Non-contact, ultrasound-based indentation method for measuring elastic properties of biological tissues using harmonic motion imaging (HMI)

Abstract

Noninvasive measurement of mechanical properties of biological tissues in vivo could play a significant role in improving the current understanding of tissue biomechanics. In this study, we propose a method for measuring elastic properties non-invasively by using internal indentation as generated by harmonic motion imaging (HMI). In HMI, an oscillating acoustic radiation force is produced by a focused ultrasound transducer at the focal region, and the resulting displacements are estimated by tracking radiofrequency signals acquired by an imaging transducer. In this study, the focal spot region was modeled as a rigid cylindrical piston that exerts an oscillatory, uniform internal force to the underlying tissue. The HMI elastic modulus EHMI was defined as the ratio of the applied force to the axial strain measured by 1D ultrasound imaging. The accuracy and the precision of the EHMI estimate were assessed both numerically and experimentally in polyacrylamide tissue-mimicking phantoms. Initial feasibility of this method in soft tissues was also shown in canine liver specimens in vitro. Very good correlation and agreement was found between the measured Young's modulus and the HMI modulus in the numerical study (r(2) > 0.99, relative error <10%) and on polyacrylamide gels (r(2) = 0.95, relative error <24%). The average HMI modulus on five liver samples was found to EHMI = 2.62 ± 0.41 kPa, compared to EMechTesting = 4.2 ± 2.58 kPa measured by rheometry. This study has demonstrated for the first time the initial feasibility of a non-invasive, model-independent method to estimate local elastic properties of biological tissues at a submillimeter scale using an internal indentation-like approach. Ongoing studies include in vitro experiments in a larger number of samples and feasibility testing in in vivo models as well as pathological human specimens.

Figure A.1

Effect of inclusion size on HMI modulus for scaling factor of 1.5 (top row) and 2 (bottom row)

Figure 1

(a) General HMI setup, (b) actual distribution of the volumic acoustic radiation force field, and (c) equivalent volumic force modeled as uniform within the focal region.

Figure 2

(a) Illustration of the focal region as a cylindrical piston exerting a vertical force, and corresponding deformations of the surrounding tissue, (b) illustration of the forces acting on this cylinder.

Figure 3

(a) Estimated displacement using 1D cross correlation, and (b) Estimated axial compressive strain. Red line indicates the region of investigation for compressive strain, i.e., end of acoustic focal zone. Note that the displacement profile is plotted in m-mode.

Figure 4

(a) Volumic force profile implemented in simulations from experimental pressure measurements, (b) Resulting axial strain using this profile and (c) Axial strain obtained using the equivalent uniform force profile (where the force value is the spatial average of (a)).

Figure 5

Effect of the size of the heterogeneity on the estimated HMI modulus. (a) Description of the geometry used for the simulation; (b) HMI modulus vs size of the inclusion. E_HMI in the uniform case is equal to 18.4kPa (corresponding to input E=20kPa)

Figure 6

HMI modulus vs Young’s modulus measured by rheometry on the six polyacrylamide phantoms (N=5–8 for each phantom). Vertical and horizontal errorbars denote standard deviations among the different samples tested by HMI and rheometry, respectively.