. Three groups were studied: normal buffer-injected control rats, streptozotocin (STZ)-injected mildly hyperglycemic (STZ-MH) rats, and STZ-injected diabetic (STZ-D) rats. 7–8 weeks after STZ injection, the rats were anesthetized, and epifluorescent, intravital microscopy was used to record the flow of fluorescent red blood cells (RBC) in the choriocapillaris. Diameter, RBC flux, and RBC velocity were measured in 153 capillary pathways in five control rats, 98 pathways in four STZ-MH rats, and 153 pathways in seven STZ-D rats. There was no difference in capillary diameter among the groups. RBC flux and velocity were lower in the STZ-injected rats compared to the controls ( p ≤ 0.023), which is similar to changes found in other capillary beds. RBC velocity and flux were significantly correlated in all three groups, but the correlations in the STZ-injected rats were much stronger than in the controls. This indicates a more heterogeneous distribution of RBCs at upstream arteriolar branch points in hyperglycemic rats, which could lead to a decrease in choriocapillaris hematocrit. These changes in the hyperglycemic choriocapillaris could contribute to impaired oxygen delivery to the photoreceptors in diabetic retina.

Statistical Dynamics of Flowing Red Blood Cells by Morphological Image Processing

Blood is a dense suspension of soft non-Brownian cells of unique importance. Physiological blood flow involves complex interactions of blood cells with each other and with the environment due to the combined effects of varying cell concentration, cell morphology, cell rheology, and confinement. We analyze these interactions using computational morphological image analysis and machine learning algorithms to quantify the non-equilibrium fluctuations of cellular velocities in a minimal, quasi-two-dimensional microfluidic setting that enables high-resolution spatio-temporal measurements of blood cell flow. In particular, we measure the effective hydrodynamic diffusivity of blood cells and analyze its relationship to macroscopic properties such as bulk flow velocity and density. We also use the effective suspension temperature to distinguish the flow of normal red blood cells and pathological sickled red blood cells and suggest that this temperature may help to characterize the propensity for stasis in Virchow's Triad of blood clotting and thrombosis.

Microcirculatory Imaging in Cardiac Anesthesia: Ketanserin Reduces Blood Pressure But Not Perfused Capillary Density

It has become possible to image the human microcirculation at the bedside using sidestream dark field (SDF) imaging. This may help the clinician when correlation between global and microvascular hemodynamics may not be straightforward. Ketanserin, a serotonin and alpha-1 adrenoceptor antagonist, is used in some countries to treat elevated blood pressure after extracorporeal circulation. This might hamper microcirculatory perfusion. Conversely, it is also conceivable that microcirculatory flow is maintained or improved as a result of flow redistribution. In order to introduce SDF imaging in cardiac anesthesia, the authors set out to directly observe the sublingual microcirculation in this setting. An observational study. A large teaching hospital. Mechanically ventilated patients with elevated arterial blood pressure immediately after extracorporeal circulation (ECC). An intravenous bolus of ketanserin, 0.15 mg/kg. Five minutes before and 10 minutes after ketanserin administration, global hemodynamic variables were recorded. In addition, the authors used SDF imaging to record video clips of the microcirculation. Analysis of these allowed for quantification of microvascular hemodynamics including determination of perfused vessel density (PVD) and microcirculatory flow index (MFI). After ketanserin administration, there was a significant reduction in systolic arterial blood pressure (129 +/- 9 to 100 +/- 15 mmHg, p = 0.0001). At the level of the microcirculation, the mean MFI did not change significantly for small (diameter <20 microm, 2.79 [interquartile range, 1.38-3] to 2.38 [1.88-2.75], p = 0.62) or large (diameter >20 microm, 2.83 [1.4-3] to 2.67 [0.35-2.84] p = 1.0) vessels. There was a significant increase in mean PVD for large vessels (1.23 +/- 0.63 to 1.70 +/- 79 mm(-1), p = 0.017) but not for small vessels (5.59 +/- 2.60 to 5.87 +/- 1.22 mm(-1), p = 0.72) where red blood cell flow was maintained. SDF imaging clearly showed a discrepancy between global and microvascular hemodynamics after the administration of ketanserin for elevated blood pressure after ECC. Ketanserin effectively lowers arterial blood pressure. However, capillary perfusion is maintained at a steady value. Both effects may be explained by an increase in shunting in the larger vessels of the microcirculation.

