Synthesis, characterization, and evaluation of the anticancer properties of pH-responsive carvacrol-zinc oxide quantum dots on breast cancer cell line (MDA-MB-231).

Since most solid tumors have a low pH value, a pH-responsive drug delivery system may offer a broad method for tumor-targeting treatment. The present study is used to analyze the anticancer activity of carvacrol-zinc oxide quantum dots (CVC-ZnO QDs) against breast cancer cells (MDA-MB-231). CVC-ZnO QDs demonstrate pH responsive and are specifically released within the acidic pH tumor microenvironment. This property enables targeted drug delivery exclusively to cancer cells while minimizing the impact on normal cells. To the synthesized ZnO QDs, the CVC was loaded and then examined by X-ray diffraction, ultraviolet-visible, Fourier transform infrared spectrophotometer, scanning electron microscopy-energy dispersive X-ray, and transmission electron microscopy. For up to 20 h, CVC release was examined in different pH-buffered solutions. The results showed that carvacrol release was stable in an acidic pH solution. Further, cytotoxicity assay, antioxidant, and lipid peroxidation activity, reactive oxygen species, mitochondrial membrane potential, nuclear damage, and the ability of CVC-ZnO QDs to cause apoptosis were all examined. Apoptosis markers such as Bcl2, Bax, caspase-3, and caspase-9, were also studied. In conclusion, the CVC-ZnO QDs destabilized the MDA-MB-231cells under its acidic tumor microenvironment and regulated apoptosis.

A unified energy-optimality criterion predicts human navigation paths and speeds.

Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality criterion that predicts disparate non-straight-line walking phenomena, with straight-line walking as a special case. We first characterized the metabolic cost of turning, deriving the cost landscape as a function of turning radius and rate. We then generalized this cost landscape to arbitrarily complex trajectories, allowing the velocity direction to deviate from body orientation (holonomic walking). We used this generalized optimality criterion to mathematically predict movement patterns in multiple contexts of varying complexity: walking on prescribed paths, turning in place, navigating an angled corridor, navigating freely with end-point constraints, walking through doors, and navigating around obstacles. In these tasks, humans moved at speeds and paths predicted by our optimality criterion, slowing down to turn and never using sharp turns. We show that the shortest path between two points is, counterintuitively, often not energy-optimal, and, indeed, humans do not use the shortest path in such cases. Thus, we have obtained a unified theoretical account that predicts human walking paths and speeds in diverse contexts. Our model focuses on walking in healthy adults; future work could generalize this model to other human populations, other animals, and other locomotor tasks.

Control theory in biology and medicine : Introduction to the special issue.

From September-December 2017, the Mathematical Biosciences Institute at Ohio State University hosted a series of workshops on control theory in biology and medicine, including workshops on control and modulation of neuronal and motor systems, control of cellular and molecular systems, control of disease / personalized medicine across heterogeneous populations, and sensorimotor control of animals and robots. This special issue presents tutorials and research articles by several of the participants in the MBI workshops.

Walking crowds on a shaky surface: stable walkers discover Millennium Bridge oscillations with and without pedestrian synchrony.

Why did the London Millennium Bridge shake when there was a big enough crowd walking on it? What features of human walking dynamics when coupled to a shaky surface produce such shaking? Here, we use a simple biped model capable of walking stably in three dimensions to examine these questions. We simulate multiple such stable bipeds walking simultaneously on a bridge, showing that they naturally synchronize under certain conditions, but that synchronization is not required to shake the bridge. Under such shaking conditions, the simulated walkers increase their step widths and expend more metabolic energy than when the bridge does not shake. We also find that such bipeds can walk stably on externally shaken treadmills, synchronizing with the treadmill motion for a range of oscillation amplitudes and frequencies. Our simulations illustrate how interactions between (idealized) bipeds through the walking surface can produce emergent collective behaviour that may not be exhibited by just a single biped.

The metabolic cost of changing walking speeds is significant, implies lower optimal speeds for shorter distances, and increases daily energy estimates.

