Numerical simulation of the vascular structure dependence of blood flow in the kidney.

A numerical simulation was performed to clarify renal blood flow determination by the vascular structures. Large and small vessels were modeled as symmetric and asymmetric branching vessels, respectively, with simple geometries to parameterize the vascular structures. Modeling individual vessels as straight pipes, Murray's law was used to determine the vessel diameters. Blood flow in the vascular structure was calculated by network analysis based on Hagen-Poiseuille's law. Blood flow simulations for a vascular network segment demonstrated that blood flow rate and pressure vary within the same-generation vessels because of an asymmetric vessel branch while they generally tend to decrease with vessel diameter; thus, the standard deviation of flow rate relative to the mean (relative standard deviation [RSD]) increased from 0.4 to 1.0 when the number of the daughter vessels increased from 3 to 10. Blood flow simulations for an entire vascular network of a kidney showed that the vessel number and branching style, rather than Strahler order, are major parameters in successfully reproducing renal blood flow measured in published experiments. The entire vascular network could generate variation in the physiological flow rate in afferent arterioles at 0.2-0.38 in RSD, which is at least compatible with 0.16 by diameter variation within the same-generation vessels.

Blood cell distribution in small and large vessels: Effects of wall and rotating motion of red blood cells.

A two-dimensional computer simulation of blood flow between two parallel plates as the tube was performed to understand the distribution of red blood cells (RBCs) and platelets (PLTs) according to the blood vessel size. The motion of the blood cells (BCs) was directly calculated using the particle method. The tube diameter and hematocrit were set as 20-500 µm and 0-0.4, respectively. In simulations with tank-treading (TT) RBCs under the planar Poiseuille flow, RBCs moved from the tube wall to form a cell-free layer (CFL). Then, the PLTs moved into the CFL, and the RBCs concentrated around the tube center, excluding the PLTs. By comparing the BC distribution between the Couette and Poiseuille flows, the range of the wall effect was estimated to be ≤50-100 µm at the hematocrit of 0.4. Tumbling (TB) RBCs uniformly distributed inside the tube, while forming rouleaux-like aggregates on the wall at 0.4 in hematocrit; at hematocrit ≤0.3, the TB RBCs tended to be excluded from the tube center as known to the tubular pinch effect. The mechanical interaction among the RBCs and tube wall facilitated TT motion even if the apparent shear rate was so small that an RBC in a dilute suspension would exhibit TB motion. These results indicate that the TT motion of RBCs combined with the wall effect plays a major role in forming CFL and avoiding aggregation of BCs and that TB motion helps BCs to distribute uniformly in large vessels where the shear rate is relatively low.

Contractile actin belt and mesh structures provide the opposite dependence of epithelial stiffness on the spontaneous curvature of constituent cells.

Actomyosin generates contractile forces within cells, which have a crucial role in determining the macroscopic mechanical properties of epithelial tissues. Importantly, actin cytoskeleton, which propagates actomyosin contractile forces, forms several characteristic structures in a 3D intracellular space, such as a circumferential actin belt lining adherence junctions and an actin mesh beneath the apical membrane. However, little is known about how epithelial mechanical property depends on the intracellular contractile structures. We performed computational simulations using a 3D vertex model, and demonstrated the longitudinal tensile test of an epithelial tube, whose inside and outside are defined as the apical and basal surfaces, respectively. As a result, these subcellular structures provide the contrary dependence of epithelial stiffness and fracture force on the spontaneous curvature of constituent cells; the epithelial stiffness increases with increasing the spontaneous curvature in the case of belt, meanwhile it decreases in the case of mesh. This qualitative difference emerges from the different anisotropic deformability of apical cell surfaces; while belt preserves isotropic apical cell shapes, mesh does not. Moreover, the difference in the anisotropic deformability determines the frequency of cell rearrangements, which in turn effectively decrease the tube stiffness. These results illustrate the importance of the intracellular contractile structures, which may be regulated to optimize mechanical functions of individual epithelial tissues.

