Waleed A. Farahat

Waleed A. Farahat
Postdoctoral Associate
Department of Mechanical Engineering
Massachusetts Insititue of Technology

77 Massachusetts Avenue, Rm 3-351
Cambridge, MA 02139

Main research thrusts

Control, feedback and optimization principles play fundamental roles in biological and physiological systems. While these principles have been effectively used to explain physiological phenomena, they have not been used equally effectively to influence and augment their behaviors. My research goals are to develop means for controlling physiological dynamical systems, and to use that control as the foundation for cellular and biomedical interventions, biological robotic systems, and scientific investigations.

I have applied / am applying this approach in two key areas, outlined opposite:

Area 1: Control of cellular systems for tissue engineering applications

Area 2: Control of muscle-actuated systems

Area 1: Control of Cellular System for Tissue Engineering

High-throughput microfluidic cell cultures for identification of cellular responses

Angiogenesis is fundamental to wound healing, cancer development and tissue engineering. Our broader objective is to implement model-based, closed-loop control approaches to angiogenesis cell cultures in vitro. These can serve as important models for better understanding the biological process as well as for therapeutic screening. A key step is the development of statistically meaningful models describing the influence of cell culture conditions on the biological process. Towards this goal, we extended a three-dimensional, microfluidic tissue culture platform to parallelize multiple cell cultures subject to common conditions. We anticipate that the resulting increase in observational throughput will allow for the development of statistically meaningful models of the process. These models can be used as the basis for systematic interventions, as well as designing feedback algorithms for controlling the process online. [Top]

References
Farahat, W., Wood, L., Zervantonakis, I., Alisha Schor, Sharon Ong, Devin Neal , Kamm, R. and Asada, H. “Ensemble Analysis of Angiogenic Growth in Three-Dimensional Microfluidic Cell Cultures.” Submitted.

Characterization of angiogenic response maps

Using the high-throughput microfluidic cell culture platforms, we are characterizing angiogenic response of human micro-vascular endothelial cells as a function of VEGF, ANG1 and S1P stimulation in vitro. Three-dimensional images acquired via confocal microscopy are analysized to quantify angiogenic metrics such as cell sprouting and penetration into the extra-cellular matrix. The aggregate results will form the basis of an angiogenic model used for feedback-control applications.

Optimal control of cell migration by modulating chemoattractant gradients

Cell migration is fundamental to a wide range of biological and physiological functions, from wound healing to cancer metastasis to the formation of biological structures such as vascular and neural networks. In these diverse examples, cell migration is influenced by a broad set of external mechanical and biochemical cues, particularly the presence of (time dependent) spatial gradients of soluble chemoattractants in the extracellular domain. Many biological models have sought to explain the mechanisms leading to the migratory response of cells as a function of these external cues. Based on such models, here we propose approaches to controling the chemotactic response of eukaryotic cells by modulating their micro environments in vitro (for example, using a microfluidic chemotaxis chamber). By explicitly modeling chemoattractant-receptor binding kinetics, diffusion dynamics in the extracellular domain, and models for chemotactic response arise. Based on those models, optimal control formulations are developed and illustrated. We present simulation results, and suggest experimental approaches to controlling cellular motility in vitro.

References
Farahat, W. and Asada, H. “Control of Eukaryotic Cell Migration via Modulation of Extracellular Chemoattractant Gradients.” Submitted to the 3rd ASME Dynamical Systems and Control, 2010.

Estimation of phenotypic state-transition probabilities in living cells

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.

References
Farahat, W. and Asada, H. “Estimation of State Transition Probabilities in Asynchronous Vector Markov Processes.” In review.

Farahat, W. and Asada, H. “Estimation of State Transition Probabilities in Asynchronous Population Markov Processes.” American Control Conference, 2010.

Farahat, W. and Asada, H. “Identification of Phenotypic State Transition Probabilities in Living Cells.” Proceedings of the 2nd ASME Dynamical Systems and Control Conference, Hollywood, 2009.

Area 2: Control of Muscle-Acutated Systems

Optimal workloop energetics of muscle-actuated systems

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 Since neurally-modulated muscle stiffness contributes to 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. [Top]

References
Farahat, W. and Herr, H. “Optimal Workloop Energetics of Muscle-Actuated Systems: An Impedance Matching View.” PLoS Computational Biology, 6(6): e1000795. doi:10.1371/journal.pcbi.1000795

Farahat, W. and Herr, H. “Impedance Matching for Enhancing Mechanical Energetics in Muscle-Actuated Systems.” 4th International Symposium on Adaptive Motion in Animals and Machines, Cleveland, 2008.

Farahat, W. and Herr, H. “Workloop Energetics of Antagonist Muscle Pairs.” 28th International Conference of the IEEE Engineering in Medicine and Biology Society, New York, 2006.

Identification of muscle contractile dynamics

Models of the mechanical impedance of skeletal muscle that are bilinear in activation and length have been useful in describing muscle contractile response under isometric conditions. However, the applicability of these models to general dynamic contractions remained questionable. Here we show that for bursting contractions, a bilinear model captures the dominant variance in muscle response (73% +/- 5.7% 1-s.d). The proposed model has a Wiener-like model structure consisting of an activation dynamics block coupled in cascade with a nonlinear memoryless output impedance function. These findings are based on experimental measurements conducted on plantaris longus muscles explanted from Rana pipien frogs. Such simplified models allow for mathematical tractability when analyzing the dynamics of multiple-muscle systems and when synthesizing electrical stimulation to control muscle response. [Top]

References
Farahat, W. and Herr, H. “Muscle Mechanical Impedance Maintains Bilinear Characteristics for a Class of Periodic Dynamic Contractions.” Submitted.

Farahat, W. and Herr, H. “A Method for Identification of Electrically Stimulated Muscle.” 27th International Conference of the IEEE Engineering in Medicine and Biology Society, Shanghai, 2005.

Muscle characterization tools

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. [Top]

References
Farahat, W. and Herr, H. “An Apparatus for Characterization and Control of Isolated Muscle.” IEEE Transactions on Neural Systems and Rehabilitation Engineering, December 2005.

Spillman, C., Naciri, J., Martin, B., Farahat, W., Herr H. and Ratna, B. “Stacking Nematic Elastomers for Artificial Muscle Applications.” Sensors and Actuators A: Physical, February 2007.