Bubble splitting in bifurcating tubes: a model study of cardiovascular gas emboli transport

Changes in lung mechanics and ventilation-perfusion match: comparison of pulmonary air- and thromboembolism in rats

BACKGROUND

Pulmonary air embolism (AE) and thromboembolism lead to severe ventilation-perfusion defects. The spatial distribution of pulmonary perfusion dysfunctions differs substantially in the two pulmonary embolism pathologies, and the effects on respiratory mechanics, gas exchange, and ventilation-perfusion match have not been compared within a study. Therefore, we compared changes in indices reflecting airway and respiratory tissue mechanics, gas exchange, and capnography when pulmonary embolism was induced by venous injection of air as a model of gas embolism or by clamping the main pulmonary artery to mimic severe thromboembolism.

METHODS

Anesthetized and mechanically ventilated rats (n = 9) were measured under baseline conditions after inducing pulmonary AE by injecting 0.1 mL air into the femoral vein and after occluding the left pulmonary artery (LPAO). Changes in mechanical parameters were assessed by forced oscillations to measure airway resistance, lung tissue damping, and elastance. The arterial partial pressures of oxygen (PaO2) and carbon dioxide (PaCO2) were determined by blood gas analyses. Gas exchange indices were also assessed by measuring end-tidal CO2 concentration (ETCO2), shape factors, and dead space parameters by volumetric capnography.

RESULTS

In the presence of a uniform decrease in ETCO2 in the two embolism models, marked elevations in the bronchial tone and compromised lung tissue mechanics were noted after LPAO, whereas AE did not affect lung mechanics. Conversely, only AE deteriorated PaO2, and PaCO2, while LPAO did not affect these outcomes. Neither AE nor LPAO caused changes in the anatomical or physiological dead space, while both embolism models resulted in elevated alveolar dead space indices incorporating intrapulmonary shunting.

CONCLUSIONS

Our findings indicate that severe focal hypocapnia following LPAO triggers bronchoconstriction redirecting airflow to well-perfused lung areas, thereby maintaining normal oxygenation, and the CO2 elimination ability of the lungs. However, hypocapnia in diffuse pulmonary perfusion after AE may not reach the threshold level to induce lung mechanical changes; thus, the compensatory mechanisms to match ventilation to perfusion are activated less effectively.

Quantification of shunt fraction using contrast ultrasound and indicator dilution in an in vitro model

Transthoracic saline contrast echocardiography is commonly used to assess intrathoracic shunt flow in vivo. Though the technique has many advantages (safe, simple, repeatable), the measurement technique lacks specificity, and the contrast agent has limited stability. This study sought to determine if the indicator dilution modeling technique could be applied to ultrasound contrast data to quantify shunt fraction and to determine if buoyant force has a significant effect on microbubble pathway determination at a "vascular" bifurcation. A model of the pulmonary circuit was perfused with blood at three distinct flow rates (low, medium and high) over shunt fractions ranging from ∼2-10 %. The buoyancy effect on contrast was quantified using a simplified in vitro model of a vascular bifurcation that had an upper and lower outflow tract where saline contrast formed from carbon monoxide (CO) gas passed through the bifurcation, was collected and quantified. The indicator dilution model was found to have a mean bias of - 3.2 % for the low flow stage, - 2.6 % for the medium flow stage and - 1.4 % for the high flow stage compared to volumetric measurements, suggesting agreement increases with increasing flow rate. Investigations of the buoyant effects revealed that at lower flow rates, contrast bubbles that encounter a bifurcation will favor the upper outflow tract over the lower. However, this effect is reduced by increasing the flow rate two-fold. These data identify that application of indicator dilution theory to contrast ultrasound data and the pathway ultrasound contrast travels in a network of tubules is flow dependent.

Investigation of the different parameters contributing to bubble sticking inside physiological bifurcations

Gas embolotherapy (GE) is a developing medical method which can be utilized either as an autonomous therapeutic method to treat vascularized solid tumors, or it can be combined with other medical procedures-such as high-intensity focused ultrasound-to improve their efficiency. This paper is dedicated to investigating the different parameters which influence bubble lodging inside human vasculature via 2D-modeling of bubble dynamics in arteries' and arterioles' bifurcations which are potential sticking positions. Values used in the simulations are in accordance with the non-dimensional physiological numbers. It is found out that inlet pressure plays a decisive role in bubble lodging; the lower the value, the higher the possibility of bubble sticking. On the other hand, gravity has a counteracting effect on bubble lodging in arteries, but not on arterioles. The initial length of the bubble is not a determining factor in sticking behavior, even though it affects the flow rate behavior. Surface tension, another critical factor, has a semi-linear impact on bubble resisting power; lowering the surface tension will reduce bubble resistance to the flow, diminishing the possibility of bubble lodging. Finally, it is shown that lower values for the static contact angle impose higher resistance to the flow.