Theoretical Models of Microvascular Oxygen Transport to Tissue

To improve understanding of microvascular O(2) transport, theoretical modeling has been pursued for many years. The large number of studies in this area attests to the complexities (i.e., biochemical, structural, and hemodynamic) involved. This article focuses on theoretical studies from the last two decades and, in particular, on models of O(2) transport to tissue by discrete microvessels. A brief discussion of intravascular O(2) transport is first given, highlighting the physiological importance of intravascular resistance to blood-tissue O(2) transfer. This is followed by a description of the Krogh tissue cylinder model of O(2) transport by a single capillary, which is shown to remain relevant in modified forms that relax many of the original biophysical assumptions. However, there are many geometric and hemodynamic complexities that require the consideration of microvascular arrays and networks. Multivessel models are discussed that have shown the physiological importance of heterogeneities in vessel spacing, O(2) supply, red blood cell flow path, as well as interactions between capillaries and arterioles. These realistic models require sophisticated methods for solving the governing partial differential equations, and a range of solution techniques are described. Finally, the issue of experimental validation of microvascular O(2) delivery models is discussed, and new directions in O(2) transport modeling are outlined.

Frequency distribution function of red blood cell velocities in single capillaries of the rat cerebral cortex using intravital laser-scanning confocal microscopy with high- speed camera

Background: Brain metabolism depends largely on oxygen and therefore constant delivery of oxygen to the brain is more important than to any other organ. Previously we reported a newly developed method to automatically calculate red blood cell (RBC) flow and its temporal modulations at the layer 1 of the rat cerebral cortex. Objective: To examine a general tendency of frame-rate dependency of RBC velocities and heterogeneity of RBC movements in single capillaries identified by fluorescein isothiocyanate (FITC)-dextran staining. Methods: In urethane-anesthetized rats with a closed cranial window, intravenously administered FITC-labeled RBCs were traced at 125, 250 or 500 frames/s (fps) with a laser-scanning confocal fluorescence microscope and their velocities were automatically calculated with home-made software KEIO-IS2. Results: RBC velocities in single capillaries were not constant but variable, and were dependent on frame rate, with average values of 0.85 ± 0.43 mm/s at 125 fps, 1.34 ± 0.73 mm/s at 250 fps, and 2.05�1.59 mm/s at 500 fps. When all capillary RBCs were plotted against their velocities (frequency distribution function of RBC velocities), RBC velocities were clustered at around 1.0 mm/s, smearing at higher velocities up to 9.4 mm/s. High RBC velocity was only detected from frame analysis with high frame rates since such high-flow RBCs were uncounted at low frame rates. RBC velocities higher than 6.5 mm/s were statistically significantly outlined from the main population (p<0.01). Such a group of capillaries was considered to belong to thoroughfare channels, although their diameter was almost the same as that of ordinary ones. Conclusion: Extra-high flow capillaries are confirmed in the cerebral cortex and these may be thoroughfare channels or non-nutritional capillaries carrying 42 % of the blood in reserve.

In vivo real-time endocytoscopic visualization of blood flow in rectal microvasculature

Endocytoscopy (ECS) is a new technology that enables endoscopists to visualize gastrointestinal mucosa at the cellular level. This reported case demonstrates the ability to visualize real-time blood flow utilizing ECS. Methylene blue dye was sprayed onto normal rectal mucosa during a routine screening colonoscopy of an asymptomatic patient. High-magnification views of colonic mucosa revealed normal mucosal cellular structure and microvasculature with normal flow of red blood cells. Individual red blood cells were seen circulating through the arterioles. Epithelial colonocytes appeared to be organized in a hexagonal pattern around crypts with borders demarcated by microvasculature. ECS can provide high-magnification views of the gastrointestinal mucosa including microvasculature in real time. This establishes possibilities for future in vivo research in areas such as cancer biology, angiogenesis, and inflammatory bowel disease.