Dynamics of Actin Stress Fibers and Focal Adhesions during Slow Migration in Swiss 3T3 Fibroblasts: Intracellular Mechanism of Cell Turning.

To understand the mechanism regulating the spontaneous change in polarity that leads to cell turning, we quantitatively analyzed the dynamics of focal adhesions (FAs) coupling with the self-assembling actin cytoskeletal structure in Swiss 3T3 fibroblasts. Fluorescent images were acquired from cells expressing GFP-actin and RFP-zyxin by laser confocal microscopy. On the basis of the maximum area, duration, and relocation distance of FAs extracted from the RFP-zyxin images, the cells could be divided into 3 regions: the front region, intermediate lateral region, and rear region. In the intermediate lateral region, FAs appeared close to the leading edge and were stabilized gradually as its area increased. Simultaneously, bundled actin stress fibers (SFs) were observed vertically from the positions of these FAs, and they connected to the other SFs parallel to the leading edge. Finally, these connecting SFs fused to form a single SF with matured FAs at both ends. This change in SF organization with cell retraction in the first cycle of migration followed by a newly formed protrusion in the next cycle is assumed to lead to cell turning in migrating Swiss 3T3 fibroblasts.

Effects of arterial blood flow on walls of the abdominal aorta: distributions of wall shear stress and oscillatory shear index determined by phase-contrast magnetic resonance imaging.

Although abdominal aortic aneurysms (AAAs) occur mostly inferior to the renal artery, the mechanism of the development of AAA in relation to its specific location is not yet clearly understood. The objective of this study was to evaluate the hypothesis that even healthy volunteers may manifest specific flow characteristics of blood flow and alter wall shear or oscillatory shear stress in the areas where AAAs commonly develop. Eight healthy male volunteers were enrolled in this prospective study, aged from 24 to 27. Phase-contrast magnetic resonance imaging (MRI) was performed with electrocardiographic triggering. Flow-sensitive four-dimensional MR imaging of the abdominal aorta, with three-directional velocity encoding, including simple morphological image acquisition, was performed. Information on specific locations on the aortic wall was applied to the flow encodes to calculate wall shear stress (WSS) and oscillatory shear index (OSI). While time-framed WSS showed the highest peak of 1.14 ± 0.25 Pa in the juxtaposition of the renal artery, the WSS plateaued to 0.61 Pa at the anterior wall of the abdominal aorta. The OSI peaked distal to the renal arteries at the posterior wall of the abdominal aorta of 0.249 ± 0.148, and was constantly elevated in the whole abdominal aorta at more than 0.14. All subjects were found to have elevated OSI in regions where AAAs commonly occur. These findings indicate that areas of constant peaked oscillatory shear stress in the infra-renal aorta may be one of the factors that lead to morphological changes over time, even in healthy individuals.

Total Cavopulmonary Connection is Superior to Atriopulmonary Connection Fontan in Preventing Thrombus Formation: Computer Simulation of Flow-Related Blood Coagulation.

The classical Fontan route, namely the atriopulmonary connection (APC), continues to be associated with a risk of thrombus formation in the atrium. A conversion to a total cavopulmonary connection (TCPC) from the APC can ameliorate hemodynamics for the failed Fontan; however, the impact of these surgical operations on thrombus formation remains elusive. This study elucidates the underlying mechanism of thrombus formation in the Fontan route by using a two-dimensional computer hemodynamic simulation based on a simple blood coagulation rule. Hemodynamics in the Fontan route was simulated with Navier-Stokes equations. The blood coagulation and the hemodynamics were combined using a particle method. Three models were created: APC with a square atrium, APC with a round atrium, and TCPC. To examine the effects of the venous blood flow velocity, the velocity at rest and during exercise (0.5 and 1.0 W/kg) was measured. The total area of the thrombi increased over time. The APC square model showed the highest incidence for thrombus formation, followed by the APC round, whereas no thrombus was formed in the TCPC model. Slower blood flow at rest was associated with a higher incidence of thrombus formation. The TCPC was superior to the classical APC in terms of preventing thrombus formation, due to significant blood flow stagnation in the atrium of the APC. Thus, local hemodynamic behavior associated with the complex channel geometry plays a major role in thrombus formation in the Fontan route.