The steady motion of microbubbles in bifurcating airways: Role of shear-thinning and surface tension

Mucous fluid is non-Newtonian secretions in the lower lung airways that accumulates when the alveolar-capillary membrane ruptures during acute respiratory distress syndrome. The mucus fluid has, therefore, different types of non-Newtonian properties like shear-thinning, viscoelasticity, and non-zero yield stress. In this paper, we numerically solved the steady Stokes equations along with arbitrary Eulerian-Lagrangian moving mesh techniques to study the microbubble propagation in a two-dimensional asymmetric bifurcating airway filled with non-Newtonian fluid where the fluid has shear-thinning behavior described by the power-law model. Numerical results show that both shear-thinning and surface tension characterized by the behavior index (n) and Capillary number (Ca), respectively, had a significant impact on microbubble flow patterns and the magnitude of the pressure gradient. At low values of both n and Ca, the microbubble leaves a thin film-thickness with the airway wall while a large and sharp peak of the pressure gradient near the thin bubble tip. Interestingly, increasing both n and Ca, leads to an increase in film thickness and a decrease in the pressure gradient magnitude in both the daughter airway walls. It is observed the magnitude of the pressure gradient is more sensitive to Ca compared to n. We concluded that shear-thinning and surface tension not only significantly impact the patterns of microbubble propagation but also the hydrodynamic stress magnitudes at the airway wall.

Minimally invasive gas embolization using acoustic droplet vaporization in a rodent model of hepatocellular carcinoma

Hepatocellular carcinoma is the third leading cause of cancer-related deaths worldwide. Many patients are not eligible for curative therapies, such as surgical resection of the tumor or a liver transplant. Transarterial embolization is one therapy clinically used in these cases; however, this requires a long procedure and careful placement of an intraarterial catheter. Gas embolization has been proposed as a fast, easily administered, more spatially selective, and less invasive alternative. Here, we demonstrate the feasibility and efficacy of using acoustic droplet vaporization to noninvasively generate gas emboli within vasculature. Intravital microscopy experiments were performed using the rat cremaster muscle to visually observe the formation of occlusions. Large gas emboli were produced within the vasculature in the rat cremaster, effectively occluding blood flow. Following these experiments, the therapeutic efficacy of gas embolization was investigated in an ectopic xenograft model of hepatocellular carcinoma in mice. The treatment group exhibited a significantly lower final tumor volume (ANOVA, p = 0.008) and growth rate than control groups - tumor growth was completely halted. Additionally, treated tumors exhibited significant necrosis as determined by histological analysis. To our knowledge, this study is the first to demonstrate the therapeutic efficacy of gas embolotherapy in a tumor model.

Bubble Dislodgment in a Capillary Network with Microscopic Multichannels and Multibifurcation Features

Bubble lodgment in a complex capillary network is a common issue in many industrial and biological processes. Research work reported in the literature only investigated bubble dislodgment in single channels and did not consider the effect of network complexity on the dislodgment. This paper focuses on the pressure required to dislodge single bubbles from a microscopic capillary network and investigates the factors affecting the dislodging pressure to facilitate the precise control of bubble flows in porous media. A capillary network with multibifurcation and a smoothly changed diameter is designed to closely mimic the structure of the physiological vascular networks. Over 600 bubble dislodgment experiments have been conducted to understand the effect of the network structure, channel dimensions, and bubble length on the dislodging pressure. The results indicate that the network structure is a dominant factor affecting the dislodging pressure that increases with the increase in network complexity. The effect of bubble length on the dislodging pressure depends on the bubble length. When the bubble length is less than a certain value, which is around 2 mm in this study, the dislodging pressure increases significantly with the decrease of bubble length. When the bubble length is larger than 2 mm, the dislodging pressure is independent of the bubble length. A model has been proposed to explain the bubble dislodgment in complex capillary networks. The impact of the network structure on the bubble dislodging pressure is characterized by a parameter c _j. The model indicates that the dislodging pressure is the function of bubble length, channel dimension, and network structure. The analysis of model parameters NB _j and MA _j shows that parameter c _j, rather than the channel size, dominates the dislodging pressure for bubbles with a length greater than 2 mm, and the increase rate of the dislodging pressure is significantly affected by both channel size and parameter c _j.

