MCMeshGAN: 3D Aneurysm Growth Predictor

• The paper presents MCMeshGAN, a multimodal conditional mesh-to-mesh GAN that generates patient-specific 3D aortic aneurysm progressions from baseline meshes and clinical data.
• Its methodology integrates a condition branch with local KCN and global GCN branches to preserve both fine local deformations and overall anatomical structure.
• Empirical results demonstrate lower mean absolute error and MIS diameter error compared to baselines, emphasizing its clinical potential in personalized aneurysm monitoring.

MCMeshGAN, short for Multimodal Conditional MeshGAN, is a multimodal conditional mesh-to-mesh generative adversarial network proposed for personalized 3D prediction of thoracic aortic aneurysm growth. It is presented as the first method of this kind for aneurysm progression modeling directly on 3D surface meshes, rather than on 2D images or handcrafted geometric summaries. The model takes a source aneurysm mesh together with age, sex, and a chosen target time interval, and generates a patient-specific target mesh at that time, supporting both retrospective reconstruction and prospective prediction (Chen et al., 27 Aug 2025).

1. Clinical problem and modeling objective

MCMeshGAN is designed for the problem of predicting how an individual patient’s aortic aneurysm will change over time, with the stated goal of improving surveillance and intervention timing. In the formulation described for thoracic aortic aneurysm progression, current practice often relies on manual diameter measurements on follow-up imaging and threshold-based clinical rules. The method is motivated by the observation that aneurysm progression is fundamentally a 3D anatomical process, whereas diameter-based assessment reduces it to a sparse, mostly 2D surrogate (Chen et al., 27 Aug 2025).

The paper defines the task as mesh-to-mesh 3D anatomical progression: given a baseline aortic surface mesh, the model generates a future mesh for the same patient. The stated technical difficulty is that aneurysm growth includes both subtle local deformations and broader global anatomical changes on non-Euclidean meshes. Standard CNNs are therefore not naturally applicable, while graph-based methods, although topology-aware, are described as vulnerable to over-smoothing in deep GCNs, which blurs local distinctions and harms fine geometric fidelity (Chen et al., 27 Aug 2025).

Within this setting, MCMeshGAN fills a specific gap: prior work, as characterized in the paper, had not provided a conditional, multimodal, mesh-to-mesh generative model for personalized aneurysm growth prediction that can simultaneously use 3D geometry, clinical attributes, and a target future time interval, while preserving both local and global anatomy. This suggests that the method should be understood not merely as a mesh generator, but as a trajectory model for patient-specific anatomical evolution (Chen et al., 27 Aug 2025).

2. Conditional formulation and geometric representation

The model’s input-output relation is stated explicitly. During training, given a source mesh $m_s$ with source clinical data $(a_s, g_s, t_s)$, the model predicts a target mesh $m_t$ from another time point $t_t$, using

$time_{interval} = t_t - t_s.$

At inference, given a source aneurysm mesh $m_s$, age $a_s$, sex $g_s$, and a chosen target interval, the generator predicts

$m_t = G(m_s, a_s, g_s \mid time_{interval}).$

Positive intervals indicate future prediction; negative intervals indicate past reconstruction (Chen et al., 27 Aug 2025).

In this formulation, multimodal denotes the combination of 3D mesh geometry with clinical variables, specifically age, sex, and the target time interval. Conditional denotes explicit control by these auxiliary variables, especially the requested temporal offset. Mesh-to-mesh GAN denotes a generative adversarial translation framework in which a source mesh is transformed into a predicted target mesh, while adversarial training is used to encourage realism (Chen et al., 27 Aug 2025).

The anatomical representation is a triangular 3D surface mesh extracted from CT. The preprocessing pipeline comprises CT segmentation using the pre-trained TotalSegmentator model, manual correction of segmentation masks, mesh extraction with the marching cubes algorithm in the IRTK library, rigid alignment, non-rigid surface registration, and standardization to 10,000 vertices for every mesh. These operations enforce one-to-one vertex correspondence and a common topology across samples. The paper does not describe prediction of a displacement field; it describes prediction of the target mesh itself, which under this representation is effectively prediction of future mesh coordinates (Chen et al., 27 Aug 2025).

