A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes.

The phenomenological model for cell shape deformation and cell migration Chen (BMM 17:1429-1450, 2018), Vermolen and Gefen (BMM 12:301-323, 2012), is extended with the incorporation of cell traction forces and the evolution of cell equilibrium shapes as a result of cell differentiation. Plastic deformations of the extracellular matrix are modelled using morphoelasticity theory. The resulting partial differential differential equations are solved by the use of the finite element method. The paper treats various biological scenarios that entail cell migration and cell shape evolution. The experimental observations in Mak et al. (LC 13:340-348, 2013), where transmigration of cancer cells through narrow apertures is studied, are reproduced using a Monte Carlo framework.

A Cellular Automata Model of Oncolytic Virotherapy in Pancreatic Cancer.

Oncolytic virotherapy is known as a new treatment to employ less virulent viruses to specifically target and damage cancer cells. This work presents a cellular automata model of oncolytic virotherapy with an application to pancreatic cancer. The fundamental biomedical processes (like cell proliferation, mutation, apoptosis) are modeled by the use of probabilistic principles. The migration of injected viruses (as therapy) is modeled by diffusion through the tissue. The resulting diffusion-reaction equation with smoothed point viral sources is discretized by the finite difference method and integrated by the IMEX approach. Furthermore, Monte Carlo simulations are done to quantitatively evaluate the correlations between various input parameters and numerical results. As we expected, our model is able to simulate the pancreatic cancer growth at early stages, which is calibrated with experimental results. In addition, the model can be used to predict and evaluate the therapeutic effect of oncolytic virotherapy.

Rapid Cancer Diagnosis and Early Prognosis of Metastatic Risk Based on Mechanical Invasiveness of Sampled Cells.

We provide an innovative, bioengineering, mechanobiology-based approach to rapidly (2-h) establish the in vivo metastatic likelihood of patient tumor-samples, where results are in direct agreement with clinical histopathology and patient outcomes. Cancer-related mortality is mostly due to local recurrence or to metastatic disease, thus early prediction of tumor-cell-fate may critically affect treatment protocols and survival rates. Metastasis and recurrence risks are currently predicted by lymph-node status, tumor size, histopathology and genetic testing, however, these are not infallible and results may require days/weeks. We have previously observed that subpopulations of invasive cancer-cells will rapidly (1-2 h) push into the surface of physiological-stiffness, synthetic polyacrylamide gels, reaching to cell-scale depths, while normal or noninvasive cells do not considerably indent gels. Here, we evaluate the mechanical invasiveness of established breast and pancreatic cell lines and of tumor-cells from fresh, suspected pancreatic cancer tumors. The mechanical invasiveness matches the in vitro metastatic potential in cell lines as determined with Boyden chamber assays. Moreover, the mechanical invasiveness directly agrees with the clinical histopathology in primary-site, pancreatic-tumors. Thus, the rapid, patient-specific, early prediction of metastatic likelihood, on the time-scale of initial resection/biopsy, can directly affect disease management and treatment protocols.

Effects of particle uptake, encapsulation, and localization in cancer cells on intracellular applications.

Endocytosis is a normal process in living cells, often used to internalize drug-containing particles and probes for intracellular mechanics. The cell type, and especially malignancy, may affect particle internalization and transport. Specifically, membrane-encapsulation following internalization can affect particle interaction with the cell interior. Hence, particle-tracking measurements that reveal intracellular mechanics and dynamics require determination of effects of encapsulation. Here, we compare closely related, breast-cancer cell lines with high- and low-metastatic potential (MP) and benign, control cells. We evaluate time-dependent particle internalization, localization with endocytotic-pathway organelles, and membrane encapsulation at 2, 6, 24, and 48 h after initial cell exposure to particles. High MP cells internalize particles more rapidly and in larger amounts than low MP and benign cells. Moreover, while only cells at the edge of two-dimensional colonies of benign cells internalized particles, all cancer cells uniformly internalize particles. Particles mostly colocalize with late endosomes (>80%), yet surprisingly, overall membrane encapsulation decreases with time, indicating release into the cytoplasm; encapsulation at 48 h is <35% in all three cell types. We discuss implications to drug delivery and show that encapsulation does not significantly affect intracellular particle-tracking experiments, showing the applicability of endocytosis.

Towards a Mathematical Formalism for Semi-stochastic Cell-Level Computational Modeling of Tumor Initiation.

A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that chase the tumor cells and engulf them. Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account. The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations. We also take into account the likelihood of seeding of tumors. The model shows the initiation of tumors and allows to study a quantification of the impact of various subprocesses and possibly even of various treatments.

Hydrodynamics of sailing of the Portuguese man-of-war Physalia physalis.

Physalia physalis, commonly known as the Portuguese man-of-war (PMW), is a peculiar looking colony of specialized polyps. The most conspicuous members of this colony are the gas-filled sail-like float and the long tentacles, budding asymmetrically beneath the float. This study addresses the sailing of the PMW, and, in particular, the hydrodynamics of its trailing tentacles, the interaction between the tentacles and the float and the actual sailing performance. This paper attempts to provide answers for two of the many open questions concerning P. physalis: why does it need a sail? and how does it harness the sail?