Static magnetic fields induce blood flow decreaseand platelet adherence in tumor microvessels

Red blood cell flow in capillaries is reduced during exposure to strong static magnetic fields (SMFs). Intratumoral microcirculation is characterized by tortuous microvessels with chaotic architecture and by irregular, sluggish blood flow with unstable rheology.It was the aim of this study to analyze SMF exposure effects on tumor microcirculation with regard to interactions of corpuscular blood components with tumor microvessel walls.In vivo fluorescence microscopy was performed in A-Mel-3 tumors growing in dorsal skinfold chamber preparations of Syrian Golden hamsters. SMFs with varying field strength (< 600 mT) were generated by changing the distance between a strong NdFeB rod magnet and the tissue region of interest.Short-time exposure above a magnetic flux density of about 150 mT resulted in a significant reduction of red blood cell velocity (vRBC) and segmental blood flow in tumor microvessels. At the maximum strength of 587 mT, a reversible reduction of vRBC (~ 40 %) and of functional vessel densitiy (~15 %) was observed.Prolongation of the exposure time from 1 min to up to 3 h resulted in comparable reductions. Microvessel diameters and leukocyte-endothelial cell interactions remained unaffected by SMF exposure. However, in contrast to tumor-free striated muscle controls, exposure at the maximum flux density induced a significant increase in platelet-endothelial cell adherence in a time-dependent manner that was reversible after reducing SMF strength.These reversible changes may have implications for functional measurements of tumor microcirculation by MRI and new therapeutic strategies using strong SMFs.

A Pilot Randomized Clinical Safety Study of Sonothrombolysis Augmentation With Ultrasound-Activated Perflutren-Lipid Microspheres for Acute Ischemic Stroke

Ultrasound transiently expands perflutren-lipid microspheres (muS), transmitting energy momentum to surrounding fluids. We report a pilot safety/feasibility study of ultrasound-activated muS with systemic tissue plasminogen activator (tPA). Stroke subjects treated within 3 hours had abnormal Thrombolysis in Brain Ischemia (TIBI) residual flow grades 0 to 3 before tPA on transcranial Doppler (TCD). Randomization included Controls (tPA+TCD) or Target (tPA+TCD+2.8 mL microS). The primary safety end point was symptomatic intracranial hemorrhage (sICH) with worsening by >or=4 NIHSS points within 72 hours. Fifteen subjects were randomized 3:1 to Target, n=12 or Control, n=3. After treatment, asymptomatic ICH occurred in 3 Target and 1 Control, and sICH was not seen in any study subject. muS reached MCA occlusions in all Target subjects at velocities higher than surrounding residual red blood cell flow: 39.8+/-11.3 vs 28.8+/-13.8 cm/s, P<0.001. In 75% of subjects, microS permeated to areas with no pretreatment residual flow, and in 83% residual flow velocity improved at a median of 30 minutes from start of microS infusion (range 30 s to 120 minutes) by a median of 17 cm/s (118% above pretreatment values). To provide perspective, current study recanalization rates were compared with the tPA control arm of the CLOTBUST trial: complete recanalization 50% versus 18%, partial 33% versus 33%, none 17% versus 49%, P=0.028. At 2 hours, sustained complete recanalization was 42% versus 13%, P=0.003, and NIHSS scores 0 to 3 were reached by 17% versus 8%, P=0.456. Perflutren microS reached and permeated beyond intracranial occlusions with no increase in sICH after systemic thrombolysis suggesting feasibility of further microS dose-escalation studies and development of drug delivery to tissues with compromised perfusion.

Counterpoint: There is not capillary recruitment in active skeletal muscle during exercise

The notion that a substantial proportion of capillaries do not contain moving red blood cells (RBCs) in muscle at rest but are “recruited,” i.e., begin flowing with RBCs during contractions, is one basis for our present understanding of blood-muscle exchange during exercise ([20][1], [28][2]).