Bubble-bubble pinch-off in symmetric and asymmetric microfluidic expansion channels for ordered foam generation

By incorporating the techniques of geometrically mediated splitting and bubble-bubble breakup, the present work offers a novel microfluidic foam generation system via production of segregated, mono- or bidisperse bubbles at capacities exceeding 10 000 bubbles per second. Bubble-bubble pinch-off is precise at high capillary numbers (Ca > 0.065), generating monodisperse or bidisperse daughter bubbles for a symmetric or an asymmetric expansion respectively. Bi- or tridisperse foam is produced as pinch-off perfectly alternates such that the system contains twice the number of fragmented bubbles as intact bubbles. A relationship between the upstream bubble extension and the capillary number demarcates the different regimes of pinch-off defined with respect to frequency and precision: non-splitting, irregular, polydisperse, and monodisperse (or bidisperse for an asymmetric expansion). For tridisperse foam generation via a fixed asymmetric expansion geometry, the wall bubble confinement can be tuned to adjust the pinch-off accuracy in order to access a spectrum of fragmented bubble size ratios. The simplicity in operating and characterizing our system will enable studies on dynamic bubble interactions and ordered, wet foam applications.

Numerical study on the impulsive growth of a gaseous plug inside a cylindrical vein with compliant coating

Introduction: Employing of gaseous plugs inside a vein for preventing of blood flow to the damaged or cancerous tissues has been known as a gas embolism in the medicine. In this research, a numerical investigation has been carried out on the delivery of the liquid drug DDFP, encapsulated in the microlipidcoated spheres (MLCSs), to target the human vein for construction of the gaseous plug inside the veins.

Methods: The encapsulated liquid drug DDFP were delivered to the vein by injection of an emulsion. Releasing of the liquid drug DDFP results in an explosive growth of a gaseous plug inside the vein. The targeted vein was served as a rigid cylinder with a compliant coating. The boundary integral equation method has been employed for the numerical simulation of the hydrodynamic behavior of the gaseous plug inside the vein.

Results: Numerical results showed that in the case of a rigid cylinder vein with an internal compliant coating, the maximum volume of the gaseous plug was smaller than the case of just a rigid cylinder vein. Furthermore, its elapsed time from the instant of bubble generation to the instant when the bubble reaches its maximum volume was shorter. Numerical results also showed that the compliant coating on the internal wall of the rigid cylindrical vein had a tendency of reducing the impact of the explosive growth of the gaseous plug.

Conclusion: This numerical research showed that the compliant coating on the internal wall of the rigid cylindrical vein had the tendency of reducing the impact of the impulsive growth of the gaseous plug. Therefore, in the case of having severed arteriosclerosis, treatment of the cancerous or damaged tissues by use of the gaseous embolism must be done very carefully in order to prevent the hazardous effects of the gaseous plug’s impulsive growth.

Dynamics of partially obstructed breakup of bubbles in microfluidic Y-junctions

For revealing the dynamics of partially obstructed breakup of bubbles in microfluidic Y-junctions, the combination of dimensionless power-law and geometric model was applied to study the effects of capillary number, bubble length, and channel angle on the bubble rupture process. In the squeezing process, the gas-liquid interface curve follows the parabolic model. For the evolution of the bubble neck during breakup, the increase of the bubble length, the channel angle, and the capillary number leads to the decrease of the focus distance α. The chord m increases with the increase of the capillary number and the decrease of the bubble length, and it would reach the maximum value when the channel angle is 90°. In the fast pinch-off stage during bubble breakup, the bubble's neck curve no longer conforms to the parabolic model so the focus and chord no longer exist. For the evolution of the bubble head during breakup, the value of γ approaches 1 with the increase of the capillary number and the bubble length, and with the close of the channel angle to 90°. It is found that the quadrilateral model can be applied for the partially obstructed rupture of bubbles in the symmetrical microfluidic Y-junction.

