Iliac vein morphology and wall shear stress: a statistical shape modelling and CFD analysis of patient-specific geometries

This study demonstrates that the level of anatomical fidelity in computational models of the common iliac veins critically influences both the statistical characterization of shape variability and the accuracy of hemodynamic risk predictions for deep vein thrombosis, revealing that simplified geometries significantly overestimate low wall shear stress areas compared to patient-specific 3D reconstructions.

The Gist

The Big Picture: Why Do Blood Clots Form?

Imagine your veins are like a network of rivers. Sometimes, the water (blood) flows smoothly, but sometimes it gets stuck, slows down, or swirls in a way that causes debris (blood clots) to pile up. This condition is called Deep Vein Thrombosis (DVT).

Doctors know that the shape of the river matters. If a river has a sharp bend or a sudden narrowing, the water slows down there, and debris is more likely to get stuck. But until now, it's been hard to predict exactly which shapes are dangerous and why.

This study is like a detective investigation. The researchers wanted to answer a simple question: Does the level of detail in our 3D models of veins change how we predict where blood clots might form?

The Three "Maps" of the Vein

To solve this, the team looked at the veins of 12 different patients using three different levels of "map detail," similar to how you might look at a city:

1. The 2D Shadow (The Silhouette): Imagine holding a flashlight against a wall and looking at the shadow of a tree. You can see the outline, but you can't see the depth or the branches sticking out the back. This is what the researchers did with 2D projections. It's a flat, simple view, like a standard X-ray.
2. The Cardboard Cutout (The Extrusion): Imagine taking that 2D shadow and gluing it onto a piece of cardboard to make it 3D, but keeping it perfectly flat and uniform, like a cardboard cutout of a person. This is the Simplified 3D model. It has depth, but it's a bit "fake" because it ignores the natural curves and twists of the real vein.
3. The Sculpture (The Full Reconstruction): This is a hyper-realistic, hand-carved wooden sculpture of the tree, capturing every twist, turn, and bump. This is the Full 3D reconstruction from MRI/CT scans. It is the most accurate representation of the patient's actual anatomy.

The Experiment: Simulating the Flow

The researchers used a super-computer to simulate blood flowing through these three types of "maps" for each patient. They were looking for "Low Wall Shear Stress" (WSS).

• The Analogy: Imagine rubbing your hand against a wall. If you rub it fast, the friction is high (High WSS). If you just let your hand rest there or move it very slowly, the friction is low (Low WSS).
• The Danger: In veins, Low WSS is bad news. It's like the water moving so slowly that it starts to stagnate, allowing blood clots to form. The researchers wanted to see how much "stagnant water" area existed in each of their three map types.

The Surprising Findings

Here is what they discovered, which is the most important part of the paper:

1. The "Cardboard Cutout" Overestimates the Danger
When they used the simplified 3D models (the cardboard cutouts), the computer predicted much larger areas of stagnant blood (up to 136% more!) compared to the realistic sculptures.

• The Metaphor: It's like looking at a flat map of a winding road and thinking the whole road is a traffic jam, when in reality, the 3D road has curves that actually help the cars (blood) keep moving. The simplified models are too "clunky" and create artificial traffic jams that don't exist in real life.

2. The "Shadow" vs. The "Sculpture" Tell Different Stories
The researchers used a mathematical tool called Statistical Shape Modelling (SSM). Think of this as a way to describe how veins vary from person to person using a list of "ingredients" (like bending, twisting, or getting wider).

• In the 2D Shadow: The math found one "super-ingredient" (Mode 1) that explained almost everything. It was very easy to say, "If the vein bends this way, the blood will stop." The connection between shape and danger was very strong and clear.
• In the Full 3D Sculpture: The math found that the differences between people were spread out over many tiny ingredients. No single "super-ingredient" stood out. The connection between shape and danger was much weaker and harder to spot.
• The Metaphor: In the 2D world, the problem looks like a single, loud alarm bell. In the 3D world, the problem is like a quiet hum coming from many different speakers at once. It's much harder to pinpoint the exact cause.

