Research/Computational Methods/01 / 02

Multiscale and Multiphysics Modeling

Biological systems involve interactions among blood flow, tissue mechanics, and transport processes across multiple spatial and temporal scales. We develop computational frameworks that couple reduced-dimensional vascular models with three-dimensional tissue domains. These frameworks retain essential local physics while reducing computational cost and enable consistent exchange of mechanical and transport variables across coupled domains. Our methods support subject-specific analyses of hemodynamics, tissue deformation, perfusion, and biological transport under physiological and externally applied loading.

A branching vascular network inside a three-dimensional tissue block — the large vessels drawn explicitly as a one-dimensional network, the small ones absorbed into the continuum, with the exchanges between them marked — Terminal-segment pressures are passed to the tissue continuum as distributed sources, and the integrated tissue flow returns to the segment that supplied it.

Hybrid-Dimensional Fluid–Structure Interaction

We couple one-dimensional deformable blood-flow models with three-dimensional tissue mechanics to represent the interaction among intravascular pressure, vessel deformation, and external loading. Pressure and cross-sectional deformation are exchanged iteratively between the fluid and structural domains. This hybrid-dimensional formulation preserves the principal fluid–structure coupling while avoiding a full three-dimensional fluid solution throughout the vascular domain.

Comparison with full three-dimensional fluid–structure interaction simulations demonstrates similar transient flow and deformation responses at substantially lower computational cost in both simplified and subject-specific geometries.

3D tissue and vessel cross-section under external pressure → the same vessel as a 1D centerline domain → pressure and cross-sectional deformation exchanged at the interface → multi-fidelity and full 3D FSI results compared — A three-dimensional vessel wall under external pressure exchanges cross-sectional area and lumen pressure with a one-dimensional flow domain, iterated to convergence at each time step.

Multiscale Vascular–Tissue Transport

We explicitly represent larger vessels with one-dimensional flow and transport equations and represent smaller vascular structures within a three-dimensional tissue continuum. Bidirectional coupling accounts for vessel–tissue exchange and maintains consistency of energy or mass transfer across the coupled domains. This framework allows localized effects of vascular architecture and tissue heterogeneity to be examined beyond homogeneous bioheat or porous-medium descriptions.

Explicit 1D vascular network, the heat or mass flux exchanged with the surrounding tissue, and the resulting field in the 3D tissue — set against the same case solved as a homogenized bioheat model — Blood flow along the vessel and conductive flux across the vessel wall produce the three-dimensional tissue temperature field, shown with the explicit network resolved inside it.

Network-to-Tissue Hemodynamics and Physiological Regulation

We connect arterial and venous networks, pre- and postcapillary compartments, and a three-dimensional perfusion domain to represent blood transport across vascular scales. The framework incorporates passive vessel mechanics and active autoregulatory responses to examine how systemic pressure, gravity, vascular stiffness, and metabolic demand affect regional perfusion. This approach provides a mechanistic basis for studying physiological compensation under changing conditions.

As an application, we use this framework to investigate how aortic pressure, body posture, vessel-wall stiffness, and autoregulation jointly affect cerebral blood flow and vascular volume. The cerebral results are treated in Cerebral Perfusion and Autoregulation.

Medical imaging → vascular segmentation → synthetic microvascular networks → multiscale blood-flow simulation → three-dimensional tissue perfusion, with supine, upright and inverted posture compared beneath — Arteries segmented from the image are extended by synthetic tree growth and solved as a pulsatile network, with the vessel area updated from pressure through the tube law.

Verification and Cross-Scale Consistency

We evaluate the coupled frameworks through comparisons with analytical solutions, full-order simulations, and established numerical solvers, as appropriate for each model. The evaluation focuses on interface consistency, conservation of transported quantities, transient response, numerical accuracy, and computational cost before application to subject-specific problems.

A short table of each framework against what it was checked with, and one representative comparison — waveform, relative error and computational time — Pressure over one cardiac cycle from the three-dimensional reference, the present reduced-order method, and a heuristic model.

Selected work

2026

Efficient multi-fidelity fluid-structure interaction modeling for pulsatile blood flow in deformable biological tissues

Annals of Biomedical Engineering

2026

Multiscale modeling of posture-dependent cerebrovascular hemodynamics with autoregulatory coupling

Computers in Biology and Medicine 203:111502

To be submitted

Multiscale transport modeling in biological tissue

Computer Methods in Applied Mechanics and Engineering

Computational Methods2 topics in this area

Multiscale and Multiphysics ModelingEfficient Computational Modeling and Uncertainty Quantification