Hyaluronidase treatment of the endothelial glycocalyx impairs adenosine mediated recruitment of coronary volume

It is hypothesized that coronary hyperemia by adenosine is accompanied by increased access for blood to the endothelial glycocalyx (EG) (VanTeeffelen, 2005). In the present study, the effect of glycocalyx degradation by hyaluronidase on adenosine mediated volume recruitment was assessed in goats. Labelled red blood cells (RBC) were infused as a bolus in the left main coronary artery in open‐chest anesthetized goats using a perfusion system. Blood samples were collected from the great cardiac vein every 0.5–1 second. Coronary red blood cell volume (Vcor) was calculated by multiplying mean RBC transit time with simultaneously measured coronary RBC flow. This measurement was done in control (con) and during adenosine (ado), before as well as after hyaluronidase treatment. Adenosine‐induced coronary volume recruitment (Vcor,ado/Vcor,con) and flow reserve (Qado/Qcon) were calculated; in control Vcor,ado/Vcor,con was 2.14 ± 0.7 and Qado/Qcon was 2.25 ± 0.8. After hyaluronidase Vcor,ado/Vcor,con reduced to 1.87 ± 0.8 (P&lt;0.05), while Qado/Qcon was not affected (2.22 ± 0.8, N.S. compared to before hyaluronidase). These data demonstrate that enzymatic degradation of the coronary EG impairs the ability of adenosine to recruit coronary vascular volume. It is concluded that recruitment of EG volume contributes to optimal matching of hyperemic coronary flow and volume. Supported by NHF grants 2005T037 and 2003B181.

Numerical Study on Flows of Red Blood Cells With Liposome-Encapsulated Hemoglobin at Microvascular Bifurcation

Flow analysis at microvascular bifurcation after partial replacement of red blood cell (RBC) with liposome-encapsulated hemoglobin (LEH) was performed using the lattice Boltzmann method. A two-dimensional symmetric Y bifurcation model with a parent vessel diameter of 20 mum and daughter branch diameters of 20 microm was considered, and the distributions of the RBC, LEH, and oxygen fluxes were calculated. When only RBCs flow into the daughter branches with unevenly distributed flows, plasma separation occurred and the RBC flow to the lower-flow branch was disproportionately decreased. On the other hand, when half of RBC are replaced by LEH, the biasing of RBC flow was enhanced whereas LEH flowed favorably into the lower-flow branch, because many LEH within the parent vessel are suspended in the plasma layer, where no RBCs exist. Consequently, the branched oxygen fluxes became nearly proportional to flows. These results indicate that LEH facilitates oxygen supply to branches that are inaccessible to RBCs.

Static Magnetic Fields Affect Capillary Flow of Red Blood Cells in Striated Skin Muscle

Blood flowing in microvessels is one possible site of action of static magnetic fields (SMFs). We evaluated SMF effects on capillary flow of red blood cells (RBCs) in unanesthetized hamsters, using a skinfold chamber technique for intravital fluorescence microscopy. By this approach, capillary RBC velocities (v(RBC)), capillary diameters (D), arteriolar diameters (D(art)), and functional vessel densities (FVD) were measured in striated skin muscle at different magnetic flux densities. Exposure above a threshold level of about 500 mT resulted in a significant (P < 0.001) reduction of v(RBC) in capillaries as compared to the baseline value. At the maximum field strength of 587 mT, v(RBC) was reduced by more than 40%. Flow reduction was reversible when the field strength was decreased below the threshold level. In contrast, mean values determined at different exposure levels for the parameters D, D(art), and FVD did not vary by more than 5%. Blood flow through capillary networks is affected by strong SMFs directed perpendicular to the vessels. Since the influence of SMFs on blood flow in microvessels directed parallel to the field as well as on collateral blood supply could not be studied, our findings should be carefully interpreted with respect to the setting of safety guidelines.