Engineered Airway Models to Study Liquid Plug Splitting at Bifurcations: Effects of Orientation and Airway Size

Delivery of biological fluids, such as surfactant solutions, into lungs is a major strategy to treat respiratory disorders including respiratory distress syndrome that is caused by insufficient or dysfunctional natural lung surfactant. The instilled solution forms liquid plugs in lung airways. The plugs propagate downstream in airways by inspired air or ventilation, continuously split at airway bifurcations to smaller daughter plugs, simultaneously lose mass from their trailing menisci, and eventually rupture. A uniform distribution of the instilled biofluid in lung airways is expected to increase the treatments success. The uniformity of distribution of instilled liquid in the lungs greatly depends on the splitting of liquid plugs between daughter airways, especially in the first few generations from which airways of different lobes of lungs emerge. To mechanistically understand this process, we developed a bioengineering approach to computationally design three-dimensional bifurcating airway models using morphometric data of human lungs, fabricate physical models, and examine dynamics of liquid plug splitting. We found that orientation of bifurcating airways has a major effect on the splitting of liquid plugs between daughter airways. Changing the relative gravitational orientation of daughter tubes with respect to the horizontal plane caused a more asymmetric splitting of liquid plugs. Increasing the propagation speed of plugs partially counteracted this effect. Using airway models of smaller dimensions reduced the asymmetry of plug splitting. This work provides a step toward developing delivery strategies for uniform distribution of therapeutic fluids in the lungs.

Bubble and macroaggregate methods differ in detection of blood flow through intrapulmonary arteriovenous anastomoses in upright and supine hypoxia in humans

Blood flow through intrapulmonary arteriovenous anastomoses (Q̇_IPAVA) increases in healthy humans breathing hypoxic gas and is potentially dependent on body position. Previous work in subjects breathing room air has shown an effect of body position when Q̇_IPAVA is detected with transthoracic saline contrast echocardiography (TTSCE). However, the potential effect of body position on Q̇_IPAVA has not been investigated when subjects are breathing hypoxic gas or with a technique capable of quantifying Q̇_IPAVA. Thus the purpose of this study was to quantify the effect of body position on Q̇_IPAVA when breathing normoxic and hypoxic gas at rest. We studied Q̇_IPAVA with TTSCE and quantified Q̇_IPAVA with filtered technetium-99m-labeled macroaggregates of albumin (^99mTc-MAA) in seven healthy men breathing normoxic and hypoxic (12% O₂) gas at rest while supine and upright. On the basis of previous work using TTSCE, we hypothesized that the quantified Q̇_IPAVA would be greatest with hypoxia in the supine position. We found that Q̇_IPAVA quantified with ^99mTc-MAA significantly increased while subjects breathed hypoxic gas in both supine and upright body positions (ΔQ̇_IPAVA = 0.7 ± 0.4 vs. 2.5 ± 1.1% of cardiac output, respectively). Q̇_IPAVA detected with TTSCE increased from normoxia in supine hypoxia but not in upright hypoxia (median hypoxia bubble score of 2 vs. 0, respectively). Surprisingly, Q̇_IPAVA magnitude was greatest in upright hypoxia, when Q̇_IPAVA was undetectable with TTSCE. These findings suggest that the relationship between TTSCE and ^99mTc-MAA is more complex than previously appreciated, perhaps because of the different physical properties of bubbles and MAA in solution. NEW & NOTEWORTHY Using saline contrast bubbles and radiolabeled macroaggregrates (MAA), we detected and quantified, respectively, hypoxia-induced blood flow through intrapulmonary arteriovenous anastomoses (Q̇_IPAVA) in supine and upright body positions in healthy men. Upright hypoxia resulted in the largest magnitude of Q̇_IPAVA quantified with MAA but the lowest Q̇_IPAVA detected with saline contrast bubbles. These surprising results suggest that the differences in physical properties between saline contrast bubbles and MAA in blood may affect their behavior in vivo.

Small-bubble transport and splitting dynamics in a symmetric bifurcation

Simulations of small bubbles traveling through symmetric bifurcations are conducted to garner information pertinent to gas embolotherapy, a potential cancer treatment. Gas embolotherapy procedures use intra-arterial bubbles to occlude tumor blood supply. As bubbles pass through bifurcations in the blood stream nonhomogeneous splitting and undesirable bioeffects may occur. To aid development of gas embolotherapy techniques, a volume of fluid method is used to model the splitting process of gas bubbles passing through artery and arteriole bifurcations. The model reproduces the variety of splitting behaviors observed experimentally, including the bubble reversal phenomenon. Splitting homogeneity and maximum shear stress along the vessel walls is predicted over a variety of physical parameters. Small bubbles, having initial length less than twice the vessel diameter, were found unlikely to split in the presence of gravitational asymmetry. Maximum shear stresses were found to decrease exponentially with increasing Reynolds number. Vortex-induced shearing near the bifurcation is identified as a possible mechanism for endothelial cell damage.

