Martin Lysy

Calibration of higher eigenmodes of cantilevers

A method is presented for calibrating the higher eigenmodes (resonant modes) of atomic force microscopy cantilevers that can be performed prior to any tip-sample interaction. The method leverages recent efforts in accurately calibrating the first eigenmode by providing the higher-mode stiffness as a ratio to the first mode stiffness. A one-time calibration routine must be performed for every cantilever type to determine a power-law relationship between stiffness and frequency, which is then stored for future use on similar cantilevers. Then, future calibrations only require a measurement of the ratio of resonant frequencies and the stiffness of the first mode. This method is verified through stiffness measurements using three independent approaches: interferometric measurement, AC approach-curve calibration, and finite element analysis simulation. Power-law values for calibrating higher-mode stiffnesses are reported for several cantilever models. Once the higher-mode stiffnesses are known, the amplitude of each mode can also be calibrated from the thermal spectrum by application of the equipartition theorem.

Model Comparison and Assessment for Single Particle Tracking in Biological Fluids

ABSTRACT State-of-the-art techniques in passive particle-tracking microscopy provide high-resolution path trajectories of diverse foreign particles in biological fluids. For particles on the order of 1 μm diameter, these paths are generally inconsistent with simple Brownian motion. Yet, despite an abundance of data confirming these findings and their wide-ranging scientific implications, stochastic modeling of the complex particle motion has received comparatively little attention. Even among posited models, there is virtually no literature on likelihood-based inference, model comparisons, and other quantitative assessments. In this article, we develop a rigorous and computationally efficient Bayesian methodology to address this gap. We analyze two of the most prevalent candidate models for 30-sec paths of 1 μm diameter tracer particles in human lung mucus: fractional Brownian motion (fBM) and a Generalized Langevin Equation (GLE) consistent with viscoelastic theory. Our model comparisons distinctly favor GLE over fBM, with the former describing the data remarkably well up to the timescales for which we have reliable information. Supplementary materials for this article are available online.

Functional derivatives applied to error propagation of uncertainties in topography to large-aperture scintillometer-derived heat fluxes

Abstract. Scintillometer measurements allow for estimations of the refractive index structure parameter Cn2 over large areas in the atmospheric surface layer. Turbulent fluxes of heat and momentum are inferred through coupled sets of equations derived from the Monin–Obukhov similarity hypothesis. One-dimensional sensitivity functions have been produced that relate the sensitivity of heat fluxes to uncertainties in single values of beam height over flat terrain. However, real field sites include variable topography. We develop here, using functional derivatives, the first analysis of the sensitivity of scintillometer-derived sensible heat fluxes to uncertainties in spatially distributed topographic measurements. Sensitivity is shown to be concentrated in areas near the center of the beam path and where the underlying topography is closest to the beam height. Relative uncertainty contributions to the sensible heat flux from uncertainties in topography can reach 20% of the heat flux in some cases. Uncertainty may be greatly reduced by focusing accurate topographic measurements in these specific areas. A new two-dimensional variable terrain sensitivity function is developed for quantitative error analysis. This function is compared with the previous one-dimensional sensitivity function for the same measurement strategy over flat terrain. Additionally, a new method of solution to the set of coupled equations is produced that eliminates computational error.

Stochastic simulation of tip-sample interactions in atomic force microscopy

Atomic force microscopy (AFM) simulators, which are used to gain insight into tip-sample physics and data interpretation, so far have been optimized for modeling deterministic cantilever dynamics. In this article, we demonstrate a method for semi-empirical simulation of the stochastic dynamics of tip-sample interactions. The detection, force, and displacement noises are separately generated directly from their numerically defined power spectral densities and used to simulate a force spectroscopy experiment in water at the mica interface. Mechanical noise of the AFM is shown to dominate over thermal noise of the cantilever upon interaction with the last two hydration layers.

