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The severity of congenital tracheal stenosis (CTS) is commonly evaluated based on the degree of stenosis. However, it does not always reflect the clinical respiratory status. We applied computational fluid dynamics (CFD) to the assessment of CTS. The aim of this study was to evaluate its validity.CFD models were constructed on 15 patients (12 preoperative models and 15 postoperative models) with CTS before and after surgery, using the computed tomographic data. Energy flux, needed to drive airflow, measured by CFD and the minimum cross-sectional area of the trachea (MCAT) were quantified and evaluated retrospectively.The energy flux correlated positively with the clinical respiratory status before and after surgery (rs = 0.611, p = 0.035 and rs = 0.591, p = 0.020, respectively). Although MCAT correlated negatively with the clinical respiratory status before surgery (rs = -0.578, p = 0.044), there was not significant correlation between the two after surgery (p = 0.572).The energy flux measured by CFD assessment reflects the respiratory status in CTS before and after surgery. CFD can be an additional objective and quantitative evaluation tool for CTS.

Despite numerous experimental observations regarding heart failure with preserved ejection fraction (HFpEF), which is characterized mainly by left ventricular hypertrophy and a left ventricular ejection fraction over 50%, myocardial dynamics under HFpEF have not yet been fully clarified, particularly regarding the relationship between myocardial strain distribution and myocardial work. To address this issue, we numerically investigated radial distribution of myocardial strain during a cardiac cycle with fixed internal volume at the end of the systolic and diastolic phases under different mechanical conditions, such as those involving myocardial thickness and elasticity of myocardial fibers. The myocardium was a modeled as a visco-hyperelastic continuous material. This model was taken into account that active contractile stress along the myocardial fiber direction depends on membrane potential change. Our numerical results showed that both radial and circumferential strains decreased as wall thickness increased, which reflected cardiac hypertrophy, but that myocardial work became larger than that observed with thin ventricular walls. Further, the change in left ventricular diastolic internal pressure caused circumferential strain, while fiber stiffness contributed to radial strain. Since peak circumferential strain was well estimated by the maximum difference between total internal and myocardial volumes, measuring the epicardial contraction rate should be helpful in understanding patients with HFpEF.

Congenital tracheal stenosis (CTS) with unilateral pulmonary agenesis (UPA) is characterized by the absence of one or both lungs in the hemithorax and is often associated with airway distortion. Some UPA patients have high mortality and morbidity even postoperatively, and it remains unclear whether surgery increases the energy flux needed to drive airflow. Here, we used pre- and postoperative patient-specific airway models to numerically investigate tracheal flow in patients with CTS, especially flow associated with right UPA (CTS-RUPA). Airflow was simulated with the large-eddy model, and energy flux was investigated to quantify airway performance and the contribution of surgical intervention. Although energy flux decreased postoperatively, clinical respiratory status did not improve. Standard surgical intervention for CTS, which expands the minimal cross-sectional area, decreased energy flux, i.e., improved airway performance. The simulation also included artificial airways with a straightened bend or reduced tracheal lumen roughness. The numerical results clearly showed interindividual differences in the percent reduction of energy flux caused by straightening the tracheal bend versus correcting tracheal lumen roughness. Although this study was limited to small sample size, these numerical results indicated that energy flux alone is insufficient to evaluate breathing performance in patients with CTS-RUPA but it can be used to estimate airway performance.

We present a numerical analysis of the lateral movement and equilibrium radial positions of red blood cells (RBCs) with major diameter 8 $\mathrm {\mu }$ m under a Newtonian fluid in a circular channel with 50 $\mathrm {\mu }$ m diameter. Each RBC, modelled as a biconcave capsule whose membrane satisfies strain-hardening characteristics, is simulated for different Reynolds numbers $Re$ and capillary numbers $Ca$ , the latter of which indicates the ratio of the fluid viscous force to the membrane elastic force. The effects of initial orientation angles and positions on the equilibrium radial position of an RBC centroid are also investigated. The numerical results show that depending on their initial orientations, RBCs have bistable flow modes, so-called rolling and tumbling motions. Most RBCs have a rolling motion. These stable modes are accompanied by different equilibrium radial positions, where tumbling RBCs are further away from the channel axis than rolling ones. The inertial migration of RBCs is achieved by alternating orientation angles, which are affected primarily by the initial orientation angles. Then the RBCs assume the aforementioned bistable modes during the migration, followed by further migration to the equilibrium radial position at much longer time periods. The power (or energy dissipation) associated with membrane deformations is introduced to quantify the state of membrane loads. The energy expenditures rely on stable flow modes, the equilibrium radial positions of RBC centroids, and the viscosity ratio between the internal and external fluids.