Evidence of self-correcting spiral flows in swimming boxfishes.

The marine boxfishes have rigid keeled exteriors (carapaces) unlike most fishes, yet exhibit high stability, high maneuverability and relatively low drag given their large cross-sectional area. These characteristics lend themselves well to bioinspired design. Based on previous stereolithographic boxfish model experiments, it was determined that vortical flows develop around the carapace keels, producing self-correcting forces that facilitate swimming in smooth trajectories. To determine if similar self-correcting flows occur in live, actively swimming boxfishes, two species of boxfishes (Ostracion meleagris and Lactophrys triqueter) were induced to swim against currents in a water tunnel, while flows around the fishes were quantified using digital particle image velocimetry. Significant pitch events were rare and short lived in the fishes examined. When these events were observed, spiral flows around the keels qualitatively similar to those observed around models were always present, with greater vortex circulation occurring as pitch angles deviated from 0 degrees . Vortex circulation was higher in live fishes than models presumably because of pectoral fin interaction with the keel-induced flows. The ability of boxfishes to modify their underlying self-correcting system with powered fin control is important for achieving high levels of both stability and maneuverability. Although the challenges of performing stability and maneuverability research on fishes are significant, the results of this study together with future studies employing innovative new approaches promise to provide valuable inspiration for the designers of bioinspired aquatic vehicles.

Speed limits on swimming of fishes and cetaceans.

Physical limits on swimming speed of lunate tail propelled aquatic animals are proposed. A hydrodynamic analysis, applying experimental data wherever possible, is used to show that small swimmers (roughly less than a metre long) are limited by the available power, while larger swimmers at a few metres below the water surface are limited by cavitation. Depending on the caudal fin cross-section, 10-15 m s(-1) is shown to be the maximum cavitation-free velocity for all swimmers at a shallow depth.

Dynamics of dolphin porpoising revisited.

Porpoising is the popular name for the high-speed surface piercing motion of dolphins and other species, in which long, ballistic jumps are alternated with sections of swimming close to the surface. The first analysis of this behavior (Au and Weihs, 1980) showed that above a certain "crossover" speed this behavior is energetically advantageous, as the reduction in drag due to movement in the air becomes greater than the added cost of leaping.Since that publication several studies documented porpoising behavior at high speeds. The observations indicated that the behavior was more complex than previously assumed. The leaps were interspersed with relatively long swimming bouts, of about twice the leap length. In the present paper, the possibility of dolphins using a combination of leaping and burst and coast swimming is examined. A three-phase model is proposed, in which the dolphin leaps out of the water at a speed U(f), which is the final speed obtained at the end of the burst phase of burst and coast swimming. The leap is at constant speed and so the animal returns to the water at U(f), goes to a shallow depth and starts horizontal coasting while losing speed, till it reaches U(i). At that point it starts active swimming, accelerating to U(f). It then starts the next leap. Ranges of speeds for which this three-stage swimming is advantageous are calculated as a function of animal and physical parameters.NotationC-Constant defined in equation (12)C(D)-Coasting drag coefficientD-Dragg-Gravitational accelerationH-Height of jumpJ-Energy required for jumpk-Ratio of swim length to jump lengthl-DistanceL-Total distance (eq. 28)m-Added massM-Animal massM(1)-Total massr-Coefficient defined in eq. (22)R-Ratio of energies, for three-phase swimmingR(2)-Ratio of energies, for burst and coast swimmingt-TimeT-ThrustU-SpeedV-Body volumeW-Weightα-Emergence (=return) angleß-Swim / coast drag penalty ratioγ-Surface effects drag ratioρ-Density of seawater and cetacean.Subscriptsa-airav-Averageb-Burst phasec-Coast phasee-Reference (maximal) thrustf-Final, at end of bursti-Initial, at start of burstj-Jump phasen-Nominal reference thrusto-Optimals-Surface swimmingw-Water.

Head stabilization in herons.

We examined head stabilization in relation to body mass and length of legs in four heron species (little egrets, Egretta garzetta; night herons, Nycticorax nycticorax; squacco herons, Ardeola ralloides; and cattle egrets, Bubulcus ibis: Aves: Ardeidae). Head stabilization, under controlled, sinusoidal, perch perturbations was mostly elicited at frequencies lower than 1 Hz. Maximal perturbation amplitudes sustained were positively correlated with leg length and maximal perturbation frequencies sustained were negatively correlated with body mass and with leg length. The species differed significantly in average maximal perturbation amplitudes sustained. Combinations of amplitude and frequency for which stabilization was achieved were bounded by a decreasing concave "envelope" curve in the frequency-amplitude plane, with inter specific differences in "envelope". As physical constraints, we tested maximal vertical acceleration, which translates into a line defined by the product of frequency2 x amplitude, and maximal vertical velocity, which translates into a line defined by the product of frequency x amplitude. Both relations were in good agreement with the experimental results for all but squacco herons. The results support predictions based on mechanical considerations and may explain the predominance of motor patterns employed by herons while foraging.