A strong implication of this design is that the learning problem is simplified from arbitrary topology generation to anatomical progression under fixed mesh structure. This also explains why the paper reports that $L_1$ loss works better than Chamfer Distance under the corresponding-vertex regime (Chen et al., 27 Aug 2025).

3. Architecture: condition branch, KCN branch, and GCN branch

MCMeshGAN is organized around three main branches: a condition branch, a local KNN-based convolutional network (KCN) branch, and a global graph convolutional network (GCN) branch, followed by a fusion module that integrates features from these branches (Chen et al., 27 Aug 2025).

The condition branch encodes age, sex, and target time interval. The paper introduces a Text2Vector encoder based on ordinal binary encoding, where each clinical attribute is represented by a $(a_s, g_s, t_s)$0 binary vector. The most explicit definition is given for temporal conditioning:

$(a_s, g_s, t_s)$1

with

$(a_s, g_s, t_s)$2

$(a_s, g_s, t_s)$3

Index 50 serves as the dividing point between past and future. Age and sex are also transformed to vectors by the same Text2Vector ordinal binary encoding scheme, although no explicit formulas are given for those variables. This branch provides both personalization and temporal control (Chen et al., 27 Aug 2025).

The local KCN branch is introduced to preserve fine local detail that deep GCNs may smooth away. Starting from mesh vertices

$(a_s, g_s, t_s)$4

a CNN-based feature extractor maps raw vertex coordinates into per-vertex features:

$(a_s, g_s, t_s)$5

For each query vertex $(a_s, g_s, t_s)$6, the branch computes its $(a_s, g_s, t_s)$7-nearest neighbors,

$(a_s, g_s, t_s)$8

gathers the corresponding features,

$(a_s, g_s, t_s)$9

and applies two parallel convolution modules, $m_t$0 and $m_t$1, before vertex interaction and aggregation:

$m_t$2

The paper sets $m_t$3 empirically. This branch is explicitly linked to fine-grained local deformations and to accurate measurement of clinically important diameter change (Chen et al., 27 Aug 2025).

The global GCN branch treats the mesh as an undirected graph

$m_t$4

with connectivity encoded by a binary adjacency matrix

$m_t$5

where $m_t$6 if vertices $m_t$7 and $m_t$8 are connected. The graph convolution is the standard Kipf–Welling layer:

$m_t$9

with

$t_t$0

and

$t_t$1

The branch consists of four graph convolutional blocks, which expand the receptive field and encode the global anatomical structure of the aorta (Chen et al., 27 Aug 2025).

The fusion module is described conceptually rather than algebraically. The paper does not provide an explicit fusion equation or exact fusion operator, but it states that the final prediction is conditioned on the combined information from the KCN branch, the GCN branch, and the condition branch. The stated answer to GCN over-smoothing is architectural: a dual-branch decomposition in which GCN is used for global context and KCN for local detail, rather than a modified graph operator or explicit anti-smoothing penalty (Chen et al., 27 Aug 2025).

4. Training protocol, losses, and TAAMesh

The paper introduces TAAMesh, a longitudinal thoracic aortic aneurysm mesh dataset consisting of 590 CT scans / records from 208 patients, with 2 to 8 longitudinal scans per patient. The modalities include CT scans, 3D meshes, and clinical data. The reported clinical variables include age, sex, maximum inscribed sphere (MIS) diameter, and corresponding clinical reports. The data come from Hammersmith Hospital, Imperial College London, under Health Research Authority approval 23/HRA/3733. The split is at the patient level with a 7:1:2 train/validation/test ratio (Chen et al., 27 Aug 2025).

Training pairs are formed longitudinally from the same patient, using source mesh $t_t$2 at time $t_t$3 and target mesh $t_t$4 at time $t_t$5, with the interval $t_t$6. Because the interval may be positive or negative, the same framework supports prospective prediction to future timepoints and retrospective reconstruction to earlier timepoints (Chen et al., 27 Aug 2025).

