Azeem Sarwar

Towards Control of Magnetic Fluids in Patients: Directing Therapeutic Nanoparticles to Disease Locations

This article describes a range of results, from passive magnet design to optimal feedback control of a distributed ferrofluid. Representing magnetic forces as the gradient of a magnetic energy allowed design and demonstration, in animal experiments, of a simple open-loop two-magnet system to inject nanoparticles into the inner ear. Then a petri-dish test bed was used to develop and test optimal closed-loop manipulation of a single ferrofluid droplet.The demonstrated algorithms exploited the quadratic dependence of the magnetic forces on control inputs while accounting for magnet time delays and spatial discontinuities in the optimal control. All dimensional parameters were reduced to three essential nondimensional numbers, and ferrofluid behavior was mapped across the entire feasible drug delivery parameter space.

Shaping Magnetic Fields to Direct Therapy to Ears and Eyes

Magnetic fields have the potential to noninvasively direct and focus therapy to disease targets. External magnets can apply forces on drug-coated magnetic nanoparticles, or on living cells that contain particles, and can be used to manipulate them in vivo. Significant progress has been made in developing and testing safe and therapeutic magnetic constructs that can be manipulated by magnetic fields. However, we do not yet have the magnet systems that can then direct those constructs to the right places, in vivo, over human patient distances. We do not yet know where to put the external magnets, how to shape them, or when to turn them on and off to direct particles or magnetized cells-in blood, through tissue, and across barriers-to disease locations. In this article, we consider ear and eye disease targets. Ear and eye targets are too deep and complex to be targeted by a single external magnet, but they are shallow enough that a combination of magnets may be able to direct therapy to them. We focus on how magnetic fields should be shaped (in space and time) to direct magnetic constructs to ear and eye targets.

On the control design and robustness analysis for high-density microcantilever arrays:

In this paper we present a basic model and control design of an array of electrostatically actuated microcantilevers. Part of the main focus of this paper is to study the feasibility and compare the performance of the centralized, decentralized and distributed schemes on a microcantilever array system. Since the implementation of a centralized controller for such systems is impractical, we consider the following two control schemes with localized architecture: (a) a H∞ decentralized controller that completely ignores the dynamics contributed by the neighbors hence treating them as an external disturbance; and (b) a H∞ distributed controller that makes use of information only from its immediate neighbors. In order to have some benchmark performance index, we first design a H ∞ centralized controller for an array of eight microcantilevers. The performance of these controllers are tested via simulations on a finite nonlinear model of the system, and compared with the benchmark performance delivered by the centralized controller. It is seen that the performance delivered by a distributed controller is quite comparable to the performance delivered by the benchmark scheme of a centralized controller. In comparison, the performance of the decentralized controller degrades by more than 100% in terms of resolution. Another main contribution of this paper is the robustness analysis with respect to the modeling uncertainties. This is important, especially in the view of the fabrication errors which result in deviation of actual dynamics of each microcantilever from its model, as well as since the control designs are derived from a linearized model of the cantilever array. In this direction, analysis and simulations of control implementations on perturbed linear as well as nonlinear models of system with finite microcantilever arrays are presented.

Stability of slowly varying spatiotemporal systems

A characterization of stability for slowly varying spatiotemporal systems based on input-output description of the plant and controller is presented. This approach generalizes the results developed for the standard case for slowly time-varying systems. The controller design is based on frozen spatially and temporally invariant descriptions of the plant. In particular, we consider the case where the controllers are not necessarily adjusted for every instance in space and time, and hence are used for some fixed window in time and space before new controllers are implemented. It is shown that the actual spatiotemporally varying system can be stabilized using frozen in space and time controllers, provided the variations in the spatiotemporal dynamics are sufficiently small.