Applications of computational models to better understand microvascular remodelling: a focus on biomechanical integration across scales.

Microvascular network remodelling is a common denominator for multiple pathologies and involves both angiogenesis, defined as the sprouting of new capillaries, and network patterning associated with the organization and connectivity of existing vessels. Much of what we know about microvascular remodelling at the network, cellular and molecular scales has been derived from reductionist biological experiments, yet what happens when the experiments provide incomplete (or only qualitative) information? This review will emphasize the value of applying computational approaches to advance our understanding of the underlying mechanisms and effects of microvascular remodelling. Examples of individual computational models applied to each of the scales will highlight the potential of answering specific questions that cannot be answered using typical biological experimentation alone. Looking into the future, we will also identify the needs and challenges associated with integrating computational models across scales.

Elastic behavior of a red blood cell with the membrane's nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion.

Direct numerical simulations of the mechanics of a single red blood cell (RBC) were performed by considering the nonuniform natural state of the elastic membrane. A RBC was modeled as an incompressible viscous fluid encapsulated by an elastic membrane. The in-plane shear and area dilatation deformations of the membrane were modeled by Skalak constitutive equation, while out-of-plane bending deformation was formulated by the spring model. The natural state of the membrane with respect to in-plane shear deformation was modeled as a sphere ([Formula: see text]), biconcave disk shape ([Formula: see text]) and their intermediate shapes ([Formula: see text]) with the nonuniformity parameter [Formula: see text], while the natural state with respect to out-of-plane bending deformation was modeled as a flat plane. According to the numerical simulations, at an experimentally measured in-plane shear modulus of [Formula: see text] and an out-of-plane bending rigidity of [Formula: see text] of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for [Formula: see text] and cupped otherwise; (ii) the experimentally measured fluid shear stress at the transition between tumbling and tank-treading motions under shear flow was reproduced for [Formula: see text]; (iii) the elongation deformation of the RBC during tank-treading motion from the simulation was consistent with that from in vitro experiments, irrespective of the [Formula: see text] value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for [Formula: see text]. The condition [Formula: see text] precludes a biconcave discoid shape at equilibrium (i); however, it gives appropriate fluid shear stress at the motion transition under shear flow (ii), suggesting that a combined effect of [Formula: see text] and the natural state with respect to out-of-plane bending deformation is necessary for understanding details of the RBC mechanics at equilibrium. Our numerical results demonstrate that moderate nonuniformity in a membrane's natural state with respect to in-plane shear deformation plays a key role in RBC mechanics.

Blood flow dynamic improvement with aneurysm repair detected by a patient-specific model of multiple aortic aneurysms.

Aortic aneurysms may cause the turbulence of blood flow and result in the energy loss of the blood flow, while grafting of the dilated aorta may ameliorate these hemodynamic disturbances, contributing to the alleviation of the energy efficiency of blood flow delivery. However, evaluating of the energy efficiency of blood flow in an aortic aneurysm has been technically difficult to estimate and not comprehensively understood yet. We devised a multiscale computational biomechanical model, introducing novel flow indices, to investigate a single male patient with multiple aortic aneurysms. Preoperative levels of wall shear stress and oscillatory shear index (OSI) were elevated but declined after staged grafting procedures: OSI decreased from 0.280 to 0.257 (first operation) and 0.221 (second operation). Graftings may strategically counter the loss of efficient blood delivery to improve hemodynamics of the aorta. The energy efficiency of blood flow also improved postoperatively. Novel indices of pulsatile pressure index (PPI) and pulsatile energy loss index (PELI) were evaluated to characterize and quantify energy loss of pulsatile blood flow. Mean PPI decreased from 0.445 to 0.423 (first operation) and 0.359 (second operation), respectively; while the preoperative PELI of 0.986 dropped to 0.820 and 0.831. Graftings contributed not only to ameliorate wall shear stress or oscillatory shear index but also to improve efficient blood flow. This patient-specific modeling will help in analyzing the mechanism of aortic aneurysm formation and may play an important role in quantifying the energy efficiency or loss in blood delivery.

