Non-Linear Size Effects and Episodic Progression in the Ascending Aorta

Abstract

Background—: Predicting ascending aortic (AsAo) growth is challenging. Conventional paradigms often assume a linear and monotonic relationship between baseline size and future growth that occurs continuously-assumptions that may oversimplify biology-driven disease progression. We first evaluated whether body size-indexed baseline AsAo diameter shows a non-linear association with subsequent growth at the population-level, and second whether patient-level growth trajectories are predominantly continuous or episodic.

Methods—: We performed a single-center, retrospective study (2012-2024). The Primary Cohort (n=3,315; ≥2 CT/MR scans) was used to model the relationship between baseline indexed AsAo size (Z-score) and subsequent annualized growth using multivariable linear regression and generalized additive models (GAMs), adjusting for clinical covariates. A Sub-Cohort (n=1,055; ≥4 scans) was used to classify longitudinal phenotypes as: Stable (Total Growth <2.0 mm), Stable-with-Noise (Total Growth <2.0 mm with alternating small changes), Continuous Growth (Total Growth ≥2.0 mm without a qualifying event), or Discontinuous/Episodic Growth (Total Growth ≥2.0 mm with ≥1 "growth event"). A growth event was defined as a diameter increase ≥2.0 mm within a single imaging interval or across two adjacent intervals (combined 0.5-5 years).

Results—: In the Primary Cohort, baseline Z-score demonstrated a significant non-linear (U-shaped) association with subsequent growth in the GAM (p<0.001), with higher growth at both small (Z<0) and severely dilated (Z>5) sizes. In the Sub-Cohort examining growth trajectory, the distribution was: Stable: 50.4% (532/1,055), Stable-with-Noise: 21.6% (228/1,055), Continuous: 5.4% (57/1,055), and Discontinuous/Episodic 22.6% (238/1,055). Among patients with measurable growth (Total Growth ≥2.0 mm, n=295), 81%(n=238) exhibited episodic growth and 58.3% (172/295) had a non-dilated baseline aorta (Z<2). Group differences (e.g., younger age and smaller baseline Z-scores in the Growth vs. Stable groups) were consistent across sensitivity analyses.

Conclusions—: AsAo growth is not well described by linear, continuous assumptions. Baseline size relates to future growth in a non-linear (U-shaped) manner, and nearly one-quarter of patients exhibit discrete growth bursts separated by periods of quiescence, with episodic behavior dominating among those who enlarge. These findings support a punctuated growth paradigm and argue for re-examining surveillance intervals, risk communication, and threshold-based decision pathways in thoracic aortic disease.

Figure 1.. Relationship Between Baseline Aortic Z-Score and Growth Rate Modeled with Simple Linear Regression.

This plot shows individual patient growth rates (orange points) against their initial Z-score, with the blue line representing the fitted linear regression model. The shaded gray area indicates the 95% confidence interval for the regression line. Plot axes are truncated for improved visualization outlier points (n=17) with an initial Z-score >12.5 or an absolute growth rate >5 mm/year not displayed.

Figure 2.. Relationship Between Baseline Aortic Z-Score and Growth Rate Modeled with a Linear Interaction for Dilation Status.

This plot shows the fitted linear regression model (blue line) with its 95% confidence interval (shaded gray area) over the raw patient data (orange points). The model includes an interaction term at the dilation threshold (red dashed line), allowing the slope of the relationship between Z-score and growth rate to differ for patients with normal versus dilated aortas. Plot axes are truncated for improved visualization outlier points (n=17) with an initial Z-score >12.5 or an absolute growth rate >5 mm/year not displayed.

Figure 3.. Non-Linear Relationship Between Baseline Aortic Size and Growth Rate.

(Left Panel) The continuous relationship from a Generalized Additive Model is displayed, with the solid line representing the predicted mean growth rate and the shaded area indicating the 95% confidence interval, plotted over the individual patient data (scatter points). The relationship is significantly non-linear (p<0.001), forming a U-shaped curve with accelerated growth at both low (Z-score < 0) and high (Z-score > 5) initial sizes. For visualization, the plot axes have been truncated, excluding 17 outliers. (Right Panel) The same model results are shown as estimated marginal means for each integer Z-score bin. Gray bars represent the 95% confidence interval of the mean estimate. The patient count (N) and corresponding median aortic diameter (mm) are labeled above each bar.

Figure 4.. Non-Linear Interaction Between Baseline Aortic Z-Score and Sex on Aortic Growth Rate in a Generalized Additive Model.

This plot visualizes the significant non-linear interaction between baseline Z-score and sex from the Generalized Additive Model. Smooth curves, representing the predicted growth rates, are shown for females (red) and males (blue), with their respective 95% confidence intervals (shaded gray areas) plotted over the raw patient data (orange points). The diverging, non-linear patterns indicate that the relationship between aortic size and growth rate differs significantly by sex across the spectrum of initial Z-scores. Plot axes are truncated for improved visualization outlier points (n=17) with an initial Z-score >12.5 or an absolute growth rate >5 mm/year not displayed.

Figure 5.. Lasagna Plots Visualizing Aortic Growth Trajectories Across Groups.

Each row represents an individual patient, ordered by total follow-up duration. Each colored cell represents a single imaging interval, with the color corresponding to the annualized aortic growth rate (mm/year) during that period. A: Stable pattern (n=532) was characterized by a predominance of slow growth (<0.5 mm/year), but total overall growth magnitude below limits of measurable change (< 2mm). B: The Discontinuous Growth pattern (n=238) displays a background of slow growth intervals punctuated by sporadic, high growth intervals (>1.5 mm/year), indicating episodic growth. Conversely, the Continuous Growth pattern (n=57) shows a mixture of slow and moderate growth up to rates of approximately 1 mm/year, reflecting relatively consistent growth over surveillance.