Physiologic Doses of Transforming Growth Factor-ß Improve the Composition of Engineered Articular Cartilage.

Conventionally, for cartilage tissue engineering applications, transforming growth factor beta (TGF-ß) is administered at doses that are several orders of magnitude higher than those present during native cartilage development. While these doses accelerate extracellular matrix (ECM) biosynthesis, they may also contribute to features detrimental to hyaline cartilage function, including tissue swelling, type I collagen (COL-I) deposition, cellular hypertrophy, and cellular hyperplasia. In contrast, during native cartilage development, chondrocytes are exposed to moderate TGF-ß levels, which serve to promote strong biosynthetic enhancements while mitigating risks of pathology associated with TGF-ß excesses. Here, we examine the hypothesis that physiologic doses of TGF-ß can yield neocartilage with a more hyaline cartilage-like composition and structure relative to conventionally administered supraphysiologic doses. This hypothesis was examined on a model system of reduced-size constructs (∅2 × 2 mm or ∅3 × 2 mm) comprised of bovine chondrocytes encapsulated in agarose, which exhibit mitigated TGF-ß spatial gradients allowing for an evaluation of the intrinsic effect of TGF-ß doses on tissue development. Reduced-size (∅2 × 2 mm or ∅3 × 2 mm) and conventional-size constructs (∅4-∅6 mm × 2 mm) were subjected to a range of physiologic (0.1, 0.3, 1 ng/mL) and supraphysiologic (3, 10 ng/mL) TGF-ß doses. At day 56, the physiologic 0.3 ng/mL dose yielded reduced-size constructs with native cartilage-matched Young's modulus (EY) (630 ± 58 kPa) and sulfated glycosaminoglycan (sGAG) content (5.9 ± 0.6%) while significantly increasing the sGAG-to-collagen ratio, leading to significantly reduced tissue swelling relative to constructs exposed to the supraphysiologic 10 ng/mL TGF-ß dose. Furthermore, reduced-size constructs exposed to the 0.3 ng/mL dose exhibited a significant reduction in fibrocartilage-associated COL-I and a 77% reduction in the fraction of chondrocytes present in a clustered morphology, relative to the supraphysiologic 10 ng/mL dose (p < 0.001). EY was significantly lower for conventional-size constructs exposed to physiologic doses due to TGF-ß transport limitations in these larger tissues (p < 0.001). Overall, physiologic TGF-ß appears to achieve an important balance of promoting requisite ECM biosynthesis, while mitigating features detrimental to hyaline cartilage function. While reduced-size constructs are not suitable for the repair of clinical-size cartilage lesions, insights from this work can inform TGF-ß dosing requirements for emerging scaffold release or nutrient channel delivery platforms capable of achieving uniform delivery of physiologic TGF-ß doses to larger constructs required for clinical cartilage repair.

Physiologic Doses of TGF-ß Improve the Composition of Engineered Articular Cartilage.

For cartilage regeneration applications, transforming growth factor beta (TGF-ß) is conventionally administered at highly supraphysiologic doses (10-10,000 ng/mL) in an attempt to cue cells to fabricate neocartilage that matches the composition, structure, and functional properties of native hyaline cartilage. While supraphysiologic doses enhance ECM biosynthesis, they are also associated with inducing detrimental tissue features, such as fibrocartilage matrix deposition, pathologic-like chondrocyte clustering, and tissue swelling. Here we investigate the hypothesis that moderated TGF-ß doses (0.1-1 ng/mL), akin to those present during physiological cartilage development, can improve neocartilage composition. Variable doses of media-supplemented TGF-ß were administered to a model system of reduced-size cylindrical constructs (Ø2-Ø3 mm), which mitigate the TGF-ß spatial gradients observed in conventional-size constructs (Ø4-Ø6 mm), allowing for a novel assessment of the intrinsic effect of TGF-ß doses on macroscale neocartilage properties and composition. The administration of physiologic TGF-ß to reduced-size constructs yields neocartilage with native-matched sGAG content and mechanical properties while providing a more hyaline cartilage-like composition, marked by: 1) reduced fibrocartilage-associated type I collagen, 2) 77% reduction in the fraction of cells present in a clustered morphology, and 3) 45% reduction in the degree of tissue swelling. Physiologic TGF-ß appears to achieve an important balance of promoting requisite ECM biosynthesis, while mitigating hyaline cartilage compositional deficits. These results can guide the development of novel physiologic TGF-ß-delivering scaffolds to improve the regeneration clinical-sized neocartilage tissues.