Takeishi N, Yamashita H, Omori T, Yokoyama N, Sugihara-Seki M. Axial and Nonaxial Migration of Red Blood Cells in a Microtube. Micromachines. 2021; 12(10):1162. https://doi.org/10.3390/mi12101162, Human red blood cells (RBCs) are subjected to high viscous shear stress, especially during microcirculation, resulting in stable deformed shapes such as parachute or slipper shape. Those unique deformed RBC shapes, accompanied with axial or nonaxial migration, cannot be fully described according to traditional knowledge about lateral movement of deformable spherical particles. Although several experimental and numerical studies have investigated RBC behavior in microchannels with similar diameters as RBCs, the detailed mechanical characteristics of RBC lateral movement—in particular, regarding the relationship between stable deformed shapes, equilibrium radial RBC position, and membrane load—has not yet been fully described. Thus, we numerically investigated the behavior of single RBCs with radii of 4 µm in a circular microchannel with diameters of 15 µm. Flow was assumed to be almost inertialess. The problem was characterized by the capillary number, which is the ratio between fluid viscous force and membrane elastic force. The power (or energy dissipation) associated with membrane deformations was introduced to quantify the state of membrane loads. Simulations were performed with different capillary numbers, viscosity ratios of the internal to external fluids of RBCs, and initial RBC centroid positions. Our numerical results demonstrated that axial or nonaxial migration of RBC depended on the stable deformed RBC shapes, and the equilibrium radial position of the RBC centroid correlated well with energy expenditure associated with membrane deformations.

Takeishi Naoki, Shigematsu Taiki, Enosaki Ryogo, Ishida Shunichi, Ii Satoshi and Wada Shigeo 2021Development of a mesoscopic framework spanning nanoscale protofibril dynamics to macro-scale fibrin clot formationJ. R. Soc. Interface.182021055420210554 http://doi.org/10.1098/rsif.2021.0554, Thrombi form a micro-scale fibrin network consisting of an interlinked structure of nanoscale protofibrils, resulting in haemostasis. It is theorized that the mechanical effect of the fibrin clot is caused by the polymeric protofibrils between crosslinks, or to their dynamics on a nanoscale order. Despite a number of studies, however, it is still unknown, how the nanoscale protofibril dynamics affect the formation of the macro-scale fibrin clot and thus its mechanical properties. A mesoscopic framework would be useful to tackle this multi-scale problem, but it has not yet been established. We thus propose a minimal mesoscopic model for protofibrils based on Brownian dynamics, and performed numerical simulations of protofibril aggregation. We also performed stretch tests of polymeric protofibrils to quantify the elasticity of fibrin clots. Our model results successfully captured the conformational properties of aggregated protofibrils, e.g., strain-hardening response. Furthermore, the results suggest that the bending stiffness of individual protofibrils increases to resist extension.

Cerebrospinal fluid (CSF) flow in the perivascular space (PVS), which surrounds the arteries in the brain, is of paramount importance in the removal of metabolic waste. Despite a number of experimental and numerical studies regarding CSF flow, the underlying mechanics of CSF flow are still debated, especially regarding whether an arterial pulsation can indeed produce net CSF flow velocity. Furthermore, the relationship between CSF flow and arterial wall pulsation has not been fully defined. To clarify these questions, we numerically investigated the CSF flow in the PVS in an axisymmetric channel with a pulsating boundary, where CSF is modeled as an incompressible, Newtonian viscous fluid in non-porous space. Our numerical results show that the net CSF flow velocity driven by the arterial pulsation is consistent with that of previous animal experiments. However, the peak oscillatory velocity is two orders of magnitude larger than the net velocity. Interestingly, the net CSF flow velocity collapses on the analytical solution derived from the lubrication theory in analogy with Taylor's swimming sheet model.