Three-dimensional modulation of cortical plasticity during pseudopodial protrusion of mouse leukocytes.

Leukocytes can rapidly migrate virtually within any substrate found in the body at speeds up to 100 times faster than mesenchymal cells that remain firmly attached to a substrate even when migrating. To understand the flexible migration strategy utilized by leukocytes, we experimentally investigated the three-dimensional modulation of cortical plasticity during the formation of pseudopodial protrusions by mouse leukocytes isolated from blood. The surfaces of viable leukocytes were discretely labeled with fluorescent beads that were covalently conjugated with concanavalin A receptors. The movements of these fluorescent beads were different at the rear, central, and front surfaces. The beads initially present on the rear and central dorsal surfaces of the cell body flowed linearly toward the rear peripheral surface concomitant with a significant collapse of the cell body in the dorsal-ventral direction. In contrast, those beads initially on the front surface moved into a newly formed pseudopodium and exhibited rapid, random movements within this pseudopodium. Bead movements at the front surface were hypothesized to have resulted from rupture of the actin cytoskeleton and detachment of the plasma membrane from the actin cytoskeletal cortex, which allowed leukocytes to migrate while being minimally constrained by a substrate.

Computational study on effect of stenosis on primary thrombus formation.

The purpose of this study was to evaluate the effects of stenosis geometry on primary thrombogenesis with respect to the dynamics of the blood flow. A two-dimensional computer simulation was carried out to simulate the formation of a primary thrombus under blood flow in two geometrically different blood vessels: one straight and the other stenosed. In the simulation, blood was modeled by particles that have characteristics of plasma and of platelets. Plasma and platelet flow was analyzed using the Moving Particle Semi-implicit (MPS) method, while the motion of adhered and aggregated platelets was expressed by mechanical spring forces. With these models, platelet motion in the flowing blood and platelet aggregation and adhesion were successfully coupled with viscous blood flow. The results of the simulation demonstrated that the presence of a stenosis induced changes in blood flow and thereby altered the formation, growth, and destruction of a thrombus. In particular, whereas in the absence of stenosis, the thrombus evenly covered the injured site, in the presence of a stenosis, thrombus formation was skewed to the downstream side. The number of platelets that adhered to the injured site increased earlier as the stenosis became more severe. These results suggest that dynamic changes in blood flow due to the presence of a stenosis affect primary thrombogenesis.

Effect of the natural state of an elastic cellular membrane on tank-treading and tumbling motions of a single red blood cell.

A two-dimensional computer simulation model was proposed for tank-treading and tumbling motions of an elastic biconcave red blood cell (RBC) under steady shear flow. The RBC model consisted of an outer cellular membrane and an inner fluid; the membrane's elastic properties were modeled by springs for stretch/compression and bending to consider the membrane's natural state in a practical manner. Membrane deformation was coupled with incompressible viscous flow of the inner and outer fluids of the RBC using a particle method. The proposed simulation model was capable of reproducing tank-treading and tumbling motions of an RBC along with rotational oscillation, which is the transition between the two motions. In simulations using the same initial RBC shape with different natural states of the RBC membrane, only tank-treading motion was exhibited in the case of a uniform natural state of the membrane, and a nonuniform natural state was necessary to generate the rotational oscillation and tumbling motion. Simulation results corresponded to published data from experimental and computational studies. In the range of simulation parameters considered, the relative membrane elastic force versus fluid viscous force was approximately 1 at the transition when the natural state nonuniformity was taken into account in estimating the membrane elastic force. A combination of natural state nonuniformity and elastic spring constant determined that change in the RBC deformation at the transition is that from a large compressive deformation to no deformation, such as rigid body.

