(F-202) Comparison between Material Properties Obtained from Ultrasound Image Based Inverse FE Method against Ex-vivo Inflation Test

Introduction:: Thoracic aortic aneurysms affect 17,000 Americans annually, with a 90% mortality rate when the aneurysm ruptures[1]. When determining the risk of rupture, the ability to account for changes in aortic material property due to its remodeling is important. However, this requires a large amount of data. Various studies have used different imaging modalities in humans to try to estimate aneurysm or aortic wall mechanics in-vivo[2]. However, there is a lack of data on (1) a set of in vivo images that could be used to estimate aortic wall mechanical properties, and (2) the corresponding data on the true mechanical properties of the wall of the same sample ex-vivo[2].

Wild-type mice infused with angiotensin II (Ang-II) are often used to study the development of thoracic aortic aneurysms. Ang-II increases the pressure within the vessel[2], and the aorta, under abnormally high pressure, will stiffen, thicken, and dilate, increasing propensity to develop an aneurysm and rupture[3]. This model system presents an opportunity to generate the desired data set.

In addition, many studies use population-based, generalized growth parameters and geometry[4]. Yet, due to large variability in complications associated with thoracic aortic aneurysm[5], mouse-specific data would be more valuable. However, difficulty in obtaining non-invasive longitudinal mechanical data impedes efforts in the development of aneurysm growth model on an animal-specific level. Therefore, this study focuses on generating non-invasive mechanical data from ultrasound images in Ang-II infused mouse models, with results validated against biaxial extension-inflation tests[6].


Materials and Methods:: Inverse finite element (FE) and computational fluid dynamics (CFD) models was used for non-invasive mechanical characterization, fitted to vessel deformation obtained from volumetric ultrasound images (Fig1). It can be described thusly: first, ultrasound images were obtained from three, 16-week-old mice, infused with 1000ng/kg/min Ang-II for 4 weeks, the aorta segmented and tracked[6]. 4D ultrasound images of the thoracic aorta were obtained using ultrasound (25-55 MHz, Vevo3100), 0.03x0.03x0.1mm resolution at 40 frames/cardiac cycle.

Flow at the ascending, descending, and aortic branches were obtained by pulsed wave doppler, and tail cuff-pressure were used to calibrate a resistor-capacitor-resistor (RCR) model of the downstream circulation for CFD[7]. CFD simulation was then performed with Ansys Fluent to obtain traction forces on the aortic wall, used as loads for an FE model of the arch in FEBio. Robin conditions were assigned at the outer wall to describe stiffness of the surrounding tissue. The unloaded geometry was obtained by gradual reduction of its radius until FE systolic radius matched the in vivo ultrasound.

A quasi-incompressible neo-Hookean model was used:
W=μ*(I₁-3)/2-μ*ln(J)+λ*(ln(J))2/2
μ=E/2(1+v), B=vE/[(1+v)(1-2v)]

where W is the strain energy density, I₁ is the first invariant of right Cauchy-Green deformation tensor, J is the determinant of the deformation gradient tensor, μ is shear modulus, B is the bulk modulus, and v=0.45 is the Poisson ratio. Levenberg-Marquardt algorithm was used to find the optimized parameter value E that minimized the disparity between deformation from ultrasound and FE model. Inverse FE result were compared against stretch inflation mechanical test[8].


Results, Conclusions, and Discussions:: There exists a neo-Hookean parameter (E) that minimizes the tracked displacement error for the three mice studied (Fig 2a). The displacement error curves for the three mice maintained the same shapes: the error increases drastically at low and plateaus at high E as the vessel becomes effectively rigid. The geometrical fit can be observed qualitatively from the ultrasound and FE images in Fig 2b and 2c during diastole and systole, respectively.

Comparison between mechanical testing and FE model is done with the stress-strain curve shown in Fig 2d. The range of stretches displayed (circumferential and axial) were within diastolic to systolic ranges. Due to the material model, the FE result is nearly linear with overlapping lines for different λ_z values, in contrast to the non-linear four-fiber family models used to fit stretch-inflation test. Extrapolation of these data beyond the ranges however is not advisable due to the exponential stiffening of collagen fibers. Fiber-based models were also tested but converged to isotropic neo-Hookean matrix. This effect likely arises from the small range of strains induced by diastolic to systolic pressure changes, and from the single loading condition (pressurization). The resulting stress-stretch curve could be described with Neo-Hookean behavior.

Comparison between in and ex-vivo material property estimations from the same tissue have been performed previously, but are uncommon[2]. Comparisons are often based on higher resolution CT on larger subjects, with 10-25% errors in the stiffness estimation[9]. The current study resulted in larger errors despite a similar methodology. However, direct comparisons between the results in this study against the others are difficult to make due to different material models, studied vessels, and image quality. Relative to the size of the aorta, the ultrasound image in the current study has ~40% lower resolution than CT scans. An increase in Gaussian noise on the image by 5% can result in increased error of material properties by 1.5%, and this effect might not be additive, but multiplicative. The actual in vivo axial pre-stretch could cause large uncertainties[11], and often directly prescribed in other studies[12]. Similarly, here, the axial pre-stretch was assigned based on the excised aorta.

Acknowledgements (Optional): : Funding provided by NIH grants U01-HL139471, R01-HL164800, and R01-HL164800. Computational resources were provided by the Minnesota Supercomputing Institute.


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