Computational fluid dynamics assessment of congenital tracheal stenosis.

PURPOSE: 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. METHODS: 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. RESULTS: 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). CONCLUSIONS: 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.

Fluid dynamic assessment of positive end-expiratory pressure in a tracheostomy tube connector during respiration.

High-flow oxygen therapy using a tracheostomy tube is a promising clinical approach to reduce the work of breathing in tracheostomized patients. Positive end-expiratory pressure (PEEP) is usually applied during oxygen inflow to improve oxygenation by preventing end-expiratory lung collapse. However, much is still unknown about the geometrical effects of PEEP, especially regarding tracheostomy tube connectors (or adapters). Quantifying the degree of end-expiratory pressure (EEP) that takes patient-specific spirometry into account would be useful in this regard, but no such framework has been established yet. Thus, a platform to assess PEEP under respiration was developed, wherein three-dimensional simulation of airflow in a tracheostomy tube connector is coupled with a lumped lung model. The numerical model successfully reflected the magnitude of EEP measured experimentally using a lung phantom. Numerical simulations were further performed to quantify the effects of geometrical parameters on PEEP, such as inlet angles and rate of stenosis in the connector. Although sharp inlet angles increased the magnitude of EEP, they cannot be expected to achieve clinically reasonable PEEP. On the other hand, geometrical constriction in the connector can potentially result in PEEP as obtained with conventional nasal cannulae.

Editorial for the Special Issue on Advances in Microfluidics for Quantifying Cell Mechanics and Biotransport.

Microfluidics is a powerful tool to precisely control fluids as well as to manipulate suspended small particles in a micrometer-sized space [...].

Airway performance in infants with congenital tracheal stenosis associated with unilateral pulmonary agenesis: effect of tracheal shape on energy flux.

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.

Development of a mesoscopic framework spanning nanoscale protofibril dynamics to macro-scale fibrin clot formation.

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.

Axial and Nonaxial Migration of Red Blood Cells in a Microtube.

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.

Cerebrospinal fluid flow driven by arterial pulsations in axisymmetric perivascular spaces: Analogy with Taylor's swimming sheet.

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.

Effects of Left Ventricular Hypertrophy and Myocardial Stiffness on Myocardial Strain Under Preserved Ejection Fraction.

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.

Deformation of a Red Blood Cell in a Narrow Rectangular Microchannel.

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 C a , 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 C a , then assumed an asymmetrical slipper shape at moderate C a , and finally attained a symmetrical parachute shape at high C a . 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 C a , measuring configurations of flowing cells will be helpful to quantify the cell state.

Fluid dynamic assessment of tracheal flow in infants with congenital tracheal stenosis before and after surgery.

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.

Capture of microparticles by bolus flow of red blood cells in capillaries.

Previous studies have concluded that microparticles (MPs) can more effectively approach the microvessel wall than nanoparticles because of margination. In this study, however, we show that MPs are not marginated in capillaries where the vessel diameter is comparable to that of red blood cells (RBCs). We numerically investigated the behavior of MPs with a diameter of 1 µm in various microvessel sizes, including capillaries. In capillaries, the flow mode of RBCs shifted from multi-file flow to bolus (single-file) flow, and MPs were captured by the bolus flow of the RBCs instead of being marginated. Once MPs were captured, they rarely escaped from the vortex-like flow structures between RBCs. These capture events were enhanced when the hematocrit was decreased, and reduced when the shear rate was increased. Our results suggest that microparticles may be rather inefficient drug carriers when targeting capillaries because of capture events, but nanoparticles, which are more randomly distributed in capillaries, may be more effective carriers.

Cell adhesion during bullet motion in capillaries.

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.

Flow of a circulating tumor cell and red blood cells in microvessels.

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)/t(R)≈1, where R is the vessel radius, a is the cell radius, and t(R) 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.

Leukocyte margination at arteriole shear rate.

We numerically investigated margination of leukocytes at arteriole shear rate in straight circular channels with diameters ranging from 10 to 22 µm. Our results demonstrated that passing motion of RBCs effectively induces leukocyte margination not only in small channels but also in large channels. A longer time is needed for margination to occur in a larger channel, but once a leukocyte has marginated, passing motion of RBCs occurs continuously independent of the channel diameter, and leukocyte margination is sustained for a long duration. We also show that leukocytes rarely approach the wall surface to within a microvillus length at arteriole shear rate.