Computational study on effect of red blood cells on primary thrombus formation

The primary thrombus formation is a critical phenomenon both physiologically and pathologically. It has been seen that various mechanical factors are involved the regulation of primary thrombus formation through a series of physiological and biochemical processes, including blood flow and intercellular molecular bridges. However, it has not been fully understood how the existence of red blood cells contributes to the process of platelet thrombus formation. We computationally analyzed the motions of platelets in plasma layer above which red blood cells flow assuming a background simple shear flow of a shear rate of 1000 s - 1 using Stokesian dynamics. In the computation, fluid mechanical interactions between platelets and red blood cells were taken into account together with the binding forces via plasma proteins between two platelets and between a platelet and injured vessel wall. The process of the platelets aggregation was significantly dependent on whether red blood cells were present. When red blood cells were absent, the aggregate formed grew more vertically compared to the case with red blood cells. Conversely, when red blood cells were present, the aggregate spread more horizontally because the red blood cells constrained the vertical growth when the height of the aggregate reached the level of the red blood cells. Our results suggest that red blood cells mechanically play a significant role in primary thrombus formation, which accelerates the horizontal spread of the thrombus, and point out the necessity of considering the presence of red blood cells when investigating the mechanism of thrombus formation.

Blood banking–induced alteration of red blood cell flow properties

Blood banking procedures are associated with damage to red blood cell (RBC) membranes, which can impair their flow properties, namely, their deformability, aggregability, and adherence to endothelial cells (ECs) and thus possibly introducing a circulatory risk to recipients. This study was undertaken to comprehensively explore the effect of cold storage and gamma irradiation on RBC flow properties. RBC flow properties were monitored as a function of shear stress with a computerized cell flow properties analyzer. Because we had previously studied storage effect on RBC aggregability (Transfusion 1999;39:277-81), here we determined the storage effect on RBC adherence and deformability, by measuring them before (control) and during storage. Gamma irradiation effect on RBC aggregability, adherence, and deformability was determined before (control) and after irradiation. Cold storage significantly elevated the number of adherent RBCs and the strength of their interaction with ECs, and was marked by decreased RBC deformability as early as 2 weeks into the storage period. The elevation of RBC-EC interaction was well correlated with translocation of phosphatidylserine to the RBC surface. Gamma irradiation induced an immediate and marked increase in the number of rigid cells, but did not affect RBC adherence and aggregability. RBC flow properties appear to be especially sensitive to cold storage and gamma irradiation because they are impaired long before the expiration date. Because impaired RBC flow properties facilitate circulatory disorders, the potential circulatory risk of transfusion RBC with blood banking-impaired rheology should be considered.

Lattice-Boltzmann simulation of blood flow in digitized vessel networks

Efficient flow of red blood cells (RBCs) and white blood cells (WBCs) through the microcirculation is necessary for oxygen and nutrient delivery as well as immune cell function. Because blood is a dense particulate suspension, consisting of 40% RBCs by volume, it is difficult to analyze the physical mechanisms by which individual blood cells contribute to the bulk flow properties of blood. Both experimental and computational approaches are hindered by these non-Newtonian properties, and predicting macroscopic blood flow characteristics such as viscosity has historically been an empirical process. In order to examine the effect of the individual cells on macroscopic blood rheology, we developed a lattice-Boltzmann model that considers the blood as a suspension of particles in plasma, accounting explicitly for cell–cell and cell–wall interactions. Previous studies have concluded that the abundance of leukocyte rolling in postcapillary venules is due to the interactions between red blood cells and leukocytes as they enter postcapillary expansions. Similar fluid dynamics may be involved in the initiation of rolling at branch points, a phenomenon linked to atherosclerosis. The lattice-Boltzmann approach is used to analyze the interactions of red and white blood cells as they flow through vascular networks digitized from normal and tumor tissue. A major advantage of the lattice-Boltzmann method is the ability to simulate particulate flow dynamically and in any geometry. Using this approach, we can accurately determine RBC–WBC forces, particle trajectories, the pressure changes in each segment that accompany cellular traffic in the network, and the forces felt by the vessel wall at any location. In this technique, intravital imaging using vascular contrast agents produces the network outline that is fed to the lattice-Boltzmann model. This powerful and flexible model can be used to predict blood flow properties in any vessel geometry and with any blood composition.