Takeishi, Naoki, Hiroaki Ito, Makoto Kaneko, and Shigeo Wada. 2019. "Deformation of a Red Blood Cell in a Narrow Rectangular Microchannel" Micromachines 10, no. 3: 199. https://doi.org/10.3390/mi10030199, The deformability of a red blood cell (RBC) is one of the most important biological parameters affecting blood flow, both in large arteries and in the microcirculation, and hence it can be used to quantify the cell state. Despite numerous studies on the mechanical properties of RBCs, including cell rigidity, much is still unknown about the relationship between deformability and the configuration of flowing cells, especially in a confined rectangular channel. Recent computer simulation techniques have successfully been used to investigate the detailed behavior of RBCs in a channel, but the dynamics of a translating RBC in a narrow rectangular microchannel have not yet been fully understood. In this study, we numerically investigated the behavior of RBCs flowing at different velocities in a narrow rectangular microchannel that mimicked a microfluidic device. The problem is characterized by the capillary number Ca, which is the ratio between the fluid viscous force and the membrane elastic force. We found that confined RBCs in a narrow rectangular microchannel maintained a nearly unchanged biconcave shape at low Ca, then assumed an asymmetrical slipper shape at moderate Ca, and finally attained a symmetrical parachute shape at high Ca. Once a RBC deformed into one of these shapes, it was maintained as the final stable configurations. Since the slipper shape was only found at moderate Ca, measuring configurations of flowing cells will be helpful to quantify the cell state.

Deformability of a red blood cell (RBC) is not only a required property for microcirculation but also an important indicator for pathological changes, which can be used for potential diagnoses of various diseases such as sepsis and vascular diseases. To date, various types of microfluidic platforms have been intensively developed for high-throughput measurements of RBC stiffness. This paper reports a novel strategy to measure the shear modulus of a RBC using on-chip feedback manipulation combined with a computational analysis of shape deformation. Here, we compared the shear deformations of a RBC flowing in a microchannel to that modeled in fluid-structure coupled simulation. The strain-velocity relationships for different values of shear modulus $G_{\mathrm{s}}$ obtained in both the experiments and simulation provide the direct correspondence of experimentally observable parameters (effective strain $\varepsilon$ , velocity $v$ ) to a defined material constant $G_{\mathrm{s}}$ .

A numerical analysis is presented of cell adhesion in capillaries whose diameter is comparable to or smaller than that of the cell. In contrast to a large number of previous efforts on leukocyte and tumor cell rolling, much is still unknown about cell motion in capillaries. The solid and fluid mechanics of a cell in flow was coupled with a slip bond model of ligand-receptor interactions. When the size of a capillary was reduced, the cell always transitioned to “bullet-like” motion, with a consequent decrease in the velocity of the cell. A state diagram was obtained for various values of capillary diameter and receptor density. We found that bullet motion enables firm adhesion of a cell to the capillary wall even for a weak ligand-receptor binding. We also quantified effects of various parameters, including the dissociation rate constant, the spring constant, and the reactive compliance on the characteristics of cell motion. Our results suggest that even under the interaction between P-selectin glycoprotein ligand-1 (PSGL-1) and P-selectin, which is mainly responsible for leukocyte rolling, a cell is able to show firm adhesion in a small capillary. These findings may help in understanding such phenomena as leukocyte plugging and cancer metastasis.

