Proper Orthogonal Decomposition Analysis Reveals Cell Migration Directionality During Wound Healing.

A proper orthogonal decomposition (POD) order reduction method was implemented to reduce the full high dimensional dynamical system associated with a wound healing cell migration assay to a low-dimensional approximation that identified the prevailing cell trajectories. The POD analysis generated POD modes that were representative of the prevalent cell trajectories. The shapes of the POD modes depended on the location of the cells with respect to the wound and exposure to disturbed (DF) or undisturbed (UF) fluid flow where the net flow was in the antegrade direction with a retrograde component or fully antegrade, respectively. For DF and UF, the POD modes of the downstream cells identified trajectories that moved upstream against the flow, while upstream POD modes exhibited sideways cell migrations. In the absence of flow, no major shape differences were observed in the POD modes on either side of the wound. The POD modes also served to reconstruct the cell migration of individual cells. With as few as three modes, the predominant cell migration trajectories were reconstructed, while the level of accuracy increased with the inclusion of more POD modes. The POD order reduction method successfully identified the predominant cell migratory trajectories under static and varying pulsatile fluid flow conditions serving as a first step in the development of artificial intelligence models of cell migration in disease and development.

Passive double pendulum in the wake of a cylinder forced to rotate emulates a cyclic human walking gait.

The goal of this work is to present a method based on fluid-structure interactions to enforce a desired trajectory on a passive double pendulum. In our experiments, the passive double pendulum represents human thigh and shank segments, and the interaction between the fluid and the structure comes from a hydrofoil attached to the double pendulum and interacting with the vortices that are shed from a cylinder placed upstream. When a cylinder is placed in flow, vortices are shed in the wake of the cylinder. When the cylinder is forced to rotate periodically, the frequency of the vortices that are shed in its wake can be controlled by controlling the frequency of cylinder's rotation. These vortices exert periodic forces on any structure placed in the wake of this cylinder. In our system, we place a double pendulum fitted with a hydrofoil at its distal end in the wake of a rotating cylinder. The vortices exert periodic forces on this hydrofoil which then forces the double pendulum to oscillate. We control the cylinder to rotate periodically, and measure the displacement of the double pendulum. By comparing the joint positions of the double pendulum with those of human hip, knee and ankle joint positions during walking, we show how the system is able to generate a human walking gait cycle on the double pendulum only using the interactions between the vortices and the hydrofoil.

Flow inside a bone scaffold: Visualization using 3D phase contrast MRI and comparison with numerical simulations.

We report on results of experimental flow measurements inside a bone scaffold model, subjected to a uniform incoming flow (applied perfusion). Understanding the flow behavior inside a tissue engineered scaffold is essential for mechanistic studies of mechanobiology, particularly flow-sensitive bone cells. Nearly all existing studies that quantify interstitial flow inside engineered bone scaffolds have been based on numerical results, in part due to the difficulties associated with quantitative measurements and visualization of flow inside large, opaque bone or bone mimics. Thus, an experimental platform to complement and validate in silico studies is needed. Therefore, we developed a flow visualization method using Phase-Contrast Magnetic Resonance Imaging (PC-MRI) to measure flow velocities within a 3D-printed microCT-based rendering of a bone scaffold. We designed and built a non-magnetic recirculating water tunnel to apply uniform perfusion to the 3D-printed model and we measured flow distribution within the scaffold and compared these experimental results with CFD results. Both magnitude and distribution of flow velocities observed at different slices of the scaffold were in quantitative agreement numerically and experimentally. This experimental approach can be used to both validate numerical studies and provide insight into the flow behavior inside tissue-engineered scaffolds for a range of applications, including fundamental mechanobiology of healthy cells, and in the context of diseases, such as cancer.

Multiphysics simulation of a compression-perfusion combined bioreactor to predict the mechanical microenvironment during bone metastatic breast cancer loading experiments.

