A stabilized linear finite element method for anisotropic poroelastodynamics with application to cardiac perfusion

Modelling the rheology of living cell cytoplasm: poroviscoelasticity and fluid-to-solid transition

Eukaryotic cell rheology has important consequences for vital processes such as adhesion, migration, and differentiation. Experiments indicate that cell cytoplasm can exhibit both elastic and viscous characteristics in different regimes, while the transport of fluid (cytosol) through the cross-linked filamentous scaffold (cytoskeleton) is reminiscent of mass transfer by diffusion through a porous medium. To gain insights into this complex rheological behaviour, we construct a computational model for the cell cytoplasm as a poroviscoelastic material formulated on the principles of nonlinear continuum mechanics, where we model the cytoplasm as a porous viscoelastic scaffold with an embedded viscous fluid flowing between the pores to model the cytosol. Baseline simulations (neglecting the viscosity of the cytosol) indicate that the system exhibits seven different regimes across the parameter space spanned by the viscoelastic relaxation timescale of the cytoskeleton and the poroelastic diffusion timescale; these regimes agree qualitatively with experimental measurements. Furthermore, the theoretical model also allows us to elucidate the additional role of pore fluid viscosity, which enters the system as a distinct viscous timescale. We show that increasing this viscous timescale hinders the passage of the pore fluid (reducing the poroelastic diffusion) and makes the cytoplasm rheology increasingly incompressible, shifting the phase boundaries between the regimes.

Modelling coronary flow and myocardial perfusion by integrating a structured-tree coronary flow model and a hyperelastic left ventricle model

BACKGROUND AND OBJECTIVE

There is an increasing demand to establish integrated computational models that facilitate the exploration of coronary circulation in physiological and pathological contexts, particularly concerning interactions between coronary flow dynamics and myocardial motion. The field of cardiology has also demonstrated a trend toward personalised medicine, where these integrated models can be instrumental in integrating patient-specific data to improve therapeutic outcomes. Notably, incorporating a structured-tree model into such integrated models is currently absent in the literature, which presents a promising prospect. Thus, the goal here is to develop a novel computational framework that combines a 1D structured-tree model of coronary flow in human coronary vasculature with a 3D left ventricle model utilising a hyperelastic constitutive law, enabling the physiologically accurate simulation of coronary flow dynamics.

METHODS

We adopted detailed geometric information from previous studies of both coronary vasculature and left ventricle to construct the coronary flow model and the left ventricle model. The structured-tree model for coronary flow was expanded to encompass the effect of time-varying intramyocardial pressure on intramyocardial blood vessels. Simultaneously, the left ventricle model served as a robust foundation for the calculation of intramyocardial pressure and subsequent quantitative evaluation of myocardial perfusion. A one-way coupling framework between the two models was established to enable the evaluation and examination of coronary flow dynamics and myocardial perfusion.

RESULTS

Our predicted coronary flow waveforms aligned well with published experimental data. Our model precisely captured the phasic pattern of coronary flow, including impeded or even reversed flow during systole. Moreover, our assessment of coronary flow, considering both globally and regionally averaged intramyocardial pressure, demonstrated that elevated intramyocardial pressure corresponds to increased impeding effects on coronary flow. Furthermore, myocardial blood flow simulated from our model was comparable with MRI perfusion data at rest, showcasing the capability of our model to predict myocardial perfusion.

CONCLUSIONS

The integrated model introduced in this study presents a novel approach to achieving physiologically accurate simulations of coronary flow and myocardial perfusion. It holds promise for its clinical applicability in diagnosing insufficient myocardial perfusion.

Effect of pulmonary regurgitation on cardiac functions based on a human bi-ventricle model

BACKGROUND AND OBJECTIVE

Assessing the severity of pulmonary regurgitation (PR) and identifying optimal clinically relevant indicators for its treatment is crucial, yet standards for quantifying PR remain unclear in clinical practice. Computational modelling of the heart is in the process of providing valuable insights and information for cardiovascular physiology research. However, the advancements of finite element computational models have not been widely applied to simulate cardiac outputs in patients with PR. Furthermore, a computational model that incorporates both the left ventricle (LV) and right ventricle (RV) can be valuable in assessing the relationship between left and right ventricular morphometry and septal motion in PR patients. To enhance our understanding of the effect of PR on cardiac functions and mechanical behaviour, we developed a human bi-ventricle model to simulate five cases with varying degrees of PR severity.

METHODS

This bi-ventricle model was built using a patient-specific geometry and a widely used myofibre architecture. The myocardial material properties were described by a hyperelastic passive constitutive law and a modified time-varying elastance active tension model. To simulate realistic cardiac functions and the dysfunction of the pulmonary valve in PR disease cases, open-loop lumped parameter models representing systemic and pulmonary circulatory systems were designed.

RESULTS

In the baseline case, pressures in the aorta and main pulmonary artery and ejection fractions of both the LV and RV were within normal physiological ranges reported in the literature. The end-diastolic volume (EDV) of the RV under varying degrees of PR was comparable to the reported cardiac magnetic resonance imaging data. Moreover, RV dilation and interventricular septum motion from the baseline to the PR cases were clearly observed through the long-axis and short-axis views of the bi-ventricle geometry. The RV EDV in the severe PR case increased by 50.3% compared to the baseline case, while the LV EDV decreased by 18.1%. The motion of the interventricular septum was consistent with the literature. Furthermore, ejection fractions of both the LV and RV decreased as PR became severe, with LV ejection fraction decreasing from 60.5% at baseline to 56.3% in the severe case and RV ejection fraction decreasing from 51.8% to 46.8%. Additionally, the average myofibre stress of the RV wall at end-diastole significantly increased due to PR, from 2.7±12.1 kPa at baseline to 10.9±26.5 kPa in the severe case. The average myofibre stress of the LV wall at end-diastole increased from 3.7±18.1 kPa to 4.3±20.3 kPa.

CONCLUSIONS

This study established a foundation for the computational modelling of PR. The simulated results showed that severe PR leads to reduced cardiac outputs in both the LV and RV, clearly observable septum motion, and a significant increase in the average myofibre stress in the RV wall. These findings demonstrate the potential of the model for further exploration of PR.