Indentation Measurements to Validate Dynamic Elasticity Imaging Methods

Abstract

We describe macro-indentation techniques for estimating the elastic modulus of soft hydrogels. Our study describes (a) conditions under which quasi-static indentation can validate dynamic shear-wave imaging estimates and (b) how each of these techniques uniquely biases modulus estimates as they couple to the sample geometry. Harmonic shear waves between 25 and 400 Hz were imaged using ultrasonic Doppler and optical coherence tomography methods to estimate shear dispersion. From the shear-wave speed of sound, average elastic moduli of homogeneous samples were estimated. These results are compared directly with macroscopic indentation measurements measured two ways. One set of measurements applied Hertzian theory to the loading phase of the force–displacement curves using samples treated to minimize surface adhesion forces. A second set of measurements applied Johnson–Kendall–Roberts theory to the unloading phase of the force–displacement curve when surface adhesions were significant. All measurements were made using gelatin hydrogel samples of different sizes and concentrations. Agreement within 5% among elastic modulus estimates was achieved for a range of experimental conditions. Consequently, a simple quasi-static indentation measurement using a common gel can provide elastic modulus measurements that help validate dynamic shear-wave imaging estimates.