Computer simulation of trabecular remodeling in human proximal femur using large-scale voxel FE models: Approach to understanding Wolff's law.

Ever since Julius Wolff proposed the law of bone transformation in the 19th century, it has been widely known that the trabecular structure of cancellous bone adapts functionally to the loading environment. To understand the mechanism of Wolff's law, a three-dimensional (3D) computer simulation of trabecular structural changes due to surface remodeling was performed for a human proximal femur. A large-scale voxel finite element model was constructed to simulate the structural changes of individual trabeculae over the entire cancellous region. As a simple remodeling model that considers bone cellular activities regulated by the local mechanical environment, nonuniformity of local stress was assumed to drive the trabecular surface remodeling to seek a uniform stress state. Simulation results demonstrated that cell-scale ( approximately 10microm) remodeling in response to mechanical stimulation created complex 3D trabecular structures of the entire bone-scale ( approximately 10cm), as illustrated in the reference of Wolff. The bone remodeling reproduced the characteristic anisotropic structure in the coronal cross section and the isotropic structures in other cross sections. The principal values and axes of a structure characterized by fabric ellipsoids corresponded to those of the apparent stress of the structure. The proposed large-scale computer simulation indicates that in a complex mechanical environment of a hierarchical bone structure of over 10(4) length scale (from approximately 10microm to approximately 10cm), a simple remodeling at the cellular/trabecular levels creates a highly complex and functional trabecular structure, as characterized by bone density and orientation.

Hemodynamic analysis of microcirculation in malaria infection.

Malaria-infected red blood cells (IRBCs) show various changes in mechanical properties. IRBCs lose their deformability and develop properties of cytoadherence and rosetting. To clarify how these changes advance microvascular occlusion, we need qualitative and quantitative information on hemodynamics in malaria infection, including the interaction among IRBCs, healthy RBCs, and endothelial cells. We developed a numerical model of blood flow with IRBCs based on conservation laws of fluid dynamics. The deformability and adhesive property of IRBCs were simply modeled using springs governed by Hook's law. Our model could express the basic behavior of IRBCs, including the rolling motion due to cytoadhesive interaction with endothelial cells and complex interaction with healthy RBCs. We confirmed that these types of interactions significantly increase the flow resistance, particularly when knobs develop.

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.

Simulation of platelet adhesion and aggregation regulated by fibrinogen and von Willebrand factor.

We propose a method to analyze platelet adhesion and aggregation computationally, taking into account the distinct properties of two plasma proteins, von Willebrand factor (vWF) and fibrinogen (Fbg). In this method, the hydrodynamic interactions between platelet particles under simple shear flow were simulated using Stokesian dynamics based on the additivity of velocities. The binding force between particles mediated by vWF and Fbg was modeled using the Voigt model. Two Voigt models with different properties were introduced to consider the distinct behaviors of vWF and Fbg. Our results qualitatively agreed with the general observation of a previous in-vitro experiment, thus demonstrating that the significant development of thrombus formation in height requires not only vWF, but also Fbg. This agreement of simulation and experimental results qualitatively validates our model and suggests that consideration of the distinct roles of vWF and Fbg is essential to investigate the physiological and pathophysiological mechanisms of thrombus formation using a computational approach.

In vitro blood flow in a rectangular PDMS microchannel: experimental observations using a confocal micro-PIV system.