Information optimization of laser scanning microscopes for real-time feedback-driven single particle tracking.

Real-time feedback-driven single particle tracking (RT-FD-SPT) is a class of microscopy techniques that uses measurements of finite excitation/detection volume in a feedback control loop to actuate that volume and track with high spatio-temporal resolution a single particle moving in three dimensions. A variety of methods have been developed, each defined by a set of user-defined choices. Selection of those values is typically done through ad hoc, off-line tuning for the best perceived performance. Here we present a mathematical framework, based on optimization of the Fisher information, to select those parameters such that the best information is acquired for estimating parameters of interest, such as the location of the particle, specifics of the excitation beam such as its dimensions or peak intensity, or the background noise. For concreteness, we focus on tracking of a fluorescently-labeled particle and apply this framework to determine the optimal parameters for three existing fluorescence-based RT-FD-SPT techniques with respect to particle localization.

Synthetic Stochastic Motion Platform for Testing Single Particle Tracking Microscopes.

We describe the design and implementation of a control system for testing the performance of single particle tracking microscopes with the method of synthetic motion. Single particle tracking (SPT) has become a common and powerful tool in the study of biomolecular transport in cellular biology, providing the ability to track individual biological macromolecules in their native environment. Existing methods for testing SPT techniques rely on physical simulations and there is a clear need for experimental-based schemes for both comparing different approaches and for characterizing the accuracy and precision of techniques on particular experimental setups. Synthetic motion, that is, using an actuator such as a nanopositioning stage to drive a particle along a known ground-truth trajectory, is a means for achieving these ends. However, the resolution, accuracy, and flexibility of this method is limited by the actuator static and dynamic characteristics. In this work we apply system identification and model inverse feedforward control to increase actuator bandwidth and address some common actuator nonlinearities, develop a set of dimensionless numbers that describe system limitations, and provide a set of guidelines for the practical use of synthetic motion in SPT.

Real-Time Feedback-Driven Single-Particle Tracking: A Survey and Perspective.

Real-time feedback-driven single-particle tracking (RT-FD-SPT) is a class of techniques in the field of single-particle tracking that uses feedback control to keep a particle of interest in a detection volume. These methods provide high spatiotemporal resolution on particle dynamics and allow for concurrent spectroscopic measurements. This review article begins with a survey of existing techniques and of applications where RT-FD-SPT has played an important role. Each of the core components of RT-FD-SPT are systematically discussed in order to develop an understanding of the trade-offs that must be made in algorithm design and to create a clear picture of the important differences, advantages, and drawbacks of existing approaches. These components are feedback tracking and control, ranging from simple proportional-integral-derivative control to advanced nonlinear techniques, estimation to determine particle location from the measured data, including both online and offline algorithms, and techniques for calibrating and characterizing different RT-FD-SPT methods. Then a collection of metrics for RT-FD-SPT is introduced to help guide experimentalists in selecting a method for their particular application and to help reveal where there are gaps in the techniques that represent opportunities for further development. Finally, this review is concluded with a discussion on future perspectives in the field.

Tracking Multiple Diffusing Particles Using Information Optimal Control.

We study the problem of tracking multiple diffusing particles using a laser scanning fluorescence microscope. The goal is to design trajectories for the laser to maximize the information contained in the measured intensity signal about the particles' trajectories. Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it. In the higher level controller, we decide which particle should be observed at each instant, with the goal of efficiently estimating each particle position while not losing track of any of them. Using simulations, we show that this technique is able to collect photons efficiently and to track multiple particles with low position estimation error.

