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.

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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.