Role of red blood cell flow behavior in hemodynamics and hemostasis

The primary role of red blood cells (RBCs) is to transport oxygen to the tissues, which is performed predominantly in the blood capillaries. However, RBCs have unique flow-affecting properties that play a key role in blood flow in all blood vessel types and sizes. While RBCs as oxygen carriers have been studied extensively, their hemodynamic function has been examined less comprehensively. This review aims to bridge this gap, focusing on the role of RBC flow properties in hemodynamics, hemostasis and thrombosis.

Red Blood Cell Stimulation of Platelet Nitric Oxide Production Indicated by Quantitative Monitoring of the Communication between Cells in the Bloodstream

ATP is a recognized stimulus of nitric oxide synthase and is released from red blood cells (RBCs) upon deformation. The objective of this work is to demonstrate that RBCs stimulate nitric oxide production in platelets by employing a continuous flow analysis system in which the stream contains both RBCs and platelets. Here, two drugs known to improve blood flow in vivo (pentoxyfilline and iloprost) are shown to increase both the release of RBC-derived ATP and the production of platelet-derived NO. A flow-based chemiluminescence assay (in vitro) was employed to quantitatively determine the amount of ATP released from erythrocytes subjected to flow-induced deformation. Prior to being subjected to flow, erythrocytes were incubated in the absence or presence of 4.8 microM pentoxyfilline or 80 nM iloprost. Erythrocytes obtained from rabbits (n=22) that were subjected to flow released 239 +/- 29 nM ATP. When treated with pentoxyfilline, the ATP released from the flowing RBCs increased to 450 +/- 94 nM ATP. An increase in RBC-derived ATP was also measured for iloprost-incubated RBCs in flow (362 +/- 45 nM ATP). Importantly, platelets that were loaded with diaminofluorofluorescein diacetate, an intracellular fluorescence probe for NO, exhibited increases in fluorescence intensity by 16% in the presence of RBCs treated with pentoxyfilline and a 10% increase when treated with iloprost. When the ATP release from the RBCs was inhibited with glybenclamide, the platelet fluorescence intensity decreased by 25 and 51% for RBCs incubated with pentoxyfilline and iloprost, respectively. In an experiment not involving the RBC, inhibition of the P2x receptor on the platelets (an ATP receptor) resulted in no increase in platelet NO production, suggesting that the NO production in the activated platelet is due to ATP.

Models of Flow-Induced Loading on Blood Cells in Laminar and Turbulent Flow, with Application to Cardiovascular Device Flow

Viscous shear stress and Reynolds stress are often used to predict hemolysis and thrombosis due to flow-induced stress on blood elements in cardiovascular devices. These macroscopic stresses are distinct from the true stress on an individual cell, which is determined by the local microscale flow field. In this paper the flow-induced stress on blood cells is calculated for laminar and turbulent flow, using simplified models for cells and for turbulent eddies. The model is applied to estimate shear stress on red blood cells in flow through a prosthetic heart valve, using the energy spectral density measured by Liu et al. [J. Biomech. Eng. 122:118-124, 2000]. Results show that in laminar flow, the maximum stress on a cell is approximately equal to the macroscopic viscous shear stress. In turbulent flow through a prosthetic heart valve, the estimated root mean square of flow-induced stress on a cell is at least an order of magnitude less than the Reynolds stress. The results support the hypothesis that smaller turbulent eddies cause higher stress on cells. However, the stress due to an eddy depends on the velocity scale of the eddy as well as its length scale. For the heart valve flow investigated, turbulence contributes to flow-induced stress on cells almost equally across a broad range of the frequency spectrum. The model suggests that Reynolds stress alone is not an adequate predictor of cell damage in turbulent flow, and highlights the importance of the energy spectral density.