An Estimation Algorithm for General Linear Single Particle Tracking Models with Time-Varying Parameters.

Single Particle Tracking (SPT) is a powerful class of methods for studying the dynamics of biomolecules inside living cells. The techniques reveal the trajectories of individual particles, with a resolution well below the diffraction limit of light, and from them the parameters defining the motion model, such as diffusion coefficients and confinement lengths. Most existing algorithms assume these parameters are constant throughout an experiment. However, it has been demonstrated that they often vary with time as the tracked particles move through different regions in the cell or as conditions inside the cell change in response to stimuli. In this work, we propose an estimation algorithm to determine time-varying parameters of systems that discretely switch between different linear models of motion with Gaussian noise statistics, covering dynamics such as diffusion, directed motion, and Ornstein-Uhlenbeck dynamics. Our algorithm consists of three stages. In the first stage, we use a sliding window approach, combined with Expectation Maximization (EM) to determine maximum likelihood estimates of the parameters as a function of time. These results are only used to roughly estimate the number of model switches that occur in the data to guide the selection of algorithm parameters in the second stage. In the second stage, we use Change Detection (CD) techniques to identify where the models switch, taking advantage of the off-line nature of the analysis of SPT data to create non-causal algorithms with better precision than a purely causal approach. Finally, we apply EM to each set of data between the change points to determine final parameter estimates. We demonstrate our approach using experimental data generated in the lab under controlled conditions.

Model Segmentation in Single Particle Tracking.

In this paper, we implement and compare two different change detection techniques applied to determining the time points in Single Particle Tracking (SPT) data where the particle changes the dynamic model of motion. The goal is to use this change detection to segment the data in order to estimate the relevant parameters of such models. We consider two well-known statistics commonly used for change detection: the likelihood ratio test (LRT) and the Kullback-Leibler divergence (KLD). We assume that our time-varying system is subject to step-like changes in the parameters that drive the process. The techniques are then applied to experimental data acquired on a microscope under controlled settings to validate our results.

Information Optimal Control for Single Particle Tracking Microscopy.

We consider the problem of designing a control policy for a laser scanning microscope (LSM) which will minimize the estimation uncertainty when identifying the state and motion model of a fluorescent biological particle. Using the information optimal design framework we pose an optimization problem which seeks to maximize the Fisher information of the particle's state. We then apply optimal control methods to determine the laser trajectory that maximizes a criterion based on the Fisher information. The resulting optimal control policy is a Bang-Singular control which moves the laser to the set of measurement locations that maximize the rate of information accumulation. Simulations demonstrate the ability of the resulting control system to position the laser to measure the particles location with a minimum uncertainty.

Volumetric chemical imaging in vivo by a remote-focusing stimulated Raman scattering microscope.

Operable under ambient light and providing chemical selectivity, stimulated Raman scattering (SRS) microscopy opens a new window for imaging molecular events on a human subject, such as filtration of topical drugs through the skin. A typical approach for volumetric SRS imaging is through piezo scanning of an objective lens, which often disturbs the sample and offers a low axial scan rate. To address these challenges, we have developed a deformable mirror-based remote-focusing SRS microscope, which not only enables high-quality volumetric chemical imaging without mechanical scanning of the objective but also corrects the system aberrations simultaneously. Using the remote-focusing SRS microscope, we performed volumetric chemical imaging of living cells and captured in real time the dynamic diffusion of topical chemicals into human sweat pores.

Feedforward Control for Single Particle Tracking Synthetic Motion.

Single particle tracking (SPT) is a method to study the transport of biomolecules with nanometer resolution. Unfortunately, recent reports show that systematic errors in position localization and uncertainty in model parameter estimates limits the utility of these techniques in studying biological processes. There is a need for an experimental method with a known ground-truth that tests the total SPT system (sample, microscope, algorithm) on both localization and estimation of model parameters. Synthetic motion is a known ground-truth method that moves a particle along a trajectory. This trajectory is a realization of a Markovian stochastic process that represents models of biomolecular transport. Here we describe a platform for creating synthetic motion using common equipment and well-known, simple methods that can be easily adopted by the biophysics community. In this paper we describe the synthetic motion system and calibration to achieve nanometer accuracy and precision. Steady state input-output characteristics are analyzed with both line scans and grid scans. The resulting relationship is described by an affine transformation, which is inverted and used as a prefilter. Model inverse feed forward control is used to increase the system bandwidth. The system model was identified from frequency response function measurements using an integrated stepped-sine with coherent demodulation built into the FPGA controller. Zero magnitude error tracking controller method was used to invert non-minimum phase zeros to achieve a stable discrete time feed forward filter.

