From Displacement to Angle: Diamond-Based 3D Rotation Sensing for High-Precision Cellular Force Measurement

TL;DR

This paper introduces a diamond-based 3D rotation sensing method for cellular force measurement, using nanodiamonds and ODMR to improve accuracy and capture complex deformations beyond traditional displacement tracking.

Contribution

The study presents a novel angle-based force measurement technique employing nanodiamonds and ODMR, surpassing displacement methods in precision and deformation analysis.

Findings

Reduces force estimation errors by at least 10%

Achieves sub-degree orientation measurement precision (~0.5°)

Enables detection of complex pillar deformations like twisting

Abstract

Cellular traction forces are conventionally measured by tracking the displacement of beads or micropillars, an approach fundamentally limited by optical diffraction and the classical Euler-Bernoulli beam assumption, which is accurate only when the traction-induced deformation is relatively small while the aspect ratio of micropillars is large. Here we introduce an alternative approach: quantifying force through direct measurement of rotational angle, in addition of displacement of the micropillar, using fluorescent nanodiamonds as embedded 3D orientation markers. Specifically, by integrating optically detected magnetic resonance (ODMR) with laser polarization modulation (LPM), we determine the complete three-dimensional orientation of nanodiamonds attached to PDMS micropillars with sub-degree precision ($\sim$0.5$^\circ$). This angle-based measurement framework bypasses the resolution constraints of displacement tracking and remains valid for stocky beams or when large deformations occur. Finite-element simulations demonstrate that our method reduces force estimation errors by at least 10% compared to conventional displacement-based approaches. Moreover, we successfully capture multidimensional pillar deformations -- including bending and twisting -- that are inaccessible to conventional displacement-only method. Taken together, our work establishes diamond-based angular force microscopy as a high-precision platform for mechanobiology.