Humans do not generally walk at constant speed, except perhaps on a treadmill. Normal walking involves starting, stopping and changing speeds, in addition to roughly steady locomotion. Here, we measure the metabolic energy cost of walking when changing speed. Subjects (healthy adults) walked with oscillating speeds on a constant-speed treadmill, alternating between walking slower and faster than the treadmill belt, moving back and forth in the laboratory frame. The metabolic rate for oscillating-speed walking was significantly higher than that for constant-speed walking (6-20% cost increase for ±0.13-0.27 m s(-1) speed fluctuations). The metabolic rate increase was correlated with two models: a model based on kinetic energy fluctuations and an inverted pendulum walking model, optimized for oscillating-speed constraints. The cost of changing speeds may have behavioural implications: we predicted that the energy-optimal walking speed is lower for shorter distances. We measured preferred human walking speeds for different walking distances and found people preferred lower walking speeds for shorter distances as predicted. Further, analysing published daily walking-bout distributions, we estimate that the cost of changing speeds is 4-8% of daily walking energy budget.

Stepping in the direction of the fall: the next foot placement can be predicted from current upper body state in steady-state walking.

During human walking, perturbations to the upper body can be partly corrected by placing the foot appropriately on the next step. Here, we infer aspects of such foot placement dynamics using step-to-step variability over hundreds of steps of steady-state walking data. In particular, we infer dependence of the 'next' foot position on upper body state at different phases during the 'current' step. We show that a linear function of the hip position and velocity state (approximating the body center of mass state) during mid-stance explains over 80% of the next lateral foot position variance, consistent with (but not proving) lateral stabilization using foot placement. This linear function implies that a rightward pelvic deviation during a left stance results in a larger step width and smaller step length than average on the next foot placement. The absolute position on the treadmill does not add significant information about the next foot relative to current stance foot over that already available in the pelvis position and velocity. Such walking dynamics inference with steady-state data may allow diagnostics of stability and inform biomimetic exoskeleton or robot design.

Sideways walking: preferred is slow, slow is optimal, and optimal is expensive.

When humans wish to move sideways, they almost never walk sideways, except for a step or two; they usually turn and walk facing forward. Here, we show that the experimental metabolic cost of walking sideways, per unit distance, is over three times that of forward walking. We explain this high metabolic cost with a simple mathematical model; sideways walking is expensive because it involves repeated starting and stopping. When walking sideways, our subjects preferred a low natural speed, averaging 0.575 m s(-1) (0.123 s.d.). Even with no prior practice, this preferred sideways walking speed is close to the metabolically optimal speed, averaging 0.610 m s(-1) (0.064 s.d.). Subjects were within 2.4% of their optimal metabolic cost per distance. Thus, we argue that sideways walking is avoided because it is expensive and slow, and it is slow because the optimal speed is low, not because humans cannot move sideways fast.

Walking speeds are lower for short distance and turning locomotion: Experiments and modeling in low-cost prosthesis users.

Preferred walking speed is a widely-used performance measure for people with mobility issues, but is usually measured in straight line walking for fixed distances or durations, and without explicitly accounting for turning. However, daily walking involves walking for bouts of different distances and walking with turning, with prior studies showing that short bouts with at most 10 steps could be 40% of all bouts and turning steps could be 8-50% of all steps. Here, we studied walking in a straight line for short distances (4 m to 23 m) and walking in circles (1 m to 3 m turning radii) in people with transtibial amputation or transfemoral amputation using a passive ankle-foot prosthesis (Jaipur Foot). We found that the study participants' preferred walking speeds are lower for shorter straight-line walking distances and lower for circles of smaller radii, which is analogous to earlier results in subjects without amputation. Using inverse optimization, we estimated the cost of changing speeds and turning such that the observed preferred walking speeds in our experiments minimizes the total cost of walking. The inferred costs of changing speeds and turning were larger for subjects with amputation compared to subjects without amputation in a previous study, specifically, being 4x to 8x larger for the turning cost and being highest for subjects with transfemoral amputation. Such high costs inferred by inverse optimization could potentially include non-energetic costs such as due to joint or interfacial stress or stability concerns, as inverse optimization cannot distinguish such terms from true metabolic cost. These experimental findings and models capturing the experimental trends could inform prosthesis design and rehabilitation therapy to better assist changing speeds and turning tasks. Further, measuring the preferred speed for a range of distances and radii could be a more comprehensive subject-specific measure of walking performance than commonly used straight line walking metrics.

