Advanced data analysis for traction force microscopy and data-driven discovery of physical equations

The plummeting cost of collecting and storing data and the increasingly available computational power in the last decade have led to the emergence of new data analysis approaches in various scientific fields. Frequently, the new statistical methodology is employed for analyzing data involving incomplete or unknown information. In this thesis, new statistical approaches are developed for improving the accuracy of traction force microscopy (TFM) and data-driven discovery of physical equations. TFM is a versatile method for the reconstruction of a spatial image of the traction forces exerted by cells on elastic gel substrates. The traction force field is calculated from a linear mechanical model connecting the measured substrate displacements with the sought-for cell-generated stresses in real or Fourier space, which is an inverse and ill-posed problem. This inverse problem is commonly solved making use of regularization methods. Here, we systematically test the performance of new regularization methods and Bayesian inference for quantifying the parameter uncertainty in TFM. We compare two classical schemes, L1- and L2-regularization with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. We find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. We further combine the Bayesian L2 regularization with the computational speed of Fast Fourier Transform algorithms to develop a fully automated method for noise reduction and robust, standardized traction-force reconstruction that we call Bayesian Fourier transform traction cytometry (BFTTC). This method is made freely available as a software package with graphical user-interface for intuitive usage. Using synthetic data and experimental data, we show that these Bayesian methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Next, we employ our methodology developed for the solution of inverse problems for automated, data-driven discovery of ordinary differential equations (ODEs), partial differential equations (PDEs), and stochastic differential equations (SDEs). To find the equations governing a measured time-dependent process, we construct dictionaries of non-linear candidate equations. These candidate equations are evaluated using the measured data. With this approach, one can construct a likelihood function for the candidate equations. Optimization yields a linear, inverse problem which is to be solved under a sparsity constraint. We combine Bayesian compressive sensing using Laplace priors with automated thresholding to develop a new approach, namely automatic threshold sparse Bayesian learning (ATSBL). ATSBL is a robust method to identify ODEs, PDEs, and SDEs involving Gaussian noise, which is also referred to as type I noise. We extensively test the method with synthetic datasets describing physical processes. For SDEs, we combine data-driven inference using ATSBL with a novel entropy-based heuristic for discarding data points with high uncertainty. Finally, we develop an automatic iterative sampling optimization technique akin to Umbrella sampling. Therewith, we demonstrate that data-driven inference of SDEs can be substantially improved through feedback during the inference process if the stochastic process under investigation can be manipulated either experimentally or in simulations

Review : Deep learning in electron microscopy

Deep learning is transforming most areas of science and technology, including electron microscopy. This review paper offers a practical perspective aimed at developers with limited familiarity. For context, we review popular applications of deep learning in electron microscopy. Following, we discuss hardware and software needed to get started with deep learning and interface with electron microscopes. We then review neural network components, popular architectures, and their optimization. Finally, we discuss future directions of deep learning in electron microscopy

How to Recognize and Control Interfacial Phenomena That Hinder the Advancement of Clean Energy Technologies

Nuclear energy and electrochemical energy storage, such as batteries, are key parts to the clean energy transition of critical infrastructure. This work aims to define, monitor, and modify interfacial layers that would improve the utility of materials in harsh environments seen in nuclear and energy storage applications. First, the studying of zirconium alloys, which is used as nuclear cladding, was done to better understand the degradation mechanisms within an extreme environment. High-resolution characterization techniques were used to correlate corrosion mechanisms to equivalent circuit models from novel in-pile electrochemical impedance spectroscopy sensors. Advancement in this sensor technology could provide further insight and monitoring of the complex degradation mechanisms in a harsh nuclear core environment. A novel method was developed to spatially map Raman spectral features throughout the oxide cross-section, revealing a direct correlation between tetragonal zirconia phase and compressive stress, thus supporting the theory of a stress-induced breakaway phenomenon. Additionally, a comparison of interface- and relaxed-tetragonal phase revealed a difference in stabilization mechanisms, where relaxed-tetragonal phase is stabilized solely from sub-stoichiometric contributions. Coupling Raman mapping with elemental analysis via energy dispersive X-ray spectroscopy and scanning Kelvin probe force microscopy led to a distinction of secondary-phase particles and their nobility relative to surrounding zirconium oxide and metal. Lastly, a p-n junction at the tetragonal/monoclinic zirconia interface was observed, supporting the theory that the tetragonal layer at the metal/oxide interface provides an additional barrier to an otherwise diffusion-limited oxidation mechanism. Other interfacial studies were conducted on next-generation battery anodes. High-capacity lithium, deemed the “Holy Grail” of battery materials, undergoes unstable interactions in most, if not all, environments. In a cell, this causes poor cycle life and/or possible safety concerns via dendritic-driven short circuiting. Novel development of lithium-metal batteries was accomplished firstly with a facile design of a closed-host, porous/dense bi-layer interfacial structure formed on lithium through a two-step ex situ/in situ process, only made possible with an electrolyte additive included in the cell. This design prevented dendrite growth, improved interfacial flexibility and ionic conduction when compared to a traditional LiF coating, reduced volume fluctuations, and prevented extensive parasitic reactions. In summary, the works presented here were done in effort to better understand and control interfacial mechanisms in both nuclear energy and energy storage fields

