Background:
Intracranial aneurysms (IAs) are heightening health concerns. The reasons behind their high rupture rate and the consequent renew of interest in wall biology remain unclear and cannot be addressed using the fluid dynamics and solid mechanics already investigated in the growth and rupture stages [1]. A solid and fluid coupling model governs aneurysm wall biology involving a heterogeneous multiscale approach at large spatial and time scales [2]. Three physio-imaging biomarkers characterizing aneurysm wall microstructure, remodeling, and inflammatory processes can be observed following the natural biological evolution from normal to rupture-prone IAs. Molecular imaging, including the use of targeted gadolinium nanoparticles, iron oxide particles conjugated to selectin-binding ligands, and fluorodeoxyglucose PET, has demonstrated the feasibility of directly visualising specific molecular processes in aneurysm walls in preclinical and early clinical settings. Integration of these molecular signals with computational flow and pharmacokinetic modelling is, however, lacking. The Aneurysm Digital Twin (ADT) framework presented here addresses this gap by training a single PINN on the coupled partial differential equations governing magnetisation dynamics (convective Bloch), blood flow (incompressible Navier-Stokes), and contrast agent transport (Tofts DCE-MRI). Patient-specific arterial input functions and 4D-flow velocity measurements are assimilated directly into the physics loss, while longitudinal state persistence is achieved through visit-to-visit weight transfer.

 

Hypothesis/Objective:
Clinical decision-making for intracranial aneurysms relies on the analysis of the aneurysm wall, where information on the biological state is extracted from MRI- and DCE- derived imaging biomarkers. These imaging technologies capture the spatiotemporal evolution of the contrast agent, which reflects the presence of specific wall microstructure, biological remodeling processes, and inflammatory states. However, the connection from clinical data to the undelying tissue dynamics remains poorly understood, and many biological feedback loops are too complex to model directly.

To unravel the mechanisms behind clinically acquired footage, this study describes the Aneurysm Digital Twin (ADT), a physics-informed neural network (PINN) framework that jointly solves the convective Bloch equations, Navier-Stokes equations, and the Tofts pharmacokinetic model, assimilating real patient arterial input functions (AIF) and 4D-flow MRI velocity measurements in a longitudinally persistent model state.

 

Methods:
Data Acquisition: The dataset used in this study were obtained from an experiment performed on a female patient (with expanded cerebral blood vessels) at the Bauchi State Specialists Hospital, Bauchi, Nigeria, using Superstar 0.35 tesla (Neusoft Medical Systems Co Ltd). Inflow 3D fast sequence (TR = 40ms, TE = 8ms, Pixel band width = 88.18342) was used.

The Aneurysm Digital Twin (ADT) is built around a HybridPINN — a 4-layer fully-connected neural network mapping (x, y, z, t) to eight simultaneous outputs: three magnetisation components (Mx, My, Mz), three velocity components (vx, vy, vz), gadolinium tissue concentration (Ct), and pressure (p). Training enforces four coupled physics residuals via automatic differentiation: the convective Bloch equations (MRI magnetisation transport with Gd-coupled R1 relaxation), incompressible Navier-Stokes (haemodynamics), the Tofts DCE-MRI ODE (contrast agent kinetics) [3, 4], and a 4D-flow assimilation loss that penalises deviation from sparse measured velocities. The resulting graphic user interface is shown in figure 1.

Three patient-specific data sources replace all population-level defaults: a measured ICA arterial input function Cp(t) from CSV replaces the Parker population AIF; DCE-fitted parameters (Ktrans, ve, vp) and per-vertex quantitative MRI maps (T1, T2 from VFA) replace manual sliders; and sparse 4D-flow velocity measurements are directly assimilated into the training objective. Between clinical visits, the model is warm-started from the previous visit’s saved weights rather than re-initialised, accumulating longitudinal physiological knowledge.

 

Results:
Warm-started models reached a target loss threshold in a median of 387 epochs versus 912 epochs for cold-start models — a 57% reduction in training time, as shown in figure 2, with smoother WSS fields and more physically consistent pressure distributions as a qualitative benefit. On AIF individualisation, the patient-measured AIF recovered dome Ktrans with 1.7% error (0.122 vs. ground truth 0.120 min⁻¹), while the Parker population AIF produced a 9.2% error (0.109 min⁻¹), confirming systematic bias in population-averaged approaches. The risk escalation detection module correctly flagged all inter-visit risk-tier increases across synthetic longitudinal test cases, tracking delta-Ktrans of +0.04 min⁻¹ per interval, with zero false positives across 20 stable-trajectory test cases. Resulting maps for hemodynamic features are demonstrated in figures 3 and 4. Figure 5 shows the results from PINN trained on the DCE-MRI Tofts model. Figure 6 demonstrates how the digital model could be employed for real-time molecular imaging while figure 7 shows the distribution of magnetization vectors useful for anatomical imaging.

 

Conclusion:
The ADT demonstrates that closing the three gaps — individualised AIF, fitted patient parameters, and persistent warm-started state — produces measurably more accurate and clinically actionable outputs than conventional PINN surrogates. The warm-start mechanism halves training cost while improving physical consistency, patient-specific AIF reduces permeability estimation error by over fivefold, and the longitudinal analytics engine reliably detects pathophysiological progression. Critically, the framework’s native coupling of DCE-MRI pharmacokinetics with haemodynamic simulation positions it as a natural substrate for molecular imaging integration. Ktrans and the gadolinium tissue concentration field Ct(x, t) are direct surrogates for blood-brain barrier permeability and endothelial inflammation — quantities that next-generation targeted molecular imaging agents (such as vessel-wall MRI with fibrin- or VCAM-1-directed probes) are designed to quantify. By replacing or augmenting the Tofts AIF with the time-activity curves of molecularly targeted tracers, the ADT could map spatial distributions of specific biological processes — thrombus organisation, macrophage infiltration, or matrix metalloproteinase activity — directly onto the vessel wall alongside WSS and pressure fields. This would transform rupture risk stratification from a purely mechanical assessment into a joint haemodynamic-molecular phenotype, where wall biology and flow environment are monitored together across visits. Prospective clinical validation against real multi-visit imaging cohorts, including emerging molecular MRI protocols, remains the necessary next step before deployment in clinical decision-making.

 

Image/Figure:
Click to view full size
Click to view full size

Image/Figure Caption:
Figures

 

Author
Bamidele Omotayo Awojoyogbe, PhD, MSc, BSc
Federal University of Technology Minna