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

Large vessels are carried as an explicit one-dimensional network, smaller ones as part of the tissue continuum, and the two exchange pressure, deformation and transported quantities across the interface.

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

External pressure deforms the tissue, the tissue sets the vessel area, the area changes the flow, and the flow returns a pressure. The loop is closed at the interface rather than inside a single three-dimensional solution.

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

Resolving the larger vessels explicitly recovers local gradients that a homogenized description averages away.

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

Arterial and venous networks, pre- and postcapillary compartments and a three-dimensional perfusion domain solved together, with posture changed at the systemic boundary.

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

What each framework is checked against, and one representative comparison of waveform, error and cost.

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 Methods 2 topics in this area

Multiscale and Multiphysics ModelingEfficient Computational Modeling and Uncertainty Quantification