3. The "Alignment" Problem
Why did the 2D and 3D models behave so differently? It came down to how they were lined up before the math started.

• 2D: They lined them up by keeping the natural angle of the vein (like lining up cars in a parking lot by their front bumpers). This kept the "natural pose" of the vein, which turned out to be very important for predicting flow.
• 3D: Because the 3D models were so complex, the computer had to line them up by their center lines (like lining up cars by their center of gravity). This stripped away the natural "pose" and orientation, leaving only the tiny, subtle differences. This made the math much more difficult.

The Takeaway for You

This study teaches us a valuable lesson about medical technology: More detail isn't always easier to interpret, and less detail isn't always "good enough."

• If you use a simplified model (like a cardboard cutout), you might scare yourself by predicting too many clots that won't actually happen.
• If you use a super-detailed model, you get the truth, but the relationship between the shape and the risk becomes so complex that it's hard to find a simple rule to follow.

The Bottom Line:
When doctors or engineers try to predict blood clots using computer simulations, they have to be very careful about how they build their models. The way they choose to represent the vein (flat shadow vs. 3D sculpture) and how they line them up changes the answer they get.

This research is a crucial step toward building better, personalized tools for treating DVT, ensuring that we don't over-treat patients based on fake "traffic jams" created by our own computer models.

Technical Summary

1. Problem Statement

Deep Vein Thrombosis (DVT) is a prevalent vascular condition where blood clots form in deep veins, often leading to Post-Thrombotic Syndrome (PTS). While anatomical variations (e.g., vessel shape, compression) and flow disturbances are known risk factors, the mechanistic links between specific venous geometries and hemodynamic risk metrics (specifically Wall Shear Stress, or WSS) remain poorly quantified.

Current clinical practice relies on anatomical imaging (MRI/CT, angiography) but lacks quantitative flow assessment. Computational Fluid Dynamics (CFD) can estimate risk metrics like low WSS (associated with coagulation), but the influence of geometric fidelity (how closely a model represents true anatomy) and alignment strategies on these predictions is not well understood. There is a critical gap in understanding whether simplified 2D or idealized 3D models are sufficient for predicting thrombosis risk compared to full patient-specific 3D reconstructions.

2. Methodology

The study employed a combined workflow of Statistical Shape Modelling (SSM) and Computational Fluid Dynamics (CFD) using data from 12 patients with DVT.

A. Data Acquisition and Geometry Reconstruction

Three levels of anatomical fidelity were constructed from patient MRI/CT data to compare their impact:

1. Full 3D Reconstruction: Direct segmentation of the common iliac veins from volumetric MRI/CT data.
2. 2D Projections: 2D contours representing the projection of the 3D geometry into a standard angiographic plane.
3. Simplified 3D Extrusions: 3D geometries generated by extruding the 2D projections, neglecting out-of-plane curvature (simulating a workflow based solely on 2D angiograms).

B. Statistical Shape Modelling (SSM)

• Tool: Deformetrica (Python library based on Large Deformation Diffeomorphic Metric Mapping - LDDMM).
• Framework:
  • Deterministic Atlas: Constructed a population template ($I_0$) and initial momenta ($m_i$) to deform the template to each subject.
  • Principal Geodesic Analysis (PGA): Performed on the deformation momenta to identify dominant modes of shape variation.
• Alignment Strategies:
  • 2D: Anatomically anchored alignment (preserving natural inflow angles and curvature).
  • 3D: Centerline-based alignment (minimizing pairwise discrepancy between centrelines, effectively removing global pose to isolate intrinsic morphological differences).

C. Computational Fluid Dynamics (CFD)

• Solver: ANSYS Fluent 2024 R2.
• Conditions: Steady-state, laminar flow, incompressible Newtonian fluid (blood density $\rho=1050$ kg/m³, viscosity $\mu=0.0035$ Pa·s).
• Boundary Conditions: Parabolic velocity inlet (baseline $Re \approx 354$), zero pressure outlet. Sensitivity analysis included $\pm 20\%$ inlet velocity variations.
• Metric: Surface area of the vessel wall exposed to low WSS, calculated at three nested thresholds: $\le 0.05$, $0.10$, and $0.15$ Pa.

