The question
Chest compressions during cardiopulmonary resuscitation are delivered against a chest wall that does not behave like a spring. It stiffens as it is compressed, it does not fully recover between compressions, and its response depends on how fast it is loaded. Every compression therefore produces a different amount of blood flow than a linear model would predict. If the mechanical response is nonlinear, how much of what reaches the circulation is being mispredicted — and what does a physically honest model change about that estimate?
Overview
This project develops a coupled computational model in which nonlinear viscoelastic chest wall mechanics drive a closed-loop representation of cardiopulmonary circulation. The two halves are usually treated separately: mechanical studies characterize thoracic compliance without propagating the result into hemodynamics, while circulation models take the compression input as a prescribed waveform. Coupling them means the mechanical nonlinearity is no longer a boundary condition but part of the dynamics.
The modeling commitment is that compliance is not constant. Introducing variable compliance and rate dependence changes both the amplitude and the timing of the pressures generated, which matters because the quantity of clinical interest — perfusion — depends on the interaction between those pressures and vascular impedance, not on peak force alone.
The limitations are worth stating plainly. This is a lumped-parameter description, not a spatially resolved one: it captures how the system responds globally, not where stresses concentrate in the thorax. Parameter values are drawn from published characterizations rather than subject-specific measurements, so the model supports comparative and mechanistic reasoning rather than patient-level prediction. It contributes to an established line of cardiopulmonary modeling by relaxing a linearity assumption within it; it does not introduce a new paradigm for resuscitation modeling.
Approach and methods
The chest wall is represented with nonlinear viscoelastic elements, so restoring force depends on both displacement and compression rate, and hysteresis between loading and unloading is retained rather than averaged out.
The circulation is a closed-loop, multi-compartment system in which each vascular segment carries compliance, resistance and inertance. A nonlinear Windkessel formulation allows arterial compliance to vary with pressure, which is the mechanism through which pathological conditions — arterial stiffening in particular — enter the model as a parameter change rather than as a separate model.
Cardiac rhythm is generated by coupled Van der Pol oscillators, whose self-sustaining limit-cycle behavior reproduces the qualitative structure of physiological rhythms and their loss of coherence, without imposing a fixed waveform on the system.
The resulting signals are non-stationary by construction, so analysis uses the group’s time-frequency toolset — synchrosqueezing and synchroextracting transforms, wavelet packet decomposition — alongside recurrence analysis, to separate genuine dynamical transitions from artifacts of the transform.
Team
- Marcus Varanis — scientific coordination; chest wall and cardiopulmonary formulation; signal analysis.
- Barbara Oliveira — master’s researcher; coupled 0D–1D cardiovascular modeling, wave-propagation effects and nonlinear stent models.
- Dilson — Iniciação Científica; supporting the coupled 0D–1D cardiovascular modeling work.
Collaborations
Prof. C. Nataraj — Villanova Center for Analytics of Dynamic Systems (VCADS), Villanova University. Joint work on cardiopulmonary modeling and the analysis of physiological dynamics.
Related publications
- Varanis, Ferraz, Longo, Balthazar. A nonlinear Windkessel model for cardiovascular dynamics: variable compliance and pathological simulations. Medical & Biological Engineering & Computing, 2026.
- Varanis, Balthazar, Ribeiro, Tusset, de Oliveira, Lima, Silva. Recurrence analysis of nonlinear ECG signals modeled with coupled Van der Pol oscillators. Springer, Mechanisms and Machine Science, vol. 142, 2025.
- Varanis, Hemmati, Filipus, de Abreu, Balthazar, Nataraj. An overview on time-frequency effects of ECG signals using synchroextracting transform. Springer, NODYCON Conference Proceedings, vol. 3, 2024.
- Ribeiro, Silva, Balthazar, de Lima, Varanis, Tusset. Influence of a non-ideal external force on the complexity of the basins of attraction of coupled Van der Pol oscillators. Brazilian Journal of Physics, 2026.
Current directions
Extending the arterial description from lumped compartments toward coupled 0D–1D representations, so that wave propagation and reflection along the arterial tree are resolved rather than absorbed into a compliance term. Within that setting, the group is examining how nonlinear models of stented vessel segments alter local impedance and how those changes propagate back to the pressures generated during compression.
For prospective students
This project sits primarily in P4 — Computational Biomedical Modeling, with its mechanical foundation in P1. Useful background: ordinary differential equations, numerical integration, and a working comfort with Python. No prior physiology is assumed; the cardiovascular material is learned alongside the modeling.
What a student actually does here is build and interrogate models: implement a compartment, verify it against a limiting case where the answer is known, introduce a nonlinearity, and then determine whether the change in output is physically meaningful or an artifact of the numerics. The work is quantitative and iterative, and the questions it answers are clinical in origin.