Incurable breast cancer bone metastasis causes widespread bone loss, resulting in fragility, pain, increased fracture risk, and ultimately increased patient mortality. Increased mechanical signals in the skeleton are anabolic and protect against bone loss, and they may also do so during osteolytic bone metastasis. Skeletal mechanical signals include interdependent tissue deformations and interstitial fluid flow, but how metastatic tumor cells respond to each of these individual signals remains underinvestigated, a barrier to translation to the clinic. To delineate their respective roles, we report computed estimates of the internal mechanical field of a bone mimetic scaffold undergoing combinations of high and low compression and perfusion using multiphysics simulations. Simulations were conducted in advance of multimodal loading bioreactor experiments with bone metastatic breast cancer cells to ensure that mechanical stimuli occurring internally were physiological and anabolic. Our results show that mechanical stimuli throughout the scaffold were within the anabolic range of bone cells in all loading configurations, were homogenously distributed throughout, and that combined high magnitude compression and perfusion synergized to produce the largest wall shear stresses within the scaffold. These simulations, when combined with experiments, will shed light on how increased mechanical loading in the skeleton may confer anti-tumorigenic effects during metastasis.

Morphology, performance and fluid dynamics of the crayfish escape response.

Sexual selection can result in an exaggerated morphology that constrains locomotor performance. We studied the relationship between morphology and the tail-flip escape response in male and female rusty crayfish (Faxonius rusticus), a species in which males have enlarged claws (chelae). We found that females had wider abdomens and longer uropods (terminal appendage of the tail fan) than males, while males possessed deeper abdomens and larger chelae, relative to total length. Chelae size was negatively associated with escape velocity, whereas longer abdomens and uropods were positively associated with escape velocity. We found no sex-specific differences in maximum force generated during the tail flip, but uropod length was strongly, positively correlated with tail-flip force in males. Particle image velocimetry (PIV) revealed that the formation of a vortex, rather than the expulsion of fluid between two closing body surfaces, generates propulsion in rusty crayfish. PIV also revealed that the pleopods (ventral abdominal appendages) contribute to the momentum generated by the tail. To our knowledge, this is the first confirmation of vortex formation in a decapod crustacean.

A bio-inspired robotic fish utilizes the snap-through buckling of its spine to generate accelerations of more than 20g.

Inspired by the fastest observed live fishes, we have designed, built and tested a robotic fish that emulates the fast-start maneuver of these fishes and generates acceleration and velocity magnitudes comparable to those of the live fishes within the same time scale. We have designed the robotic fish such that it uses the snap-through bucking of its spine to generate the fast-start response. We have used a dynamic snap-through buckling model and a series of experiments on a beam under snap-through buckling to describe the robotic fish's motion. Our under-actuated robot relies on passive dynamics of a continuous beam to generate organic waveforms. In its transient fast-start maneuver, our robotic fish produces mode shapes very similar to those observed in live fishes, by going through a snap-through bifurcation. We have also used a nonlinear structural model subjected to a non-conservative eccentric compressive force, which is constrained to act tangential to the structure at all times, coupled with a simple fluid dynamic model to approximate the transient behavior of the robot. We relate the numerical results from our nonlinear model to the dynamics observed in the live system proposing an updated kinematic model to understand the mode shapes observed in the fast-start maneuver of the live fishes. We also report on deploying the robotic fish in a river.

A reduced-order model of a patient-specific cerebral aneurysm for rapid evaluation and treatment planning.

We discuss a computationally-efficient numerical Reduced Order Model (ROM) for patient-specific cerebral aneurysms, which can be used to examine the rupture-related hemodynamic parameters over a range of relevant physiological flow parameters, rapidly. The ROMs were derived using a Proper Orthogonal Decomposition (POD) technique, which also took advantage of the method of Snapshot POD. Initially a series of Computational Fluid Dynamics(CFD) training runs were performed, which were subsequently improved using a QR-decomposition technique to satisfy the various boundary conditions in physiological flow problems. We used the obtained ROMs to study the influence of Pulsatility Index (PI) on a patient-specific aneurysm's Wall Shear Stress (WSS) and Oscillatory Shear Index (OSI). In addition, we discuss how each of the obtained high-energy POD modes represents a separate significant flow pattern that is believed to influence the aneurysm's WSS and OSI.

Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability.

The interaction of flexible structures with viscoelastic flows can result in very rich dynamics. In this paper, we present the results of the interactions between the flow of a viscoelastic polymer solution and a cantilevered beam in a confined microfluidic geometry. Cantilevered beams with varying length and flexibility were studied. With increasing flow rate and Weissenberg number, the flow transitioned from a fore-aft symmetric flow to a stable detached vortex upstream of the beam, to a time-dependent unstable vortex shedding. The shedding of the unstable vortex upstream of the beam imposed a time-dependent drag force on the cantilevered beam resulting in flow-induced beam oscillations. The oscillations of the flexible beam were classified into two distinct regimes: a regime with a clear single vortex shedding from upstream of the beam resulting in a sinusoidal beam oscillation pattern with the frequency of oscillation increasing monotonically with Weissenberg number, and a regime at high Weissenberg numbers characterized by 3D viscoelastic instabilities where the frequency of oscillations plateaued. The critical onset of the flow transitions, the mechanism of vortex shedding and the dynamics of the cantilevered beam response are presented in detail here as a function of beam flexibility and flow viscoelasticity.