The implementation details reported in the paper are specific. The framework uses PyTorch Geometric for GCN baselines. Training is performed on an Intel Xeon Silver 4114 CPU and a single Tesla V100 32GB GPU, with Adam, learning rate

$t_t$7

Adam parameter

$t_t$8

1000 epochs, batch size 1, and $t_t$9 in the KNN module. The paper does not mention data augmentation (Chen et al., 27 Aug 2025).

The loss design is described only partially in symbolic terms. The paper states that three losses are evaluated: $time_{interval} = t_t - t_s.$0 loss, Chamfer Distance (CD) loss, and adversarial loss. It does not provide explicit formulas for these losses, nor the final weighted objective, nor weighting coefficients between losses. What is stated is that adversarial loss improves realism and anatomical plausibility, $time_{interval} = t_t - t_s.$1 works better than CD because meshes are non-rigidly registered into one-to-one vertex correspondence, and the best final model uses $time_{interval} = t_t - t_s.$2 adversarial loss. The paper also does not define additional regularizers such as Laplacian smoothness, edge-length preservation, normal consistency, explicit diameter loss, or deformation regularization (Chen et al., 27 Aug 2025).

The adversarial framework itself is only partially specified. MCMeshGAN is explicitly described as a GAN, and adversarial loss is reported to improve realism, but no detailed discriminator architecture is given in the text provided. The absence of a layer-by-layer discriminator description distinguishes MCMeshGAN from earlier mesh GANs such as MeshGAN, which used a BEGAN-style autoencoder discriminator built with Chebyshev spectral graph convolutions for fixed-topology 3D face generation (Cheng et al., 2019).

5. Evaluation, ablations, and empirical findings

Evaluation uses geometric mesh metrics in millimeters—MAE, CD, and HD—together with a clinically meaningful metric, MIS diameter error, defined as the error in maximum inscribed sphere diameter estimation. The paper does not provide formal formulas for these metrics, but it states their respective roles: average pointwise or vertexwise error, set-to-set nearest-neighbor surface discrepancy, worst-case surface discrepancy, and clinical accuracy of maximum diameter estimation (Chen et al., 27 Aug 2025).

The compared baselines are PointNet++, GCNConv, GCN2Conv, SSGConv, and PMLP, each adapted with the same condition branch for fairness. The paper also evaluates variants of several baselines with +Condition+KCN to test whether the KCN module improves them (Chen et al., 27 Aug 2025).

On the test set, MCMeshGAN reports the best performance among all compared methods:

Model	MAE / CD / HD	MIS Error
MCMeshGAN	$time_{interval} = t_t - t_s.$3 mm / $time_{interval} = t_t - t_s.$4 mm / $time_{interval} = t_t - t_s.$5 mm	$time_{interval} = t_t - t_s.$6 mm
SSGConv + Condition	$time_{interval} = t_t - t_s.$7 mm / $time_{interval} = t_t - t_s.$8 mm / $time_{interval} = t_t - t_s.$9 mm	$m_s$0 mm
GCN2Conv + Condition + KCN	$m_s$1 mm / $m_s$2 mm / $m_s$3 mm	$m_s$4 mm

The paper emphasizes that MCMeshGAN best matches ground-truth geometry across the core metrics and achieves the lowest MIS diameter error, which it treats as particularly clinically meaningful. Compared with the strong KCN-augmented baseline GCN2Conv + Condition + KCN, the reported improvements are $m_s$5 in MAE, $m_s$6 in CD, $m_s$7 in HD, and $m_s$8 in MIS Error (Chen et al., 27 Aug 2025).

