We demonstrate ensemble three-dimensional cell cultures and quantitative analysis of angiogenic growth from uniform endothelial monolayers. Our approach combines two key elements: a micro-fluidic assay that enables parallelized angiogenic growth instances subject to common extracellular conditions, and an automated image acquisition and processing scheme enabling high-throughput, unbiased quantification of angiogenic growth. Because of the increased throughput of the assay in comparison to existing three-dimensional morphogenic assays, statistical properties of angiogenic growth can be reliably estimated. We used the assay to evaluate the combined effects of vascular endothelial growth factor (VEGF) and the signaling lipid sphingoshine-1-phosphate (S1P). Our results show the importance of S1P in amplifying the angiogenic response in the presence of VEGF gradients. Furthermore, the application of S1P with VEGF gradients resulted in angiogenic sprouts with higher aspect ratio than S1P with background levels of VEGF, despite reduced total migratory activity. This implies a synergistic effect between the growth factors in promoting angiogenic activity. Finally, the variance in the computed angiogenic metrics (as measured by ensemble standard deviation) was found to increase linearly with the ensemble mean. This finding is consistent with stochastic agent-based mathematical models of angiogenesis that represent angiogenic growth as a series of independent stochastic cell-level decisions.

No abstract

Integrative approaches to studying the coupled dynamics of skeletal muscles with their loads while under neural control have focused largely on questions pertaining to the postural and dynamical stability of animals and humans. Prior studies have focused on how the central nervous system actively modulates muscle mechanical impedance to generate and stabilize motion and posture. However, the question of whether muscle impedance properties can be neurally modulated to create favorable mechanical energetics, particularly in the context of periodic tasks, remains open. Through muscle stiffness tuning, we hypothesize that a pair of antagonist muscles acting against a common load may produce significantly more power synergistically than individually when impedance matching conditions are met between muscle and load. Since neurally modulated muscle stiffness contributes to the coupled muscle-load stiffness, we further anticipate that power-optimal oscillation frequencies will occur at frequencies greater than the natural frequency of the load. These hypotheses were evaluated computationally by applying optimal control methods to a bilinear muscle model, and also evaluated through in vitro measurements on frog Plantaris longus muscles acting individually and in pairs upon a mass-spring-damper load. We find a 7-fold increase in mechanical power when antagonist muscles act synergistically compared to individually at a frequency higher than the load natural frequency. These observed behaviors are interpreted in the context of resonance tuning and the engineering notion of impedance matching. These findings suggest that the central nervous system can adopt strategies to harness inherent muscle impedance in relation to external loads to attain favorable mechanical energetics.

An apparatus for characterization and control of muscle tissue is presented. The apparatus is capable of providing generalized mechanical boundary conditions to muscle tissue, as well as implementing real-time feedback control via electrical stimulation. The system is intended to serve as an experimental platform for implementing a wide variety of muscle control and identification studies that will serve as fundamental investigations of muscle mechanics, energetics, functional electrical stimulation, and fatigue. In one illustration of the capabilities of the apparatus, pilot experimental results of muscle workloops against a finite-admittance passive load are presented, illustrating how richer boundary conditions may reveal interesting muscle behavior.

We present a model structure and a method for identifying the dynamics of electrically stimulated muscle. The model structure is sufficiently rich to describe a wide set of muscle behavior. It consists of (i) an input static nonlinearity representing the muscle's recruitment properties, (ii) a linear dynamical system representing the contraction dynamics, (iii) an output static nonlinearity representing generalized force- length and force-velocity relationships, and (iv) prefilters for the mechanical input that capture impedance and history dependence properties of the muscle. It is assumed that each of the subsystems is linearly parameterized. We present parameter estimation methods, and verify via simulation successful convergence of the estimates to their true values with small variances.

Living cells stochastically switch their phenotypic states in response to environmental cues to maintain persistence and viability. Estimating the state transition probabilities from biological observations of cell populations gives valuable insight to the underlying processes, and gives insights as to how the transition statistics are influenced by external factors. In this work, we present two Bayesian estimation approaches. The first is applicable when individual cell state trajectories are observed. The second approach is applicable when only aggregate population statistics are available. Estimation of transition probabilities when individual cell state trajectories are available is a straightforward problem, whereas estimation from only aggregate statistics can be computationally expensive. In the latter case, we present an algorithm that relies on three key ideas to cut down computational time: i) approximating high-dimensional multinomial distributions with multi-variate Gaussians, ii) employing Monte-Carlo techniques to efficiently integrate over high dimensional spaces, and iii) explicitly incorporating sampling constraints by computing lower dimensional distributions over the constrained variable. Simulation results demonstrate the viability of the algorithm.

The capability of muscle to produce mechanical work under periodic motions has been traditionally estimated using the workloop technique. We extend this method by allowing a pair of antagonist muscles to interact against a common load with non-zero admittance. We present an experimental approach to measuring the work done by a two-muscle system and show preliminary data. A complimentary problem is to maximize the work produced by the muscle pair in this setting. We formulate this problem in an optimal control framework. We derive conditions for the optimal activation of muscles to produce the maximum work, and show computed solutions.

We address the problem of estimating the probability transition matrix of an asynchronous vector Markov process from aggregate (longitudinal) population observations. This problem is motivated by estimating phenotypic state transitions probabilities in populations of biological cells, but can be extended to multiple contexts of populations of Markovian agents. We adopt a Bayesian estimation approach, which can be computationally expensive if exact marginalization is employed. To compute the posterior estimates efficiently, we use Monte Carlo simulations coupled with Gibb's sampling techniques that explicitly incorporate sampling constraints from the desired distributions. Such sampling techniques can attain significant computational advantages. Illustration of the algorithm is provided via simulation examples.