What Loss Functions Do Humans Optimize When They Perform Regression and Classification.

Studying how humans perceive patterns in visually presented data is useful for understanding data-based decision-making and potentially understanding visually mediated sensorimotor control. We conducted experiments to examine how human subjects perform the simplest machine learning or statistical estimation tasks: linear regression and binary classification on 2D scatter plots. We used inverse optimization to infer the loss function humans optimize when they perform these tasks. Minimizing the sum of regression error raised to the power of 1.7 best-described human performing regression on sparse data. Loss functions with lower exponents, which are less sensitive to outliers, were better descriptors for regression tasks performed on less sparse data consisting of more data points. For the classification task, minimizing a logistic loss function was on average a better descriptor of human choices than an exponential loss function applied to only misclassified data. People changed their strategies as data density increased. These results represent overall trends across subjects and trials but there was large inter- and intra-subject variability in human choices. Future work may examine other loss function families and other tasks. Such understanding of human loss functions may inform the design of applications that interact with humans better and imitate humans more effectively.

Human force control may trade-off force error with central tendency and recency biases.

Understanding how humans control force is useful for understanding human movement behaviors and sensorimotor control. However, it is not well understood how the human nervous system handles different control criteria such as accuracy and energetic cost. We conducted force tracking experiments where participants applied force isometrically while receiving visual force feedback, tracking step changes in target forces. The experiments were designed to disambiguate different plausible objective function components. We found that force tracking error was largely explained by a trade-off between error-reducing tendency and force biases, but we did not need to include an effort-saving tendency. Central tendency bias, which is a shift towards the center of the task distribution, and recency bias, which is a shift towards recent action, were necessary to explain many of our observations. Surprisingly, we did not observe such biases when we removed force requirements for pointing to the target, suggesting that such biases may be task-specific. This study provides insights into the broader field of motor control and human perceptions where behavioral or perceptual biases are involved.

Metabolic cost for isometric force scales nonlinearly and predicts how humans distribute forces across limbs.

Muscles consume metabolic energy for force production and movement. A mathematical model of metabolic energy cost will be useful in predicting instantaneous costs during human exercise and in computing effort-minimizing movements via simulations. Previous in vivo data-derived models usually assumed either zero or linearly increasing cost with force, but a nonlinear relation could have significant metabolic or behavioural implications. Here, we show that metabolic cost scales nonlinearly with joint torque with an exponent of about 1.64, using calorimetric measurements of isometric squats. We then demonstrate that this metabolic nonlinearity is reflected in human behaviour: minimizing this nonlinear cost predicts how humans share forces between limbs in additional experiments involving arms and legs. This shows the utility of the nonlinear energy cost in predictive models and its generalizability across limbs. Finally, we show mathematical evidence that the same nonlinear metabolic objective may underlie force sharing at the muscle level.

Computer optimization of a minimal biped model discovers walking and running.

Although people's legs are capable of a broad range of muscle-use and gait patterns, they generally prefer just two. They walk, swinging their body over a relatively straight leg with each step, or run, bouncing up off a bent leg between aerial phases. Walking feels easiest when going slowly, and running feels easiest when going faster. More unusual gaits seem more tiring. Perhaps this is because walking and running use the least energy. Addressing this classic conjecture with experiments requires comparing walking and running with many other strange and unpractised gaits. As an alternative, a basic understanding of gait choice might be obtained by calculating energy cost by using mechanics-based models. Here we use a minimal model that can describe walking and running as well as an infinite variety of other gaits. We use computer optimization to find which gaits are indeed energetically optimal for this model. At low speeds the optimization discovers the classic inverted-pendulum walk, at high speeds it discovers a bouncing run, even without springs, and at intermediate speeds it finds a new pendular-running gait that includes walking and running as extreme cases.

Towards skin-acetone monitors with selective sensitivity: Dynamics of PANI-CA films.