Computational analysis of microbubble flows in bifurcating airways: role of gravity, inertia, and surface tension

Although mechanical ventilation is a life-saving therapy for patients with severe lung disorders, the microbubble flows generated during ventilation generate hydrodynamic stresses, including pressure and shear stress gradients, which damage the pulmonary epithelium. In this study, we used computational fluid dynamics to investigate how gravity, inertia, and surface tension influence both microbubble flow patterns in bifurcating airways and the magnitude/distribution of hydrodynamic stresses on the airway wall. Direct interface tracking and finite element techniques were used to simulate bubble propagation in a two-dimensional (2D) liquid-filled bifurcating airway. Computational solutions of the full incompressible Navier-Stokes equation were used to investigate how inertia, gravity, and surface tension forces as characterized by the Reynolds (Re), Bond (Bo), and Capillary (Ca) numbers influence pressure and shear stress gradients at the airway wall. Gravity had a significant impact on flow patterns and hydrodynamic stress magnitudes where Bo > 1 led to dramatic changes in bubble shape and increased pressure and shear stress gradients in the upper daughter airway. Interestingly, increased pressure gradients near the bifurcation point (i.e., carina) were only elevated during asymmetric bubble splitting. Although changes in pressure gradient magnitudes were generally more sensitive to Ca, under large Re conditions, both Re and Ca significantly altered the pressure gradient magnitude. We conclude that inertia, gravity, and surface tension can all have a significant impact on microbubble flow patterns and hydrodynamic stresses in bifurcating airways.

Numerical Simulation of Bubble Transport in a Bifurcating Microchannel: A Preliminary Study

In this paper, we present the computational fluid dynamics (CFD) simulations of bubble transport in a first generation bifurcating microchannel. In the present study, the human arteriole is modeled as a two-dimensional (2D) rectangular bifurcating microchannel. The microchannel is filled with blood and a single perfluorocarbon (PFC) bubble is introduced in the parent channel. The simulations are carried out to identify the lodging and dislodging pressures for two nondimensional bubble sizes, Ld (ratio of the dimensional bubble length to the parent tube diameter), that is for Ld = 1 and Ld = 2. Subsequently, the bubble transport and splitting behavior due to the presence of symmetry and asymmetry in the daughter channels of the microchannel is studied for these bubble sizes. The splitting behavior of the bubble under the effect of gravity is also assessed and reported here. For the symmetric bifurcation model, the splitting ratio (SR) (ratio of bubble volume in bottom daughter channel to bubble volume in top daughter channel), of the bubble was found to be 1. For the asymmetric model, the splitting ratio was found to be less than 1. The loss in the bubble volume in the asymmetric model was attributed to surface tension effects and the resistance offered by the flow, which led to the bubble sticking and sliding along the walls of the channel. With the increase in roll angle, Φ (angle which the plane makes with the horizontal to study the effects of gravity), there was a decline in the splitting ratio.

Phase-change contrast agents for imaging and therapy

Phase-change contrast agents (PCCAs) for ultrasound-based applications have resulted in novel ways of approaching diagnostic and therapeutic techniques beyond what is possible with microbubble contrast agents and liquid emulsions. When subjected to sufficient pressures delivered by an ultrasound transducer, stabilized droplets undergo a phase-transition to the gaseous state and a volumetric expansion occurs. This phenomenon, termed acoustic droplet vaporization, has been proposed as a means to address a number of in vivo applications at the microscale and nanoscale. In this review, the history of PCCAs, physical mechanisms involved, and proposed applications are discussed with a summary of studies demonstrated in vivo. Factors that influence the design of PCCAs are discussed, as well as the need for future studies to characterize potential bioeffects for administration in humans and optimization of ultrasound parameters.

