Optimal calibration of optical tweezers with arbitrary integration time and sampling frequencies: a general framework [Invited].

Optical tweezers (OT) have become an essential technique in several fields of physics, chemistry, and biology as precise micromanipulation tools and microscopic force transducers. Quantitative measurements require the accurate calibration of the trap stiffness of the optical trap and the diffusion constant of the optically trapped particle. This is typically done by statistical estimators constructed from the position signal of the particle, which is recorded by a digital camera or a quadrant photodiode. The finite integration time and sampling frequency of the detector need to be properly taken into account. Here, we present a general approach based on the joint probability density function of the sampled trajectory that corrects exactly the biases due to the detector's finite integration time and limited sampling frequency, providing theoretical formulas for the most widely employed calibration methods: equipartition, mean squared displacement, autocorrelation, power spectral density, and force reconstruction via maximum-likelihood-estimator analysis (FORMA). Our results, tested with experiments and Monte Carlo simulations, will permit users of OT to confidently estimate the trap stiffness and diffusion constant, extending their use to a broader set of experimental conditions.

Flexion-rotation test and C0-C2 axial rotation test. Are they equally reliable for novice clinicians?

OBJECTIVE: To analyse the inter- and intra-examiner reliability for the neck flexion-rotation test and the C0-C2 axial rotation test when applied in asymptomatic subjects by two novice physiotherapists. DESIGN: Repeated measures reliability study design. The study was approved by the Research Ethics Committee of [X], in compliance with the Declaration of Helsinki (CSEULS-PI: 004/2020). METHODS: 32 asymptomatic adults were included, recruited by convenience sampling. Two sessions were scheduled for each subject, with an intersession break of 30 min. Two inexperienced raters blinded to their own previous and peer results performed three movements to both sides using the flexion-rotation test and the C0-C2 axial rotation test in randomised order of rater, test and direction. A third researcher collected the data measured by inertial sensors and displayed to the Pro Motion Capture software. RESULTS: Both raters showed good-excellent intra-examiner reliability (ICC(2,3) ranging from 0.88 to 0.94) and moderate to good inter-examiner reliability (ICC(2,3) ranging from 0.58 to 0.86) to measure the rotation ROM with the FRT. The C0-C2 axial rotation test resulted in poor to moderate intra-examiner reliability (ICC(2,3) ranging from 0.33 to 0.74) and poor inter-examiner reliability using (ICC(2,3) ranging from 0.16 to 0.37). CONCLUSION: Although performed by novice raters, the FRT showed good to excellent intra and inter-examiner reliability. Results for the C0-C2 axial rotation test were less reliable. We suggest that novice physiotherapists use the FRT instead of the C0-C2 axial rotation test in order to determine C1-C2 dysfunction.

High-performance reconstruction of microscopic force fields from Brownian trajectories.

The accurate measurement of microscopic force fields is crucial in many branches of science and technology, from biophotonics and mechanobiology to microscopy and optomechanics. These forces are often probed by analysing their influence on the motion of Brownian particles. Here we introduce a powerful algorithm for microscopic force reconstruction via maximum-likelihood-estimator analysis (FORMA) to retrieve the force field acting on a Brownian particle from the analysis of its displacements. FORMA estimates accurately the conservative and non-conservative components of the force field with important advantages over established techniques, being parameter-free, requiring ten-fold less data and executing orders-of-magnitude faster. We demonstrate FORMA performance using optical tweezers, showing how, outperforming other available techniques, it can identify and characterise stable and unstable equilibrium points in generic force fields. Thanks to its high performance, FORMA can accelerate the development of microscopic and nanoscopic force transducers for physics, biology and engineering.