The ablation study attributes this result to several interacting factors. Full MCMeshGAN with age, sex, KCN, GCN, $m_s$9, and adversarial loss gives MAE $a_s$0, CD $a_s$1, and HD $a_s$2. Removing age degrades performance to MAE $a_s$3, CD $a_s$4, and HD $a_s$5. Removing sex also degrades performance to MAE $a_s$6, CD $a_s$7, and HD $a_s$8. A KCN-only model without GCN gives MAE $a_s$9, CD $g_s$0, and HD $g_s$1, while a GCN-only model without KCN gives MAE $g_s$2, CD $g_s$3, and HD $g_s$4. Removing adversarial loss, even with both branches present, yields MAE $g_s$5, CD $g_s$6, and HD $g_s$7. Using CD loss instead of $g_s$8, together with both branches and adversarial loss, yields MAE $g_s$9, CD $m_t = G(m_s, a_s, g_s \mid time_{interval}).$0, and HD $m_t = G(m_s, a_s, g_s \mid time_{interval}).$1 (Chen et al., 27 Aug 2025).

Qualitative examples are reported for follow-up generation at 3, 15, 39, and 45 months from a baseline mesh. The predicted meshes are described as showing strong agreement with corresponding ground-truth follow-up meshes, with low CD maps and small diameter errors. The paper also states that MCMeshGAN better preserves local deformations, smoother and more realistic surfaces, and overall anatomical plausibility, while also acknowledging that slight surface roughness remains (Chen et al., 27 Aug 2025).

6. Temporal controllability, relation to prior mesh GANs, and limitations

A central property of MCMeshGAN is temporal controllability. Because the target interval is directly encoded and fed to the generator, a baseline mesh can be used to generate multiple predictions at different future or past times relative to the source timepoint. The interval can be positive for future prediction or negative for past reconstruction, and the paper explicitly frames this as support for both retrospective and prospective modeling. In the conditioning ablation, age is reported to have greater impact than sex, which the paper suggests is likely because age spans a larger continuous range, 35 to 93 years, whereas sex is binary (Chen et al., 27 Aug 2025).

In the broader lineage of mesh-native adversarial generation, MCMeshGAN differs from earlier systems in both application domain and conditioning strategy. MeshGAN was introduced as the first intrinsic GAN architecture operating directly on 3D meshes for faces, using fixed-topology dense-correspondence face meshes, Chebyshev spectral graph convolutions, and a BEGAN autoencoder discriminator (Cheng et al., 2019). MCMeshGAN, by contrast, is described as multimodal, conditional, and mesh-to-mesh, with direct incorporation of clinical metadata and time interval for 3D aneurysm growth prediction. Relative to GAN frameworks that encode mesh geometry and texture as aligned UV-space signals and support class-, attribute-, and text-conditional generation of textured meshes from single-view image supervision, MCMeshGAN remains focused on registered anatomical surface meshes and clinical progression rather than geometry-texture synthesis (Pavllo et al., 2020).

The paper’s stated contributions are fourfold: the first multimodal conditional mesh-to-mesh translation model for 3D aneurysm growth prediction; a dual-branch architecture combining global GCN features and local KCN features; integration of age, sex, and time interval for personalized prediction; and introduction of the TAAMesh longitudinal 3D aneurysm mesh dataset (Chen et al., 27 Aug 2025).

Its stated limitations are equally specific. The model can still produce rough mesh surfaces; it was evaluated only on the authors’ private dataset; there is no public longitudinal aneurysm mesh benchmark for broader validation; no external validation is reported; and the framework has not yet been integrated into a real clinical workflow. The method also depends implicitly on strong topology assumptions because all meshes undergo non-rigid registration and are standardized to 10,000 vertices. A plausible implication is that the model’s success depends not only on its generator design but also on the availability of high-quality longitudinal mesh registration and correspondence (Chen et al., 27 Aug 2025).

The source code for MCMeshGAN and the baseline methods is reported as publicly available at https://github.com/ImperialCollegeLondon/MCMeshGAN. The data themselves are described as curated from Hammersmith Hospital, but the text provided does not state that TAAMesh has been publicly released. In the paper’s own framing, MCMeshGAN represents a step toward personalized 3D disease trajectory modeling, with future work required on surface smoothness, generalization, and clinical deployment (Chen et al., 27 Aug 2025).