Multiple patient-specific parameters, such as wall thickness, wall strength, and constitutive properties, are required for the computational assessment of abdominal aortic aneurysm (AAA) rupture risk. Unfortunately, many of these quantities are not easily accessible and could only be determined by invasive procedures, rendering a computational rupture risk assessment obsolete. This study investigates two different approaches to predict these quantities using regression models in combination with a multitude of noninvasively accessible, explanatory variables. We have gathered a large dataset comprising tensile tests performed with AAA specimens and supplementary patient information based on blood analysis, the patients medical history, and geometric features of the AAAs. Using this unique database, we harness the capability of state-of-the-art Bayesian regression techniques to infer probabilistic models for multiple quantities of interest. After a brief presentation of our experimental results, we show that we can effectively reduce the predictive uncertainty in the assessment of several patient-specific parameters, most importantly in thickness and failure strength of the AAA wall. Thereby, the more elaborate Bayesian regression approach based on Gaussian processes consistently outperforms standard linear regression. Moreover, our study contains a comparison to a previously proposed model for the wall strength.
This paper presents an improved identification method of the constitutive properties of lung parenchyma. We aim to determine the non-linear viscoelastic behavior of lung parenchyma with a particular focus on the compressible properties - i.e. the ability to change volume. Uniaxial tensile tests are performed on living precision-cut rat lung slices. Image registration is used to compute the displacement field at the surface of the sample. The constitutive model consists of a hyperelastic potential split into volumetric and isochoric contributions and a viscous contribution. This allows for the description of the experimentally observed hysteresis loop. The identification is performed numerically: each test is simulated using the realistic geometry of the sample; the difference between the measured and computed displacements is minimized with an optimization algorithm. We compare several hyperelastic potentials and we can determine the most suitable law for rat lung parenchyma. An exponential potential or a polynomial potential with a first order term and a third or higher order term give similarly satisfactory results. The identified parameters are: for the volumetric contribution: κ=7.25e4Pa, for the exponential form: k1=4.34e3Pa, k2=5.92, for the polynomial form: C1=2.87e3Pa, C3=3.83e4Pa. The identification of the time parameter for the viscous contribution shows that it depends on the loading frequency (0.2Hz: τ=0.257s, 0.4Hz: τ=0.123s, 0.8Hz: τ=0.050s). Adding a viscous contribution significantly increases the accuracy of the identification.
The present results indicate that in AAA, increased locally acting biomechanical conditions (stress and strain) involve increased synthesis of collagen and proteoglycans with increased failure tension. These findings confirm the presence of adaptive biological processes to maintain the mechanical stability of AAA wall.
Our results show for the first time that gene expressions of destabilizing factors within AAA tissue might be correlated to geometric and mechanical properties of the AAA wall. However, we found no influence of local mechanical conditions on gene expression of these factors. Therefore, these preliminary results are still ambiguous.
We present a computational framework for the calibration of parameters describing cardiovascular models with a focus on the application of growth of abdominal aortic aneurysms (AAA). The growth rate in this sort of pathology is considered a critical parameter in the risk management and is an essential indicator for the assessment of surveillance intervals. Parameters describing growth of AAAs are not measurable directly and need to be estimated from available data often given by medical imaging technologies. Registration procedures often applied in standard workflows of parameter identification to extract the image encoded information are a source of significant systematic error. The concept of surface currents provides means to effectively avoid this source of errors by establishing a mathematical framework to compare surface information, directly accessible from image data. By utilizing this concept it is possible to inversely estimate growth parameters using sophisticated numerical models of AAAs from measurements available as surface information. In this work we present a framework to obtain spatial distributions of parameters governing growth of arterial tissue, and we show how the use of surface currents can significantly improve the results. We further present the application to patient specific follow-up data resulting in a spatial map of volumetric growth rates enabling, for the first time, prediction of further AAA expansion.
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