A new inverse method for estimation of in vivo mechanical properties of the aortic wall

Abstract

The aortic wall is always loaded in vivo, which makes it challenging to estimate the material parameters of its nonlinear, anisotropic constitutive equation from in vivo image data. Previous approaches largely relied on either computationally expensive finite element models or simplifications of the geometry or material models. In this study, we investigated a new inverse method based on aortic wall stress computation. This approach consists of the following two steps: (1) computing an “almost true” stress field from the in vivo geometries and loading conditions, (2) building an objective function based on the “almost true” stress fields, constitutive equations and deformation relations, and estimating the material parameters by minimizing the objective function. The method was validated through numerical experiments by using the in vivo data from four ascending aortic aneurysm (AsAA) patients. The results demonstrated that the method is computationally efficient. This novel approach may facilitate the personalized biomechanical analysis of aortic tissues in clinical applications, such as in the rupture risk analysis of ascending aortic aneurysms.

A deep learning approach to estimate chemically-treated collagenous tissue nonlinear anisotropic stress-strain responses from microscopy images

“…Iterative finite element simulation and optimization methods [55, 56] were developed to determine human aorta material properties from strain measurements. Our group has also proposed a stress-matching based method [57] to estimate human aorta material properties. Recently, a machine learning based method [58], utilizing recurrent neural networks, was proposed for modelling the indentation force response of soft tissue, which used a robotic system to measure tissue forces and deformation.…”

“…Recently, a machine learning based method [58], utilizing recurrent neural networks, was proposed for modelling the indentation force response of soft tissue, which used a robotic system to measure tissue forces and deformation. These methods can recover mechanical properties from multiple deformed states of the subjects by using noninvasive or minimally invasive measurement data from force sensors and motor controller [58], CT [57], MR [54] or ultrasound scanners [55, 56]. Temporal deformation measurement of the subjects under external loading is needed by these methods, which contains stress-strain information implicitly or explicitly.…”

A machine learning approach as a surrogate of finite element analysis–based inverse method to estimate the zero‐pressure geometry of human thoracic aorta

“…Then a dataset from 3125 (125 shapes from SSM × 25 sets of material parameters) virtual patients was obtained, consisting of 3 shapes per virtual patient at the systolic phase, diastolic phase, and zero-pressure state. We note that on the basis of the previous studies, [35][36][37] the material parameters of the constitutive model (Equation A1) can be identified from the aorta shapes at 2 cardiac phases with known blood pressure levels (eg, systole and diastole), which implies the 2 geometries contain material property information.…”

“…Given a pair of input shapes at the systolic and diastolic phases, the ML model will output the zero‐pressure shape in 3 steps: (1) encode each of the input shapes as a set of scalar values, ie, shape code; (2) transform the shape code of the input shapes to the shape code of the output shape using a nonlinear mapping; and (3) decode the shape code of the output shape into the zero‐pressure shape. Note that on the basis of the previous studies, the material parameters of the aorta wall tissue can be identified from the aorta shapes at 2 cardiac phases with known blood pressure levels (eg, at systole and diastole), which implies that material property information is already embedded in the 2 input shapes. Therefore, the ML model does not require material parameters as input.…”

A Probabilistic and Anisotropic Failure Metric for Ascending Thoracic Aortic Aneurysm Risk Stratification

“…The areas under the curves (AUC), which reflect the discriminative powers of the failure metrics, are 0.5489, 0.8448, 0.7644 and 0.8621, respectively, for Method 1~ Method 4. The diameter criterion has the lowest AUC, while the highest AUC is achieved by FP evaluated under elevated blood pressure using the patient-specific hyperelastic properties, which highlights the potential benefits of incorporating patient-specific hyperelastic properties[53][54][55][56][57][58] in the risk stratification. specific hyperelastic properties, the performance is not improved by evaluating FP under elevated blood pressure by using a representative set of hyperelastic parameters.In general, to evaluate a diagnostic method, an AUC of 0.5 suggests no discrimination, 0.7 to 0.8 is considered acceptable, and 0.8 to 0.9 is considered excellent[59].…”