Maximum likelihood estimation for single particle, passive microrheology data with drift

Volume limitations and low yield thresholds of biological fluids have led to widespread use of passive microparticle rheology. The mean-squared-displacement (MSD) statistics of bead position time series (bead paths) are either applied directly to determine the creep compliance [Xu et al., Rheol. Acta 37, 387–398 (1998)] or transformed to determine dynamic storage and loss moduli [Mason and Weitz, Phys. Rev. Lett. 74, 1250–1253 (1995)]. A prevalent hurdle arises when there is a nondiffusive experimental drift in the data. Commensurate with the magnitude of drift relative to diffusive mobility, quantified by a Peclet number, the MSD statistics are distorted, and thus the path data must be “corrected” for drift. The standard approach is to estimate and subtract the drift from particle paths, and then calculate MSD statistics. We present an alternative, parametric approach using maximum likelihood estimation that simultaneously fits drift and diffusive model parameters from the path data; the MSD statistics (and consequently the compliance and dynamic moduli) then follow directly from the best-fit model. We illustrate and compare both methods on simulated path data over a range of Peclet numbers, where exact answers are known. We choose fractional Brownian motion as the numerical model, because it affords tunable, subdiffusive MSD statistics consistent with typical 30 s long, experimental observations of microbeads in several biological fluids. Finally, we apply and compare both methods on data from human bronchial epithelial cell culture mucus.

A Multiresolution Method for Parameter Estimation of Diffusion Processes

Diffusion process models are widely used in science, engineering, and finance. Most diffusion processes are described by stochastic differential equations in continuous time. In practice, however, data are typically observed only at discrete time points. Except for a few very special cases, no analytic form exists for the likelihood of such discretely observed data. For this reason, parametric inference is often achieved by using discrete-time approximations, with accuracy controlled through the introduction of missing data. We present a new multiresolution Bayesian framework to address the inference difficulty. The methodology relies on the use of multiple approximations and extrapolation and is significantly faster and more accurate than known strategies based on Gibbs sampling. We apply the multiresolution approach to three data-driven inference problems, one of which features a multivariate diffusion model with an entirely unobserved component.

Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery

Abstract In mucosal drug delivery, two design goals are desirable: 1) insure drug passage through the mucosal barrier to the epithelium prior to drug removal from the respective organ via mucus clearance; and 2) design carrier particles to achieve a prescribed arrival time and drug uptake schedule at the epithelium. Both goals are achievable if one can control “one‐sided” diffusive passage times of drug carrier particles: from deposition at the mucus interface, through the mucosal barrier, to the epithelium. The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake. For 100 nm and smaller drug‐loaded nanoparticulates, as well as pure drug powders or drug solutions, diffusion is normal (i.e., Brownian) and rapid, easily passing through the mucosal barrier prior to clearance. Major challenges in quantitative control over mucosal drug delivery lie with larger drug‐loaded nanoparticulates that are comparable to or larger than the pores within the mucus gel network, for which diffusion is not simple Brownian motion and typically much less rapid; in these scenarios, a timescale competition ensues between particle passage through the mucus barrier and mucus clearance from the organ. In the lung, as a primary example, coordinated cilia and air drag continuously transport mucus toward the trachea, where mucus and trapped cargo are swallowed into the digestive tract. Mucus clearance times in lung airways range from minutes to hours or significantly longer depending on deposition in the upper, middle, lower airways and on lung health, giving a wide time window for drug‐loaded particle design to achieve controlled delivery to the epithelium. We review the physical and chemical factors (of both particles and mucus) that dictate particle diffusion in mucus, and the technological strategies (theoretical and experimental) required to achieve the design goals. First we describe an idealized scenario — a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion — where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one‐sided, diffusive passage time distribution. Furthermore, we describe how the theory of Brownian motion provides the scaling of one‐sided diffusive passage times with respect to mucus viscosity and layer depth, and under reasonable caveats, one can also prescribe passage time scaling due to heterogeneity in viscosity and layer depth. Small‐molecule drugs and muco‐inert, drug‐loaded carrier particles 100 nm and smaller fall into this class of rigorously controllable passage times for drug delivery. Second we describe the prevalent scenarios in which drug‐loaded carrier particles in mucus violate simple Brownian motion, instead exhibiting anomalous sub‐diffusion, for which all theoretical control over diffusive passage times is lost, and experiments are prohibitive if not impossible to measure one‐sided passage times. We then discuss strategies to overcome these roadblocks, requiring new particle‐tracking experiments and emerging advances in theory and computation of anomalous, sub‐diffusive processes that are necessary to predict and control one‐sided particle passage times from deposition at the mucosal interface to epithelial uptake. We highlight progress to date, remaining hurdles, and prospects for achieving the two design goals for 200 nm and larger, drug‐loaded, non‐dissolving, nanoparticulates. Graphical Abstract Figure. No Caption available.