Most research aimed at measuring biomarkers on the skin is only concerned with sensing chemicals in sweat using electrical signals, but these methods are not truly non-invasive nor non-intrusive because they require substantial amounts of sweat to get a reading. This project aims to create a truly non-invasive wearable sensor that continuously detects the gaseous acetone (a biomarker related to metabolic disorders) that ambiently comes out of the skin. Composite films of polyaniline and cellulose acetate, exhibiting chemo-mechanical actuation upon exposure to gaseous acetone, were tested in the headspaces above multiple solutions containing acetone, ethanol, and water to gauge response sensitivity, selectivity, and repeatability. The bending of the films in response to exposures to these environments was tracked by an automatic video processing code, which was found to out-perform an off-the-shelf deep neural network-based tracker. Using principal component analysis, we showed that the film bending is low dimensional with over 90% of the shape changes being captured with just two parameters. We constructed forward models to predict shape changes from the known exposure history and found that a linear model can explain 40% of the observed variance in film tip angle changes. We constructed inverse models, going from third order fits of shape changes to acetone concentrations where about 45% of the acetone variation and about 30% of ethanol variation are captured by linear models, and non-linear models did not perform substantially better. This suggests there is sufficient sensitivity and inherent selectivity of the films. These models, however, provide evidence for substantial hysteretic or long-time-scale responses of the PANI films, seemingly due to the presence of water. Further experiments will allow more accurate discrimination of unknown exposure environments. Nevertheless, the sensor will operate with high selectivity in low sweat body locations, like behind the ear or on the nails.

Optimal speeds for walking and running, and walking on a moving walkway.

Many aspects of steady human locomotion are thought to be constrained by a tendency to minimize the expenditure of metabolic cost. This paper has three parts related to the theme of energetic optimality: (1) a brief review of energetic optimality in legged locomotion, (2) an examination of the notion of optimal locomotion speed, and (3) an analysis of walking on moving walkways, such as those found in some airports. First, I describe two possible connotations of the term "optimal locomotion speed:" that which minimizes the total metabolic cost per unit distance and that which minimizes the net cost per unit distance (total minus resting cost). Minimizing the total cost per distance gives the maximum range speed and is a much better predictor of the speeds at which people and horses prefer to walk naturally. Minimizing the net cost per distance is equivalent to minimizing the total daily energy intake given an idealized modern lifestyle that requires one to walk a given distance every day--but it is not a good predictor of animals' walking speeds. Next, I critique the notion that there is no energy-optimal speed for running, making use of some recent experiments and a review of past literature. Finally, I consider the problem of predicting the speeds at which people walk on moving walkways--such as those found in some airports. I present two substantially different theories to make predictions. The first theory, minimizing total energy per distance, predicts that for a range of low walkway speeds, the optimal absolute speed of travel will be greater--but the speed relative to the walkway smaller--than the optimal walking speed on stationary ground. At higher walkway speeds, this theory predicts that the person will stand still. The second theory is based on the assumption that the human optimally reconciles the sensory conflict between the forward speed that the eye sees and the walking speed that the legs feel and tries to equate the best estimate of the forward speed to the naturally preferred speed. This sensory conflict theory also predicts that people would walk slower than usual relative to the walkway yet move faster than usual relative to the ground. These predictions agree qualitatively with available experimental observations, but there are quantitative differences.

A controller for walking derived from how humans recover from perturbations.

Humans can walk without falling despite some external perturbations, but the control mechanisms by which this stability is achieved have not been fully characterized. While numerous walking simulations and robots have been constructed, no full-state walking controller for even a simple model of walking has been derived from human walking data. Here, to construct such a feedback controller, we applied thousands of unforeseen perturbations to subjects walking on a treadmill and collected data describing their recovery to normal walking. Using these data, we derived a linear controller to make the classical inverted pendulum model of walking respond to perturbations like a human. The walking model consists of a point-mass with two massless legs and can be controlled only through the appropriate placement of the foot and the push-off impulse applied along the trailing leg. We derived how this foot placement and push-off impulse are modulated in response to upper-body perturbations in various directions. This feedback-controlled biped recovers from perturbations in a manner qualitatively similar to human recovery. The biped can recover from perturbations over twenty times larger than deviations experienced during normal walking and the biped's stability is robust to uncertainties, specifically, large changes in body and feedback parameters.

Step-to-step variations in human running reveal how humans run without falling.