Microbubble transport through a bifurcating vessel network with pulsatile flow

Motivated by two-phase microfluidics and by the clinical applications of air embolism and a developmental gas embolotherapy technique, experimental and theoretical models of microbubble transport in pulsatile flow are presented. The one-dimensional time-dependent theoretical model is developed from an unsteady Bernoulli equation that has been modified to include viscous and unsteady effects. Results of both experiments and theory show that roll angle (the angle the plane of the bifurcating network makes with the horizontal) is an important contributor to bubble splitting ratio at each bifurcation within the bifurcating network. When compared to corresponding constant flow, pulsatile flow was shown to produce insignificant changes to the overall splitting ratio of the bubble despite the order one Womersley numbers, suggesting that bubble splitting through the vasculature could be modeled adequately with a more modest constant flow model. However, bubble lodging was affected by the flow pulsatility, and the effects of pulsatile flow were evident in the dependence of splitting ratio of bubble length. The ability of bubbles to remain lodged after reaching a steady state in the bifurcations is promising for the effectiveness of gas embolotherapy to occlude blood flow to tumors, and indicates the importance of understanding where lodging will occur in air embolism. The ability to accurately predict the bubble dynamics in unsteady flow within a bifurcating network is demonstrated and suggests the potential for bubbles in microfluidics devices to encode information in both steady and unsteady aspects of their dynamics.

Pulmonary transit of agitated contrast is associated with enhanced pulmonary vascular reserve and right ventricular function during exercise

Pulmonary transit of agitated contrast (PTAC) occurs to variable extents during exercise. We tested the hypothesis that the onset of PTAC signifies flow through larger-caliber vessels, resulting in improved pulmonary vascular reserve during exercise. Forty athletes and fifteen nonathletes performed maximal exercise with continuous echocardiographic Doppler measures [cardiac output (CO), pulmonary artery systolic pressure (PASP), and myocardial velocities] and invasive blood pressure (BP). Arterial gases and B-type natriuretic peptide (BNP) were measured at baseline and peak exercise. Pulmonary vascular resistance (PVR) was determined as the regression of PASP/CO and was compared according to athletic and PTAC status. At peak exercise, athletes had greater CO (16.0 ± 2.9 vs. 12.4 ± 3.2 l/min, P < 0.001) and higher PASP (60.8 ± 12.6 vs. 47.0 ± 6.5 mmHg, P < 0.001), but PVR was similar to nonathletes ( P = 0.71). High PTAC (defined by contrast filling of the left ventricle) occurred in a similar proportion of athletes and nonathletes (18/40 vs. 10/15, P = 0.35) and was associated with higher peak-exercise CO (16.1 ± 3.4 vs. 13.9 ± 2.9 l/min, P = 0.010), lower PASP (52.3 ± 9.8 vs. 62.6 ± 13.7 mmHg, P = 0.003), and 37% lower PVR ( P < 0.0001) relative to low PTAC. Right ventricular (RV) myocardial velocities increased more and BNP increased less in high vs. low PTAC subjects. On multivariate analysis, maximal oxygen consumption (V̇o2max) ( P = 0.009) and maximal exercise output ( P = 0.049) were greater in high PTAC subjects. An exercise-induced decrease in arterial oxygen saturation (98.0 ± 0.4 vs. 96.7 ± 1.4%, P < 0.0001) was not influenced by PTAC status ( P = 0.96). Increased PTAC during exercise is a marker of pulmonary vascular reserve reflected by greater flow, reduced PVR, and enhanced RV function.

Initial investigation of acoustic droplet vaporization for occlusion in canine kidney

Acoustic droplet vaporization (ADV) shows promise for spatially and temporally targeted tissue occlusion. In this study, substantial tissue occlusion was achieved in operatively exposed and transcutaneous canine kidneys by generating ADV gas bubbles in the renal arteries or segmental arteries. Fifteen canines were anesthetized, among which 10 underwent laparotomy to externalize the left kidney and five were undisturbed for transcutaneous ADV. The microbubbles were generated by phase conversion of perfluoropentane droplets encapsulated in albumin or lipid shells in the blood. A 3.5-MHz single-element therapy transducer was aligned with an imaging array in a water tank with direct access to the renal artery or a segmental artery. In vivo color flow and spectral Doppler imaging were used to identify the target arteries. Tone bursts of 1 kHz pulse repetition frequency with 0.25% duty cycle vaporized the droplets during bolus passage. Both intracardiac (IC) and intravenous (IV) injections repeatedly produced ADV in chosen arteries in externalized kidneys, as seen by B-mode imaging. Concurrent with this in two cases was the detection by pulse-wave Doppler of blood flow reversal, along with a narrowing of the waveform. Localized cortex occlusion was achieved with 87% regional flow reduction in one case using IC injections. Vaporization from IV injections resulted in a substantial echogenicity increase with an average half-life of 8 min per droplet dose. Gas bubbles sufficient to produce some shadowing were generated by transcutaneous vaporization of intrarenal artery or IV-administered droplets, with a tissue path up to 5.5 cm.

