Importance of localized dilatation and distensibility in identifying determinants of thoracic aortic aneurysm with neural operators

TL;DR

The importance of obtaining full-field measurements of both dilatation and distensibility in the aneurysmal aorta to identify the mechanobiological insults that drive disease progression, which will advance personalized treatment strategies that target the underlying pathologic mechanisms are demonstrated.

Abstract

Thoracic aortic aneurysms (TAAs) arise from diverse mechanical and mechanobiological disruptions to the aortic wall that increase the risk of dissection or rupture. Evidence links TAA development to dysfunctions in the aortic mechanotransduction axis, including loss of elastic fiber integrity and cell-matrix connections. Because distinct insults create different mechanical vulnerabilities, there is a critical need to identify interacting factors that drive progression. Here, we use a finite element framework to generate synthetic TAAs from hundreds of heterogeneous insults spanning varying degrees of elastic fiber damage and impaired mechanosensing. From these simulations, we construct spatial maps of localized dilatation and distensibility to train neural networks that predict the initiating combined insult. We compare several architectures (Deep Operator Networks, UNets, and Laplace Neural Operators) and multiple input data formats to define a standard for future subject-specific modeling. We also quantify predictive performance when networks are trained using only geometric data (dilatation) versus both geometric and mechanical data (dilatation plus distensibility). Across all networks, prediction errors are significantly higher when trained on dilatation alone, underscoring the added value of distensibility information. Among the tested models, UNet consistently provides the highest accuracy across all data formats. These findings highlight the importance of acquiring full-field measurements of both dilatation and distensibility in TAA assessment to reveal the mechanobiological drivers of disease and support the development of personalized treatment strategies.

Figures (15)

• Figure 1: Synthetic data generation pipeline. (a) Insult distributions along the circumferential ($\theta$) and axial ($z$) directions are randomly generated with Gaussian Random Field (GRF) methods to define normalized insult profiles ($\vartheta^\ast(\theta,z) \in [0,1]$) that are mapped to the initial loaded aortic geometry to define the insult region (see \ref{['sec:SI']} for further details). (b) For each profile, $\vartheta^{\ast}$ delineates multiple cases of mechanobiological insults defined by combinations of compromised integrity of elastic fibers ($\vartheta_{c^e}(\theta,z) \in [0,0.48]$) and dysfunctional mechanosensing ($\vartheta_{\delta}(\theta,z) \in [0,0.28]$) as inputs to (c) the nonlinear FE simulation to compute the long-term evolved state of the TAA. (d) Maps for dilatation ($d$) and distensibility ($\mathcal{D}$) are obtained from the final geometry under multiple in vivo loading conditions (diastolic and systolic pressures), either processed as heat maps or converted to 8-bit grayscale maps, to serve as training data for the neural networks. $\vartheta_{c^e} + \vartheta_{\delta}$ combinations are constrained to produce closely matched maximum dilatations ($d_{max} \approx 1.5$) for each case to focus attention on detecting the underlying pathologic mechanism at the time when a dilatation first reaches aneurysmal status.
• Figure 2: Schematic representation of two DeepONet architectures. Each branch net is a (a) CNN or (b) FNN that embeds the dilatation ($d$) and distensibility ($\mathcal{D}$) maps as either grayscale or heat maps. Each trunk net takes the coordinates $\{\hat{\theta}, \hat{z}\}$ to define the output domains of the corresponding insult contributor. The solution operators for each insult ($\mathbb G_{\bm{\theta}}^i$ ($i = c^e, \delta$)) are formed from element-wise dot products of the outputs of the branch and trunk networks, with shared learnable parameters ($\bm \theta$). Minimization of the loss function ($\mathcal{L}_{\bm{\theta}}$), defined as the combination of both operator outputs, determines the optimal parameters that enable estimation of the insult profiles and contributors ($\hat{\vartheta_i}$).
• Figure 3: Schematic representation of the UNet architecture. Maps of dilatation ($d$) and distensibility ($\mathcal{D}$) are encoded via successive layers of two-dimensional convolution (Conv2D), group normalization, and Gaussian Error Linear Unit (GELU) activation. Down- and up-sampling the input by factors of 2 is achieved through two-dimensional max-pooling operations (Maxpool2D) and two-dimensional transpose convolutional operations (Conv2DTranspose), respectively. Finally, skip connections are implemented to propagate information from earlier layers.
• Figure 4: Schematic diagram of the LNO architecture. The dilatation ($d$) and distensibility ($\mathcal{D}$) are lifted to a higher dimension via shallow neural network $\mathcal{P}$, to which Laplace layers are applied, each yielding the output $u(t) =f[ K_\phi(s)V(s)]$, where $K_\phi(s)$ is the Laplace transform of the kernel integral transformation and $V(s)$ is the Laplace transform of the lifted input function. Each layer contains pole-residue methods to obtain the transient and steady-state responses ($u_{tr}(t)$ and $u_{st}(t)$, respectively), with residues $\beta_n$, coefficients $\alpha_\ell$, and response poles $\gamma_n$ and $\lambda_\ell$. Finally, the outputs (insult profiles) are projected back into the target dimension using the shallow network $\mathcal{Q}$.
• Figure 5: Performance of four different neural networks in predicting insult contributors to aneurysmal dilatation. Relative $\mathcal{L}_2$ errors are reported separately for compromised (a) elastic (eln) fiber integrity and (b) mechanosensing over all testing cases considered: dilatation ($d$) only in grayscale and heat map formats, and dilatation and distensibility ($d$ & $\mathcal{D}$) in grayscale and heat map formats.