Perfusion applied to a 3D model of bone metastasis results in uniformly dispersed mechanical stimuli.

Breast cancer most frequently metastasizes to the skeleton. Bone metastatic cancer is incurable and induces wide-spread bone osteolysis, resulting in significant patient morbidity and mortality. Mechanical cues in the skeleton are an important microenvironmental parameter that modulate tumor formation, osteolysis, and tumor cell-bone cell signaling, but which mechanical signals are the most beneficial and the corresponding molecular mechanisms are unknown. We focused on interstitial fluid flow based on its well-known role in bone remodeling and in primary breast cancer. We created a full-scale, microCT-based computational model of a 3D model of bone metastasis undergoing applied perfusion to predict the internal mechanical environment during in vitro experimentation. Applied perfusion resulted in uniformly dispersed, heterogeneous fluid velocities, and wall shear stresses throughout the scaffold's interior. The distributions of fluid velocity and wall shear stress did not change within model sub-domains of varying diameter and location. Additionally, the magnitude of these stimuli is within the range of anabolic mechanical signals in the skeleton, verifying that our 3D model reflects previous in vivo studies using anabolic mechanical loading in the context of bone metastasis. Our results indicate that local populations of cells throughout the scaffold would experience similar mechanical microenvironments.

Flow-induced buckling of flexible shells with non-zero Gaussian curvatures and thin spots.

We study the influence of one or multiple thin spots on the flow-induced instabilities of flexible shells of revolution with non-zero Gaussian curvatures. The shell's equation of motion is described by a thin doubly-curved shell theory and is coupled with perturbed flow pressure, calculated based on an inviscid flow model. We show that for shells with positive Gaussian curvatures conveying fluid, the existence of a thin spot results in a localized flow-induced buckling response of the shell in the neighborhood of the thin spot, and significantly reduces the critical flow velocity for buckling instability. For shells with negative Gaussian curvatures, the buckling response is extended along the shell's characteristic lines and the critical flow velocity is only slightly reduced. We also show that the length scale of the localized deformation generated by a thin spot is proportional to the shell's global thickness when the stiffness of the thin spot is negligible compared with the stiffness of the rest of the shell. When two thin spots exist at a distance, their influences are independent from each other for shells with positive Gaussian curvatures, but large-scale deformations can be created due to multiple thin spots on shells with negative curvatures, depending on the thin spots' relative position.

A reduced-order model for wall shear stress in abdominal aortic aneurysms by proper orthogonal decomposition.

In this paper, we introduce a method to construct a Reduced-Order Model (ROM) to study the physiological flow and the Wall Shear Stress (WSS) conditions in Abdominal Aortic Aneurysms (AAA). We start the process by running a training case using Computational Fluid Dynamics (CFD) simulations with time-varying flow parameters, such that these parameters cover the range of parameters that we would like to consider in our ROM. We use the inflow angle as the variable parameter in the current study. Then we use the snapshot Proper Orthogonal Decomposition (POD) to construct the reduced-order bases, which are subsequently enhanced using a QR-factorization technique to satisfy the relevant fluid boundary conditions. The resulting ROM enables us to study the flow pattern and the WSS distribution over a range of system parameters computationally very efficiently. We have used this method to show how the WSS varies significantly for an AAA with a simplified geometry, over a range of inflow angles usually considered mild in clinical terms. We have validated the ROM results with CFD results. This approach enables comprehensive analysis of the model system across a range of inflow angles and frequencies without the need to re-compute the simulation for small changes.

Wake-body resonance of long flexible structures is dominated by counterclockwise orbits.

We identify a dominant mechanism in the interaction between a slender flexible structure undergoing free vibrations in sheared cross-flow and the vortices forming in its wake: energy is transferred from the fluid to the body under a resonance condition, defined as wake-body frequency synchronization close to a natural frequency of the structure; this condition occurs within a well-defined region of the span, which is dominated by counterclockwise, figure-eight orbits. Clockwise orbits are associated with damping fluid forces.