A boundary element model of the transport of a semi-infinite bubble through a microvessel bifurcation

Motivated by a developmental gas embolotherapy technique for selective occlusion of blood flow to tumors, we examined the transport of a pressure-driven semi-infinite bubble through a liquid-filled bifurcating channel. Homogeneity of bubble splitting as the bubble passes through a vessel bifurcation affects the degree to which the vascular network near the tumor can be uniformly occluded. The homogeneity of bubble splitting was found to increase with bubble driving pressure and to decrease with increased bifurcation angle. Viscous losses at the bifurcation were observed to affect the bubble speed significantly. The potential for oscillating bubble interfaces to induce flow recirculation and impart high stresses on the vessel endothelium was also observed.

Droplet motion in microfluidic networks: Hydrodynamic interactions and pressure-drop measurements

We present experimental, numerical, and theoretical studies of droplet flows in hydrodynamic networks. Using both millifluidic and microfluidic devices, we study the partitioning of monodisperse droplets in an asymmetric loop. In both cases, we show that droplet traffic results from the hydrodynamic feedback due to the presence of droplets in the outlet channels. We develop a recently-introduced phenomenological model [W. Engl, Phys. Rev. Lett. 95, 208304 (2005)] and successfully confront its predictions to our experimental results. This approach offers a simple way to measure the excess hydrodynamic resistance of a channel filled with droplets. We discuss the traffic behavior and the variations in the corresponding hydrodynamic resistance length L_{d} and of the droplet mobility beta , as a function of droplet interdistance and confinement for channels having circular or rectangular cross sections.

A Boundary Element Model of Microbubble Sticking and Sliding in the Microcirculation

A pressure driven 2-D channel flow at very low Reynolds numbers (Stokes flow) with a bubble sticking and sliding along one of the walls is studied computationally using the boundary element method (BEM). The moving three phase contact lines are modeled using a Tanner law wherein the contact line speed is linearly proportional to the deviation of the contact angle from its equilibrium value. Results are presented with and without the effect of contact angle hysteresis. Including contact angle hysteresis allows us to predict the stick-slide behavior of bubbles, which in turn affects the long term evolution and dynamics of the bubbles. It is shown that the initial rapid contraction or expansion of the bubbles to achieve local equilibrium with the surrounding pressure field results in cusps and bulges in the wall normal stress profiles. The wall shear stress also increases (with opposite signs upstream and downstream of the bubble) as the fluid rushes in or out of the channel inlet and outlet. In the long term, bubbles slowly expand as they slide along the channel wall. Contact lines are found to correspond to peaks in the wall normal and shear stress profiles at all times. The effectiveness of bubbles in occluding flow through the channel is also examined.

Microbubble expansion in a flexible tube

We have utilized a computational model of the expansion of a microbubble in a liquid-filled flexible tube to investigate the potential for acoustic vaporization of perfluorocarbon droplets to damage blood vessels during a novel gas embolotherapy technique for the potential treatment of tumors. This model uses a fixed grid, multi-domain, interface tracking, direct numerical simulation method that treats all interfaces and boundaries as sharp discontinuities for high accuracy. In the current work, we examined effects of initial bubble size on the flows and wall stresses that result from droplet vaporization. The remaining dimensionless parameters that govern the system response (Reynolds, Weber, and Strouhal numbers, initial bubble pressure, and wall stiffness and tension) were selected to model an arteriole. The results for a flexible tube are significantly different from those for a rigid tube. Two major flow regimes occur due to the combined effect of bubble and tube deformation: in flow at the tube ends and out flow near the bubble surface. The flexibility of the tube largely dissipates the extreme pressure that develops in the rigid tube model. Both the magnitude and the overall expansion time of the rapidly changing pressure are greatly reduced in the flexible tube. Smaller initial bubble diameters, relative to the vessel diameter, result in lower wall stresses. This study indicates that wall flexibility can significantly influence the wall stresses that result from acoustic vaporization of intravascular perfluorocarbon droplets, and suggests that acoustic activation of droplets in larger, more flexible vessels may be less likely to damage or rupture vessels than activation in smaller and stiffer vessels.