Automated Fluorescence and Reflectance Coregistered 3-D Tissue Imaging System

An automated system was developed to image the 3-D distribution of fluorescent magnetic nanoparticles in tissue samples. It enables easy measurement of magnetic nanoparticle distributions, for small and large tissue samples (currently up to a maximum size of 25 mm × 25 mm × 25 mm), in 3-D, with about 70 resolution in plane and 1 μm in the vertical direction. There is a linear correlation between particle concentration and fluorescence intensity, hence the system provides a quantitative measure of the nanoparticle distribution, but the tissue sample is destroyed during the imaging process. The system was demonstrated by measuring the particle distribution in rat ear and brain samples.

Design and additive manufacturing of MRI gradient coils

The current manufacturing process of MRI gradient coils is a lengthy process because of material property requirements that address high voltages and currents, and complex 3D geometries (necessary to achieve desired gradient profiles and high magnetic field strengths). To address these requirements we developed software and fast 3D printer technology that automates the design, optimization, and manufacturing of these gradient coils. Our design software applies the principles of 3D printing (rapid prototyping) to control the gradient coil manufacturing process. Our 3D printer is the first printer to combine electrical conductors (e.g. silver) and high-grade electrical insulators (e.g., Kapton) for manufacturing MRI gradient coils. We have applied the additive manufacturing (3D printing) methods to the design and manufacturing of ultra-strong and ultra-fast (rise time ≤ 10 μs) magnetic gradient coils for high-performance magnetic resonance imaging (MRI) systems. Experiments with bi-planar 3D-printed gradient coils installed in a tabletop MRI system (0.34 T) show that we can get images with in-plane resolution of 50 μm and good image signal-to-noise in seconds using fast pulse sequences (fast gradient echo).

System identification of spatiotemporally invariant systems

We present a distributed projection algorithm for system identification of spatiotemporally invariant systems. Each subsystem communicates only with its immediate neighbor to share its current estimate along with a cumulative improvement index. Based on the cumulative improvement index, the best estimate available is picked in order to carry out the next iterate. For small estimation error, the scheme switches over to a “smart” averaging routine. The proposed algorithm guarantees to bring the local estimates arbitrarily close to one another. We demonstrate that the proposed scheme has a clear advantage over the standard projection algorithm and is amenable to indirect distributed adaptive control of spatiotemporally invariant systems. Our proposed algorithm is also suitable to address the estimation problem in distributed networks that arise in a variety of applications, such as environment monitoring, target localization and potential sensor network problems.

Modeling and Distributed Control of an Electrostatically Actuated Microcantilever Array

This paper presents a basic model and control design of an array of electrostatically actuated microcantilevers that can be put to use for high throughput applications, such as, multi cantilever imaging applications in atomic force microscopy (AFM). We consider a model of infinite array which belongs to the class of spatially invariant systems, and design a Hinfin distributed controller while making use of the information from only the immediate neighbors. The performance of this controller is tested via simulations on a finite nonlinear model of the system. Based on the achieved resolution and bandwidth, the device holds high potential for AFM applications in contact mode such as, indenting, pushing, cutting, and lithography.

Adaptive Control of Spatially Invariant Systems: A Slowly Varying Approach

We present a general class of adaptive controllers for spatially invariant systems based on certainty-equivalence approach. At each step, the plant is estimated via the distributed projection algorithm as presented in Sarwar , that guarantees to result in a gradually varying spatiotemporal estimated plant for large enough time. Given an instance in space and time, the estimated plant is thought of as a linear spatially invariant system, with the defining operators fixed at that time and space instance. The spatiotemporal local controllers, assumed to exist, are designed to stabilize the corresponding frozen linear spatially invariant systems. We show that as long as the rates of spatiotemporal variations of the estimated plant and the spatiotemporal controller eventually become sufficiently small, a globally stable adaptive scheme can be guaranteed.

Indirect adaptive control of spatially invariant systems

We present a general class of indirect adaptive controllers for spatiotemporally invariant systems. The control design is based on certainty-equivalence approach, where at each step system parameters are estimated and the controller is implemented using the estimated parameters. At each estimation stage a modeling error is committed which affects the output of the plant. We show that under suitable assumptions on the rates of variation of the estimated plant, which follow from utilizing a distributed projection algorithm, a globally stable adaptive scheme can be guaranteed.