Humans can run without falling down, usually despite uneven terrain or occasional pushes. Even without such external perturbations, intrinsic sources like sensorimotor noise perturb the running motion incessantly, making each step variable. Here, using simple and generalizable models, we show that even such small step-to-step variability contains considerable information about strategies used to run stably. Deviations in the center of mass motion predict the corrective strategies during the next stance, well in advance of foot touchdown. Horizontal motion is stabilized by total leg impulse modulations, whereas the vertical motion is stabilized by differentially modulating the impulse within stance. We implement these human-derived control strategies on a simple computational biped, showing that it runs stably for hundreds of steps despite incessant noise-like perturbations or larger discrete perturbations. This running controller derived from natural variability echoes behaviors observed in previous animal and robot studies.

How well can spring-mass-like telescoping leg models fit multi-pedal sagittal-plane locomotion data?

Idealized mathematical models of animals, with point-mass bodies and spring-like legs, have been used by researchers to study various aspects of terrestrial legged locomotion. Here, we fit a bipedal spring-mass model to the ground reaction forces of human running, a horse trotting, and a cockroach running. We find that, in all three cases, while the model captures center-of-mass motions and vertical force variations well, horizontal forces are less well reproduced, primarily due to variations in net force vector directions that the model cannot accommodate. The fits result in different apparent leg stiffnesses in the three animals. Assuming a simple fixed leg-angle touch-down strategy, we find that the gaits of these models are stable in different speed-step length regimes that overlap with those used by humans and horses, but not with that used by cockroaches.

Rocking and rolling: a can that appears to rock might actually roll.

A beer bottle or soda can on a table, when slightly tipped and released, falls to an upright position and then rocks up to a somewhat opposite tilt. Superficially this rocking motion involves a collision when the flat circular base of the container slaps the table before rocking up to the opposite tilt. A keen eye notices that the after-slap rising tilt is not generally just diametrically opposite the initial tilt but is veered to one side or the other. Cushman and Duistermaat [Regular Chaotic Dyn. 11, 31 (2006)] recently noticed such veering when a flat disk with rolling boundary conditions is dropped nearly flat. Here, we generalize these rolling disk results to arbitrary axi-symmetric bodies and to frictionless sliding. More specifically, we study motions that almost but do not quite involve a face-down collision of the round container's bottom with the tabletop. These motions involve a sudden rapid motion of the contact point around the circular base. Surprisingly, similar to the rolling disk, the net angle of motion of this contact point is nearly independent of initial conditions. This angle of turn depends simply on the geometry and mass distribution but not on the moment of inertia about the symmetry axis. We derive simple asymptotic formulas for this "angle of turn" of the contact point and check the result with numerics and with simple experiments. For tall containers (height much bigger than radius) the angle of turn is just over pi and the sudden rolling motion superficially appears as a nearly symmetric collision leading to leaning on an almost diametrically opposite point on the bottom rim.

Energy-Optimal Human Walking With Feedback-Controlled Robotic Prostheses: A Computational Study.

Lower-limb amputees typically experience reduced mobility and higher metabolic rates than non-amputees. It may be possible to improve their mobility and metabolic rate with an optimized robotic prosthesis. Here, we use large-scale trajectory optimization on a simulated transtibial amputee with a robotic prosthesis to obtain metabolic energy-minimizing walking gaits with multiple prosthesis feedback controllers. Using such optimizations, we obtained trends in the energetics and kinematics for various prosthesis work levels. We find that the net metabolic rate has a non-monotonic relationship with the net prosthesis work rate: too much or too little prosthesis work results in higher metabolic rates. We predict that metabolic rate could be reduced below that of a non-amputee, although such gaits are highly asymmetric and not seen in experiments with amputees wearing robotic prostheses. We predict higher metabolic rates with SACH foot, a passive prosthesis. Walking gaits with left-right symmetry in kinematics or ground reaction forces have higher metabolic rates than asymmetric gaits, suggesting a potential reason for asymmetries in amputee walking. Our findings suggest that a computational framework such as the one presented here could augment the experimental approaches to prosthesis design iterations, although quantitatively accurate simulation-based prediction of experiments remains an open problem.

Correction to 'Walking with wider steps changes foot placement control, increases kinematic variability and does not improve linear stability'.

[This corrects the article DOI: 10.1098/rsos.160627.].