The temporal evolutions of displacements, strains, stresses, and fluid pressure in a poroelastic material under sustained compression are theoretically expressed as sums of an infinite number of exponentials. However, estimation of an infinite number of time constants is impractical in experimental settings. In the past, empirical models containing a finite number of exponentials have been proposed and used to approximate the theoretical poroelastic models. At the present time, however, the degree of error associated with such approximations is unclear. In this paper, we present an analysis of the error encountered when approximating a poroelastic model containing an infinite number of exponentials with a single or double exponential model. As a testing platform, the presented error analysis is applied to the estimation of effective Poisson’s ratio (EPR) and fluid pressure in a uniform cylindrical poroelastic sample and a cylindrical poroelastic sample containing an inclusion under stress relaxation. Our results show that, when the infinite number of exponentials in the theoretical models are approximated with finite number of exponentials, significant error is invoked only in the first few time samples of the EPR and fluid pressure, while the error is negligible for the remaining time samples. We also show that, when estimating clinically relevant mechanical parameters such as Poisson’s ratio or the product of aggregate modulus and interstitial permeability, such approximation invokes small error (<3%) in comparison to the general model with infinite number of exponentials. Therefore, such approximation may be acceptable in techniques aiming at reconstructing mechanical parameters from poroelastographic data.

中文翻译：

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与理论多孔弹性模型的单指数和双指数近似相关的误差分析

多孔弹性材料在持续压缩下的位移、应变、应力和流体压力的时间演变理论上表示为无穷多个指数的总和。然而，在实验环境中估计无限数量的时间常数是不切实际的。过去，已经提出并使用包含有限数量指数的经验模型来逼近理论多孔弹性模型。然而，目前，与这种近似相关的误差程度尚不清楚。在本文中，我们分析了在使用单指数或双指数模型逼近包含无限数量指数的多孔弹性模型时遇到的误差。作为测试平台，所提出的误差分析应用于估计均匀圆柱形多孔弹性样品和包含应力松弛下的夹杂物的圆柱形多孔弹性样品中的有效泊松比 (EPR) 和流体压力。我们的结果表明，当理论模型中的无限数量的指数近似于有限数量的指数时，仅在 EPR 和流体压力的前几个时间样本中调用显着误差，而在剩余时间内误差可以忽略不计样品。我们还表明，在估计临床相关的机械参数（例如泊松比或聚合模量和间隙渗透率的乘积）时，与具有无限数量指数的一般模型相比，这种近似会引起较小的误差 (<3%)。所以，