| Autor: |
Zaitsev VY; A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Uljanova St., 46, Nizhny Novgorod 603950, Russia., Matveev LA; A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Uljanova St., 46, Nizhny Novgorod 603950, Russia., Matveyev AL; A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Uljanova St., 46, Nizhny Novgorod 603950, Russia., Plekhanov AA; Privolzhsky Research Medical University, 10/1 Minin and Pozharsky Sq., Nizhny Novgorod 603005, Russia., Gubarkova EV; Privolzhsky Research Medical University, 10/1 Minin and Pozharsky Sq., Nizhny Novgorod 603005, Russia., Kiseleva EB; Privolzhsky Research Medical University, 10/1 Minin and Pozharsky Sq., Nizhny Novgorod 603005, Russia., Sovetsky AA; A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, Uljanova St., 46, Nizhny Novgorod 603950, Russia. |
| Abstrakt: |
We propose a nonlinear stress-strain law to describe nonlinear elastic properties of biological tissues using an analogy with the derivation of nonlinear constitutive laws for cracked rocks. The derivation of such a constitutive equation has been stimulated by the recently developed experimental technique-quasistatic Compression Optical Coherence Elastography (C-OCE). C-OCE enables obtaining nonlinear stress-strain dependences relating the applied uniaxial compressive stress and the axial component of the resultant strain in the tissue. To adequately describe nonlinear stress-strain dependences obtained with C-OCE for various tissues, the central idea is that, by analogy with geophysics, nonlinear elastic response of tissues is mostly determined by the histologically confirmed presence of interstitial gaps/pores resembling cracks in rocks. For the latter, the nonlinear elastic response is mostly determined by elastic properties of narrow cracks that are highly compliant and can easily be closed by applied compressing stress. The smaller the aspect ratio of such a gap/crack, the smaller the stress required to close it. Upon reaching sufficiently high compressive stress, almost all such gaps become closed, so that with further increase in the compressive stress, the elastic response of the tissue becomes nearly linear and is determined by the Young's modulus of the host tissue. The form of such a nonlinear dependence is determined by the distribution of the cracks/gaps over closing pressures; for describing this process, an analogy with geophysics is also used. After presenting the derivation of the proposed nonlinear law, we demonstrate that it enables surprisingly good fitting of experimental stress-strain curves obtained with C-OCE for a broad range of various tissues. Unlike empirical fitting, each of the fitting parameters in the proposed law has a clear physical meaning. The linear and nonlinear elastic parameters extracted using this law have already demonstrated high diagnostic value, e.g., for differentiating various types of cancerous and noncancerous tissues. |