Boxfishes (Teleostei: Ostraciidae) as a model system for fishes swimming with many fins: kinematics.

Swimming movements in boxfishes were much more complex and varied than classical descriptions indicated. At low to moderate rectilinear swimming speeds (<5 TL s(-1), where TL is total body length), they were entirely median- and paired-fin swimmers, apparently using their caudal fins for steering. The pectoral and median paired fins generate both the thrust needed for forward motion and the continuously varied, interacting forces required for the maintenance of rectilinearity. It was only at higher swimming speeds (above 5 TL s(-1)), when burst-and-coast swimming was used, that they became primarily body and caudal-fin swimmers. Despite their unwieldy appearance and often asynchronous fin beats, boxfish swam in a stable manner. Swimming boxfish used three gaits. Fin-beat asymmetry and a relatively non-linear swimming trajectory characterized the first gait (0--1 TL s(-1)). The beginning of the second gait (1--3 TL s(-1)) was characterized by varying fin-beat frequencies and amplitudes as well as synchrony in pectoral fin motions. The remainder of the second gait (3--5 TL s(-1)) was characterized by constant fin-beat amplitudes, varying fin-beat frequencies and increasing pectoral fin-beat asynchrony. The third gait (>5 TL s(-1)) was characterized by the use of a caudal burst-and-coast variant. Adduction was always faster than abduction in the pectoral fins. There were no measurable refractory periods between successive phases of the fin movement cycles. Dorsal and anal fin movements were synchronized at speeds greater than 2.5 TL s(-1), but were often out of phase with pectoral fin movements.

Boxfishes as unusually well-controlled autonomous underwater vehicles.

Boxfishes (family Ostraciidae) are tropical reef-dwelling marine bony fishes that have about three-fourths of their body length encased in a rigid bony test. As a result, almost all of their swimming movements derive from complex combinations of movements of their median and paired fins (MPF locomotion). In terms of both body design and swimming performance, they are among the most sophisticated examples known of naturally evolved vertebrate autonomous underwater vehicles. Quantitative studies of swimming performance, biomechanics, and energetics in one model species have shown that (i) they are surprisingly strong, fast swimmers with great endurance; (ii) classical descriptions of how they swim were incomplete: they swim at different speeds using three different gaits; (iii) they are unusually dynamically well controlled and stable during sustained and prolonged rectilinear swimming; and (iv) despite unusually high parasite (fuselage) drag, they show energetic costs of transport indistinguishable from those of much better streamlined fishes using body and caudal fin (BCF) swimming modes at similar water temperatures and over comparable ranges of swimming speeds. We summarize an analysis of these properties based on a dynamic model of swimming in these fishes. This model accounts for their control, stability, and efficiency in moving through the water at moderate speeds in terms of gait changes, of water-flow patterns over body surfaces, and of complex interactions of thrust vectors generated by fin movements.

Microstructural evolution of lipid aggregates in nucleating model and human biles visualized by cryogenic transmission electron microscopy.

Obtaining reliable information on the physical state and ultrastructure of bile is difficult because of its mixed aqueous-lipid composition and thermodynamic metastability. We have used time-lapse cryogenic transmission electron microscopy (cryo-TEM) combined with video-enhanced light microscopy (VELM) to study microstructural evolution in nucleating bile. A well-characterized model bile and gallbladder biles from cholesterol and pigment gallstone patients were studied sequentially during cholesterol nucleation and precipitation. In model bile, cholesterol crystallization was preceded by the appearance of the following distinct microstructures: spheroidal micelles (3-5 nm), discoidal membrane patches (50-150 nm) often in multiple layers (2-10), discs (50-100 nm), and unilamellar (50-200 nm) and larger multilamellar vesicles (MLVs). The membrane patches and discs appeared to be short-lived intermediates in a micelle-to-vesicle transition. Vesicular structures formed by growth and closure of patches as well as by budding off from vesicles with fewer bilayers. MLVs became more abundant, uniform, and concentric as a function of time. In native bile, all the above microstructures, except discoidal membrane patches, were observed. However, native MLVs were more uniform and concentric from the beginning. When cholesterol crystals appeared by light microscopy, MLVs were always detected by cryo-TEM. Edges of early cholesterol crystals were lined up with micelles and MLVs in a way suggesting an active role in feeding crystal growth from these microstructures. These findings, for the first time documented by cryo-TEM in human bile, provide a microstructural framework that can serve as a basis for investigation of specific factors that influence biliary cholesterol nucleation and crystal formation.

Energetic advantages of burst-and-coast swimming of fish at high speeds.

A theoretical model describes how an intermittent swimming style can be energetically advantageous over continuous swimming at high average velocities. Kinematic data are collected from high-speed ciné pictures of free swimming cod and saithe at high velocities in a burst-and-coast style. These data suggest that fish make use of the advantages shown by choosing initial and final burst velocities close to predicted optimal values. The limiting role of rapid glycogen depletion in fast white anaerobic muscle fibres is discussed.