D. Statistical Analysis

• Correlation: Spearman's rank correlation ($\rho_S$) between SSM latent modes and low-WSS burden metrics.
• Significance: Permutation testing (2,000 permutations) and Benjamini-Hochberg False Discovery Rate (FDR) correction to handle multiple testing.
• Robustness: Leave-one-out (LOO) analysis and bootstrap confidence intervals.

3. Key Contributions

1. Systematic Fidelity Comparison: The first study to systematically compare 2D projections, simplified 3D extrusions, and full 3D reconstructions within a unified SSM-CFD framework for venous anatomy.
2. Alignment Strategy Impact: Demonstrated that the choice of alignment (anatomical vs. centerline) fundamentally alters the latent variance structure of the shape model.
3. Quantification of Simplification Bias: Quantified the systematic overestimation of low-WSS areas in simplified geometries compared to patient-specific models.
4. Workflow Integration: Established a reproducible, automated pipeline (using PyFluent and Deformetrica) for mapping principal shape deformations to localized hemodynamic risk zones.

4. Key Results

A. Geometric Fidelity and Low-WSS Areas

• Overestimation: Idealized geometries (2D projections and simplified 3D extrusions) consistently produced larger low-WSS areas than full patient-specific 3D reconstructions.
• Magnitude: The average increase in low-WSS area for simplified models ranged from 78% to 136% across the three thresholds compared to full 3D shapes.
• Conclusion: Simplified models introduce a systematic bias that exaggerates thrombosis risk regions.

B. Statistical Shape Model Structure

• 2D SSM: Exhibited a hierarchical variance spectrum. Mode 1 explained ~33% and Mode 2 explained ~21% of the variance. These modes captured large-scale global features (bending, tapering).
• 3D SSM: Exhibited a flat variance spectrum. Mode 1 explained only ~17.4%, with subsequent modes contributing ~7–9% each. The centerline alignment removed global pose, leaving only subtle, diffuse local variations (radius, taper, minor curvature).

C. Shape-Flow Correlations

• 2D SSM: Showed strong, significant univariate associations. Mode 1 (global bending/tapering) had strong negative correlations with low-WSS area ($\rho_S \approx -0.58$ to $-0.93$) and survived FDR correction for the 0.10 and 0.15 Pa thresholds.
• 3D SSM: Showed weak, heterogeneous associations. No single mode survived FDR correction. The correlation was distributed across multiple modes, reflecting the flat variance spectrum where flow effects are spread out rather than concentrated in one dominant direction.

D. Sensitivity

• Inflow Velocity: While absolute low-WSS areas changed with inlet velocity ($\pm 20\%$), the relative ranking of patients (who had the highest risk) remained stable. This confirms that geometric differences are the primary driver of variability, not boundary condition fluctuations within a physiological range.

5. Significance and Implications

• Model Selection is Critical: The study proves that the choice of geometric representation (2D vs. 3D) and alignment strategy is not merely a technical detail but fundamentally alters hemodynamic inferences. Simplified models may lead to false positives in risk stratification.
• Clinical Workflow: For accurate DVT risk assessment, full 3D patient-specific reconstructions are superior to 2D projections or idealized extrusions.
• Methodological Insight: The divergence between 2D and 3D results highlights that "shape" is context-dependent. In 2D, global pose is a major source of variance; in 3D (with centerline alignment), variance is dominated by subtle local morphological nuances.
• Future Directions: The authors emphasize the need for larger cohorts to enable multivariate analysis (currently limited by $n=12$) and the development of robust shape biomarkers for personalized DVT treatment planning.

Conclusion: The paper concludes that while SSM-CFD integration is a powerful tool for understanding venous thrombosis, the fidelity of the anatomical model and the alignment strategy critically determine the validity of the hemodynamic risk predictions. Simplified models systematically overestimate risk, and the "dominant" shape-flow relationship observed in 2D does not translate directly to 3D due to differences in how anatomical variability is encoded.