We present a numerical analysis of the rheology of a suspension of red blood cells (RBCs) in a wall-bounded shear flow. The flow is assumed as almost inertialess. The suspension of RBCs, modelled as biconcave capsules whose membrane follows the Skalak constitutive law, is simulated for a wide range of viscosity ratios between the cytoplasm and plasma,$\unicode[STIX]{x1D706}=0.1$–10, for volume fractions up to$\unicode[STIX]{x1D719}=0.41$and for different capillary numbers ($Ca$). Our numerical results show that an RBC at low$Ca$tends to orient to the shear plane and exhibits so-called rolling motion, a stable mode with higher intrinsic viscosity than the so-called tumbling motion. As$Ca$increases, the mode shifts from the rolling to the swinging motion. Hydrodynamic interactions (higher volume fraction) also allow RBCs to exhibit tumbling or swinging motions resulting in a drop of the intrinsic viscosity for dilute and semi-dilute suspensions. Because of this mode change, conventional ways of modelling the relative viscosity as a polynomial function of$\unicode[STIX]{x1D719}$cannot be simply applied in suspensions of RBCs at low volume fractions. The relative viscosity for high volume fractions, however, can be well described as a function of an effective volume fraction, defined by the volume of spheres of radius equal to the semi-middle axis of a deformed RBC. We find that the relative viscosity successfully collapses on a single nonlinear curve independently of$\unicode[STIX]{x1D706}$except for the case with$Ca\geqslant 0.4$, where the fit works only in the case of low/moderate volume fraction, and fails in the case of a fully dense suspension.

Tracheal flow in infants with congenital tracheal stenosis (CTS) was numerically investigated using subject-specific airway models before and after reconstructive surgery. We quantified tracheal flow based on airway resistance during inhalation, and compared it between controls and patients before and after surgery. The airway resistance in each subject was assessed using geometrical parameters of the trachea: the minimum cross-sectional area Amin, the minimum cross-sectional area normalized by the standard deviation of the cross-sectional area Amin/σA, the area ratio of the minimum and maximum cross-sectional area Amin/Amax, and ratio of the normalized standard deviation of cross-sectional area to the mean cross-sectional area σA/Amean. Our numerical results demonstrated that such geometrical parameters could be used to assess the severity of CTS. Since subjects can be more clearly categorized as controls and most preoperative patients in terms of the airway resistance, a simulation using subject-specific airway models can lead us to a precise understanding of tracheal flow, and also provide knowledge about therapeutic decision. Our numerical results also demonstrated that significant surgical expansion of cross-sectional area did not help recover tracheal flow because of expansion loss. These results will be helpful not only when making therapeutic decisions about surgery but also when assessing quality of life in postoperative patients. Graphical abstract.

Takeishi N., Imai Y., Yamaguchi T., et al. Flow of a circulating tumor cell and red blood cells in microvessels. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 92, 6, 063011. https://doi.org/10.1103/PhysRevE.92.063011., Quantifying the behavior of circulating tumor cells (CTCs) in the blood stream is of fundamental importance for understanding metastasis. Here, we investigate the flow mode and velocity of CTCs interacting with red blood cells (RBCs) in various sized microvessels. The flow of leukocytes in microvessels has been described previously; a leukocyte forms a train with RBCs in small microvessels and exhibits margination in large microvessels. Important differences in the physical properties of leukocytes and CTCs result from size. The dimensions of leukocytes are similar to those of RBCs, but CTCs are significantly larger. We investigate numerically the size effects on the flow mode and the cell velocity, and we identify similarities and differences between leukocytes and CTCs. We find that a transition from train formation to margination occurs when (R-a)/tR≈1, where R is the vessel radius, a is the cell radius, and tR is the thickness of RBCs, but that the motion of RBCs differs from the case of leukocytes. Our results also show that the velocities of CTCs and leukocytes are larger than the average blood velocity, but only CTCs move faster than RBCs for microvessels of R/a≈1.5-2.0. These findings are expected to be useful not only for understanding metastasis, but also for developing microfluidic devices.

Computational fluid dynamics (CFD) study of the behavior of red blood cells (RBCs) in flow provides us informative insight into the mechanics of blood flow in microvessels. However, the size of computational domain is limited due to computational expense. Recently, we proposed a graphics processing unit (GPU) computing method for patient-specific pulmonary airflow simulations (Miki et al., in press). In this study, we extend this method to micro-scale blood flow simulations, where a lattice Boltzmann method (LBM) of fluid mechanics is coupled with a finite element method (FEM) of membrane mechanics by an immersed boundary method (IBM). We also present validation and performance of our method for micro-scale blood flow simulations.Copyright © 2012 by ASME