In situ deformation transmission electron microscopy investigation of the mechanical behaviours of nanomaterials

Due to their superior properties, nanomaterials (NMs) have many significant applications. The mechanical properties of NMs including nanowires (NWs) and nanofilms are a crucial factor in designing devices where predictable and reproducible operation is important. However, due to the difficulty of mechanical testing at nanoscale, mechanical properties of NMs have not been as extensively investigated. This thesis aims to apply an in situ deformation transmission electron microscopy (TEM) technique combined with finite element analysis (FEA) to investigate the mechanical behaviours of NMs. The first chapter of this thesis presents a summary of the applications, synthesis methods, nanomechanical characterisation techniques, and mechanical behaviours of nanomaterials. The second chapter provides a general description of the methods used in this thesis. Details of the experimental and modelling procedures are also described. In the third chapter, quantitative investigation of the effects of loading misalignment and tapering of NWs on the measured compression and tensile mechanical properties is presented. In the fourth chapter, the Young’s moduli of GaAs NWs with two distinct structures – defect-free single crystalline wurtzite and wurtzite containing a high density of stacking faults (SFs) – are measured. The presence of a high density of SFs was found to increase the Young’s modulus by 12%. Determination of the elastic modulus of NMs with sizes of a few nanometres is a significant challenge. In the fifth chapter, a method combining in situ compression TEM and FEA is developed to measure the Young’s modulus of nanoscale films with thicknesses down to ~ 2 nm by using a core–shell NW structure. Major conclusions are drawn from this PhD research in the last chapter. Some possible future work is proposed as extension of what has been achieved

Inverse and forward modeling tools for biophotonic data

Biophotonic data require specific treatments due to the difficulty of directly extracting information from them. Therefore, artificial intelligence tools including machine learning and deep learning brought into play. These tools can be grouped into inverse modeling, preprocessing and data modeling categories. In each of these three categories, one research question was investigated. First, the aim was to develop a method that can acquire the Raman-like spectra from coherent anti-Stokes Raman scattering (CARS) spectra without apriori knowledge. In general, CARS spectra suffer from the non-resonant background (NRB) contribution, and existing methods were commonly implemented to remove it. However, these methods were not able to completely remove the NRB and need additional preprocessing afterward. Therefore, deep learning via the long-short-term memory network was applied and outperformed these existing methods. Then, a denoising technique via deep learning was developed for reconstructing high-quality (HQ) multimodal images (MM) from low-quality (LQ) ones. Since the measurement of HQ MM images is time-consuming, which is impractical for clinical applications, we developed a network, namely incSRCNN, to directly predict HQ images using only LQ ones. This network shows better performance when compared with standard methods. Finally, we intended to improve the accuracy of the classification model in particular when LQ Raman data or Raman data with varying quality are obtained. Therefore, a novel method based on functional data analysis was implemented, which converts the Raman data into functions and then applies functional dimension reduction followed by a classification method. The results showed better performance for the functional approach in comparison with the classical method

Mechanics of Interactions and Atomic-Scale Wear of Tips ian Amplitude Modulation Atomic Force Microscopy

Wear is one of the main factors that hinders the performance of probes for atomic force microscopy (AFM), including for the widely-used amplitude modulation (AM-AFM) mode. Unfortunately, a comprehensive scientific understanding of nanoscale wear is lacking. We initially investigate and discuss the mechanics of the tip-sample interaction in AM-AFM. Starting from existing analytical formulations, we introduce a method for conveniently choosing an appropriate probe and free oscillation amplitude that avoids exceeding a critical contact stress to minimize tip/sample damage. We then introduce a protocol for conducting consistent and quantitative AM-AFM wear experiments. The protocol involves determining the tip-sample contact geometry, calculating the peak repulsive force and normal stress over the course of the wear test, and quantifying the wear volume using high-resolution transmission electron microscopy (TEM) imaging. The peak repulsive tip-sample interaction force is estimated from a closed-form equation accompanied by an effective tip radius measurement procedure, which combines TEM and blind tip reconstruction. The contact stress is estimated by applying Derjaguin-Müller-Toporov contact mechanics model and also numerically solving a general contact mechanics model recently developed for the adhesive contact of arbitrary axisymmetric punch shapes. We discuss the important role that the assumed tip shape geometry plays in calculating both the interaction forces and the contact stresses. We find that contact stresses are significantly affected by the tip geometry, while the peak repulsive force is mainly determined by experimentally-controlled parameters, most critically, the free oscillation amplitude. The applicability of this protocol is demonstrated experimentally by assessing the performance of diamond-like carbon-coated and silicon nitride-coated silicon probes scanned over ultrananocrystalline diamond substrates in repulsive-mode AM-AFM. There is no sign of fracture or plastic deformation in the case of diamond-like carbon (DLC); wear could be characterized as a gradual atom-by-atom process. In contrast, silicon nitride wears through apparent removal of the cluster of atoms and plastic deformation. DLC\u27s gradual wear mechanism can be described using reaction rate theory, which predicts an exponential dependence of the rate of atom removal on the contact average normal stress, allowing us to estimate kinetic parameters governing the wear process