We present a data-informed, highly personalized, probabilistic approach for the quantification of abdominal aortic aneurysm (AAA) rupture risk. Our novel framework builds upon a comprehensive database of tensile test results that were carried out on 305 AAA tissue samples from 139 patients, as well as corresponding non-invasively and clinically accessible patient-specific data. Based on this, a multivariate regression model is created to obtain a probabilistic description of personalized vessel wall properties associated with a prospective AAA patient. We formulate a probabilistic rupture risk index that consistently incorporates the available statistical information and generalizes existing approaches. For the efficient evaluation of this index, a flexible Kriging-based surrogate model with an active training process is proposed. In a case-control study, the methodology is applied on a total of 36 retrospective, diameter matched asymptomatic (group 1, n = 18) and known symptomatic/ruptured (group 2, n = 18) cohort of AAA patients. Finally, we show its efficacy to discriminate between the two groups and demonstrate competitive performance in comparison to existing deterministic and probabilistic biomechanical indices.

The present paper is motivated by one of the most fundamental challenges in inverse problems, that of quantifying model discrepancies and errors. While significant strides have been made in calibrating model parameters, the overwhelming majority of pertinent methods is based on the assumption of a perfect model. Motivated by problems in solid mechanics which, as all problems in continuum thermodynamics, are described by conservation laws and phenomenological constitutive closures, we argue that in order to quantify model uncertainty in a physically meaningful manner, one should break open the black-box forward model. In particular we propose formulating an undirected probabilistic model that explicitly accounts for the governing equations and their validity. This recasts the solution of both forward and inverse problems as probabilistic inference tasks where the problem's state variables should not only be compatible with the data but also with the governing equations as well. Even though the probability densities involved do not contain any black-box terms, they live in much higher-dimensional spaces. In combination with the intractability of the normalization constant of the undirected model employed, this poses significant challenges which we propose to address with a linearlyscaling, double-layer of Stochastic Variational Inference. We demonstrate the capabilities and efficacy of the proposed model in synthetic forward and inverse problems (with and without model error) in elastography.

Background and aims: The study aimed to assess the potential of proteoglycans (PG) and collagens as serological biomarkers in the abdominal aortic aneurysm (AAA). Furthermore, we investigated the underlying mechano-biological interactions and signaling pathways. Methods: Tissue and serum samples from patients with ruptured AAA (rAAA, n=29), elective AAA (eAAA, n=78), and healthy individuals (n=8) were evaluated by histology, immunohistochemistry and Enzyme-linked Immunosorbent Assay (ELISA), mechanical properties were assessed by tensile tests. Regulatory pathways were determined by membrane-based sandwich immunoassay. Results: In AAA samples, collagen type I and III (Col1, Col3), chondroitin sulfate (CS), and dermatan sulfate (DS) were significantly increased compared to controls (3.0-, 3.2-, 1.3-, and 53-fold; p<0.01). Col1 and endocan were also elevated in the serum of AAA patients (3.6- and 6.0-fold; p<0.01), while DS was significantly decreased (2.5-fold; p<0.01). Histological scoring showed increased total PGs and focal accumulation in rAAA compared to eAAA. Tissue β-stiffness was higher in rAAA compared to eAAA (2.0-fold, p=0.02). Serum Col1 correlated with maximum tensile force and failure tension (r=0.448 and 0.333; p<0.01 and =0.02), tissue endocan correlated with α-stiffness (r=0.340; p<0.01). Signaling pathways in AAA were associated with ECM synthesis and VSMC proliferation. In particular, Src family kinases, PDGF- and EGF-related proteins seem to be involved. Conclusions: Our findings reveal a structural association between collagen and PGs and their response to changes in mechanical loads in AAA. Particularly Col1 and endocan reflect the mechano-biological conditions of the aortic wall also in the patient’s serum and might serve for AAA risk stratification.

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