Progress in microfabricated technologies has attracted the attention of researchers in several areas, including microcirculation. Microfluidic devices are expected to provide powerful tools not only to better understand the biophysical behavior of blood flow in microvessels, but also for disease diagnosis. Such microfluidic devices for biomedical applications must be compatible with state-of-the-art flow measuring techniques, such as confocal microparticle image velocimetry (PIV). This confocal system has the ability to not only quantify flow patterns inside microchannels with high spatial and temporal resolution, but can also be used to obtain velocity measurements for several optically sectioned images along the depth of the microchannel. In this study, we investigated the ability to obtain velocity measurements using physiological saline (PS) and in vitro blood in a rectangular polydimethysiloxane (PDMS) microchannel (300 microm wide, 45 microm deep) using a confocal micro-PIV system. Applying this combination, measurements of trace particles seeded in the flow were performed for both fluids at a constant flow rate (Re = 0.02). Velocity profiles were acquired by successive measurements at different depth positions to obtain three-dimensional (3-D) information on the behavior of both fluid flows. Generally, the velocity profiles were found to be markedly blunt in the central region, mainly due to the low aspect ratio (h/w = 0.15) of the rectangular microchannel. Predictions using a theoretical model for the rectangular microchannel corresponded quite well with the experimental micro-PIV results for the PS fluid. However, for the in vitro blood with 20% hematocrit, small fluctuations were found in the velocity profiles. The present study clearly shows that confocal micro-PIV can be effectively integrated with a PDMS microchannel and used to obtain blood velocity profiles along the full depth of the microchannel because of its unique 3-D optical sectioning ability. Advantages and disadvantages of PDMS microchannels over glass capillaries are also discussed.

In vitro confocal micro-PIV measurements of blood flow in a square microchannel: the effect of the haematocrit on instantaneous velocity profiles.

A confocal microparticle image velocimetry (micro-PIV) system was used to obtain detailed information on the velocity profiles for the flow of pure water (PW) and in vitro blood (haematocrit up to 17%) in a 100-microm-square microchannel. All the measurements were made in the middle plane of the microchannel at a constant flow rate and low Reynolds number (Re=0.025). The averaged ensemble velocity profiles were found to be markedly parabolic for all the working fluids studied. When comparing the instantaneous velocity profiles of the three fluids, our results indicated that the profile shape depended on the haematocrit. Our confocal micro-PIV measurements demonstrate that the root mean square (RMS) values increase with the haematocrit implying that it is important to consider the information provided by the instantaneous velocity fields, even at low Re. The present study also examines the potential effect of the RBCs on the accuracy of the instantaneous velocity measurements.

Differentiation of stenosed and aneurysmal arteries by pulse wave propagation analysis based on a fluid-solid interaction computational method.

Pulse Wave Velocity (PWV) is recognized by clinicians as an index of the mechanical properties of human blood vessels. However, the measured PWV of real human blood vessels will not always obey the Moens-Korteweg equation, which describes the PWV in ideal elastic tubes. Waveform analysis has been studied as an alternative diagnosis for cardiovascular disease, and reflected waves that occur in the diseased region may be a key for the estimation of the severity of disease. In this study, we modeled stenosed and aneurysmal arteries in a three-dimensional coupled fluid-solid interaction scheme, and analyzed the pulse wave propagation in order to assess the reflected waves that occurred in the diseased region. A commercial code (Radioss, MECALOG, France) was used to solve the fluid-solid interactions. A steady flow with Reynolds number 1000 was imposed at the inlet of the artery as the basic flow, then a single rectangular pulse with Reynolds number 4000 was imposed upon the basic flow to produce a propagating wave. We showed that the reflected waves from the stenosis and the aneurysm are different in their phase, and the wavelength of the reflected waves from the aneurysm is affected by the aneurysm length.

Particle method for computer simulation of red blood cell motion in blood flow.

A particle method for the computer simulation of blood flow was proposed to analyze the motion of a deformable red blood cell (RBC) in flowing blood plasma. The RBC and plasma were discretized by particles that have the characteristics of an elastic membrane and a viscous fluid, respectively. The membrane particles were connected to their neighboring membrane particles by springs, and the motion of the particles was determined on the basis of the minimum energy principle. The incompressible flow of plasma that was expressed by the motion of the fluid particles was determined by the moving-particle semi-implicit (MPS) method. The RBC motion and plasma flow were weakly coupled. The two-dimensional simulation of blood flow between parallel plates demonstrated the capability of the proposed method to express the blood flow phenomena observed in experiments, such as the downstream motion of the RBC and the deformation of the RBC into a parachute shape.