Estimation of general time-varying single particle tracking linear models using local likelihood.

In this work, we study a general approach to the estimation of single particle tracking models with time-varying parameters. The main idea is to use local Maximum Likelihood (ML), applying a sliding window over the data and estimating the model parameters in each window. We combine local ML with Expectation Maximization to iteratively find the ML estimate in each window, an approach that is amenable to generalization to nonlinear models. Results using controlled-experimental data generated in our lab show that our proposed algorithm is able to track changes in the parameters as they evolve during a trajectory under real-world experimental conditions, outperforming other algorithms of similar nature.

Monte Carlo Simulation of Brownian Motion using a Piezo-Actuated Microscope Stage.

Single particle tracking is a powerful tool for studying and understanding the motions of biological macromolecules integral to cellular processes. In the past three decades there has been continuous and rapid development of these techniques in both optical microscope design and in algorithms to estimate the statistics and positions of the molecule's trajectory. Although there has been great progress, comparison between different microscope configurations and estimation algorithms has been difficult beyond simulated data. In this paper we explore using a piezo actuated microscope stage to reproduce Brownian motion. Our goal is to use this as a tool to test performance of single particle tracking optical microscopes and estimation algorithms. In this study, Monte Carlo simulations were used to assess the ability of piezo actuated microscope stages for reproducing Brownian motion. Surprisingly, the dynamics of the stage together with configuration of the system allow for preservation of the Brownian motion statistics. Further, feed forward model inverse control allows for low error tracking of Brownian motion trajectories over a wide range of diffusion constants, varying stage response times, and trajectory discrete time steps. These results show great promise in using a piezo actuated microscope stage for testing single particle tracking experimental setups.

Axial localization with modulated-illumination extended-depth-of-field microscopy.

High-speed volumetric imaging represents a challenge in microscopy applications. We demonstrate a technique for acquiring volumetric images based on the extended depth of field microscopy with a fast focal scan and modulated illumination. By combining two frames with different illumination ramps, we can perform local depth ranging of the sample at speeds of up to half the camera frame rate. Our technique is light efficient, provides diffraction-limited resolution, enables axial localization that is largely independent of sample size, and can be operated with any standard widefield microscope based on fluorescence or darkfield contrast as a simple add-on. We demonstrate the accuracy of axial localization and applications of the technique to various dynamic extended samples, including in-vivo mouse brain.

Dual fluorescence-absorption deconvolution applied to extended-depth-of-field microscopy.

Fast imaging over large volumes can be obtained in a simple manner with extended-depth-of-field (EDOF) microscopy. A standard technique of Wiener deconvolution can correct for the blurring inherent in EDOF images. We compare Wiener deconvolution with an alternative, parameter-free technique based on the dual reconstruction of fluorescence and absorption layers in a sample. This alternative technique provides significantly enhanced reconstruction contrast owing to a quadratic positivity constraint that intrinsically favors sparse solutions. We demonstrate the advantages of this technique with mouse neuronal images acquired in vivo.

Extended depth-of-field microscopy with a high-speed deformable mirror.

We present a wide-field fluorescence microscopy add-on that provides a fast, light-efficient extended depth-of-field (EDOF) using a deformable mirror with an update rate of 20 kHz. Out-of-focus contributions in the raw EDOF images are suppressed with a deconvolution algorithm derived directly from the microscope 3D optical transfer function. Demonstrations of the benefits of EDOF microscopy are shown with GCaMP-labeled mouse brain tissue.