L26 - Mixed Effect Models Enhance Growth Prediction of Abdominal Aortic Aneurysms

Introduction: : Abdominal Aortic Aneurysms (AAAs) are non-uniform dilations of the abdominal aorta, which are characterized by wall degeneration that makes them unable to withstand intraluminal pressure. If ruptured, life threatening internal bleeding could occur, which has up to an 80% mortality rate, making AAA rupture the 14th leading cause of death in the U.S. (Silverberg et al.). Physicians assess rupture risk and prognosis of AAAs by measuring the maximum diameter (Dmax). For diameters between 3 and 4 cm, surveillance is recommended annually, 4 to 5 cm semiannually, while surgery is recommended for diameters larger than 5.5 cm in males, and between 5 and 5.4 cm in females (Chaikof et al.). However, small AAAs rupture during surveillance while larges remain stable after reaching the surgical threshold (Galyfos et al., Ng et al.). Linear and exponential growth models were postulated to predict AAA growth (Hirose et al., Martufi et al.), but not without controversy (Akkoyun et al., Siika et al., Olson et al., Kuvers et al.). The aim of this work is to study the effect of fixed and mixed-effect models to describe AAA growth based on Dmax and aneurysm volume (V), enabling growth models to account for population and subject-specific variations, which could lead to improved patient-specific outcomes.

Materials and

Methods: : We quantified aneurysm growth in a cohort of 40 AAA surveillance program participants from Allegheny Health Network (Pittsburgh, PA) and Northwestern Memorial Hospital (Chicago, IL), using 140 CTA scan datasets. 3D geometries of the outer wall surface were generated using AAAVasc (Shum et al.), and morphology quantification was performed from which Dmax and V were estimated at each screening. Dmax was calculated as the maximum hydraulic diameter of an orthogonal plane to the AAA centerline, which was smoothed using Fourier series expansion, while V was estimated as the total volume encapsulated by geometry. Fixed and mixed effects models were applied to both Dmax and V utilizing linear and exponential growth formulations as detailed in Table 1. Equations (1) and (2) describe linear and exponential growth models with fixed effects, whereas Equations (3) and (4) incorporate both fixed and mixed effects. In these models, α represents the baseline measurement (intercept), and β indicates growth rate over time, derived from population averages. Subject-specific deviations in baseline and growth rates are accounted for by random effects u0j and u1j, respectively. The model parameters were estimated using MATLAB on absolute values and measurements relative to baseline to evaluate parameter influences. Growth predictions were estimated at each surveillance screening; model performance and goodness of fit were assessed using the coefficient of determination (R²).

Results, Conclusions, and Discussions:: Four different models were fit to Dmax and V and their coefficients of determination summarized in Table 2, while the model ground truth and predictions are shown in Figure 1. The goodness of fit for Dmax and V showed poor performance for both linear and exponential models on absolute measurements using only fixed effects with an average R2 = 0.06 for both models. Applying normalization by the baseline improves the performance with a higher average R2 = 0.69 and 0.68 for linear and exponential models, respectively. An improved performance is achieved on relative variables for fixed effects, since the intercept α becomes a shared value for all the subjects; the intercept takes a value of 1 by the normalization process of the data. However, in some variables even after normalization the parameter β is not able to generate a good fit for the data. Growth modeling using mixed-effect models significantly improved the performance of linear and exponential growth models. For relative measures, the mixed-effects approach demonstrated significantly higher R2 values, primarily due to the inclusion of the random effect u1j. The latter effectively captured subject-specific growth rates and enhanced model performance achieving mean R2 values of 0.94 for linear and 0.96 for exponential growth models. The top models based on performance were mixed effects with linear and exponential forms for absolute measures with R2 values of 0.99 for Dmax and V, respectively. This improvement is achieved by incorporating both the fixed and random effects u0j and u1j, which are sufficient to represent AAA growth on a patient-specific basis generating a meaningful model that captures the population behavior while accounting for patient-specific deviations.
Subject-specific variations are present in the growth of AAAs, which can be modeled incorporating mixed-effects modeling. This work showed that normalizing the data is not sufficient to allow linear and exponential models to represent AAA growth accurately. Thus, the use of mixed-effects models seems to be a promising approach for AAA growth prediction and personalized assessments that could result in improved clinical management.

Acknowledgements and/or References (Optional):: This work was partially supported by the National Institutes of Health (Grant No. R01HL159300)