Richard Figliola

A modular numerical method for implicit 0D/3D coupling in cardiovascular finite element simulations

Implementation of boundary conditions in cardiovascular simulations poses numerical challenges due to the complex dynamic behavior of the circulatory system. The use of elaborate closed-loop lumped parameter network (LPN) models of the heart and the circulatory system as boundary conditions for computational fluid dynamics (CFD) simulations can provide valuable global dynamic information, particularly for patient specific simulations. In this paper, the necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented. A circuit analogy closed-loop LPN is solved numerically, and pressure and flow information is iteratively passed between the 0D and 3D domains at interface boundaries, resulting in a time-implicit scheme. For Neumann boundaries, an implicit method, regardless of the LPN, is presented to achieve the desired stability and convergence properties. Numerical procedures for passing flow and pressure information between the 0D and 3D domains are described, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared. The issue of divergence in the presence of backflow is addressed via a stabilized boundary formulation. The requirements for coupling Dirichlet boundary conditions are also discussed and this approach is compared in detail to that of the Neumann coupled boundaries. Having the option to select between Dirichlet and Neumann coupled boundary conditions increases the flexibility of current framework by allowing a wide range of components to be used at the 3D-0D interface.

A Simulation Protocol for Exercise Physiology in Fontan Patients Using a Closed Loop Lumped-Parameter Model

BACKGROUND Reduced exercise capacity is nearly universal among Fontan patients, though its etiology is not yet fully understood. While previous computational studies have attempted to model Fontan exercise, they did not fully account for global physiologic mechanisms nor directly compare results against clinical and physiologic data. METHODS In this study, we developed a protocol to simulate Fontan lower-body exercise using a closed-loop lumped-parameter model describing the entire circulation. We analyzed clinical exercise data from a cohort of Fontan patients, incorporated previous clinical findings from literature, quantified a comprehensive list of physiological changes during exercise, translated them into a computational model of the Fontan circulation, and designed a general protocol to model Fontan exercise behavior. Using inputs of patient weight, height, and if available, patient-specific reference heart rate (HR) and oxygen consumption, this protocol enables the derivation of a full set of parameters necessary to model a typical Fontan patient of a given body-size over a range of physiologic exercise levels. RESULTS In light of previous literature data and clinical knowledge, the model successfully produced realistic trends in physiological parameters with exercise level. Applying this method retrospectively to a set of clinical Fontan exercise data, direct comparison between simulation results and clinical data demonstrated that the model successfully reproduced the average exercise response of a cohort of typical Fontan patients. CONCLUSION This work is intended to offer a foundation for future advances in modeling Fontan exercise, highlight the needs in clinical data collection, and provide clinicians with quantitative reference exercise physiologies for Fontan patients.

Blockage of natural convection boundary layer flow in a multizone enclosure

Abstract Two separate mechanisms can be responsible for natural convection flow between the hot and cold zones of a multizone enclosure: (1) bulk density differences created by temperature differences between the fluid in the hot and cold zones (bulk-density-driven flow) and, (2) thermosyphon “pumping” generated by boundary layers or plumes (motion-pressure-driven flow). This paper reports the results of an experimental study that examines the transition between flow regimes, as a function of aperture size, in a two-zone enclosure with heated and cooled end walls. A constant heat flux boundary condition was maintained on one vertical end wall, and an isothermal cold temperature sink was maintained on the opposite vertical end wall. All of the remaining surfaces were highly insulated. The transition between the boundary-layer-driven regime and the bulk-density-driven regime was established as a function of the geometry of the aperture in a partition that separated the hot and cold zones. The results of the study demonstrate that transition from the boundary-layer-driven regime to the bulk-density-driven regime is caused by blockage of the boundary layer flow when the area of the flow aperture is reduced below a critical value. A preliminary model has been developed which predicts that the critical aperture area for the onset of flow blockage is directly proportional to the number of active heat transfer surfaces and inversely proportional to the Rayleigh number which characterizes the level of heating and cooling provided to the active heat transfer surfaces.

Mock circulatory system of the Fontan circulation to study respiration effects on venous flow behavior.

We describe an in vitro model of the Fontan circulation with respiration to study subdiaphragmatic venous flow behavior. The venous and arterial connections of a total cavopulmonary connection (TCPC) test section were coupled with a physical lumped parameter (LP) model of the circulation. Intrathoracic and subdiaphragmatic pressure changes associated with normal breathing were applied. This system was tuned for two patients (5 years, 0.67 m2; 10 years, 1.2 m2) to physiological values. System function was verified by comparison to the analytical model on which it was based and by consistency with published clinical measurements. Overall, subdiaphragmatic venous flow was influenced by respiration. Flow within the arteries and veins increased during inspiration but decreased during expiration, with retrograde flow in the inferior venous territories. System pressures and flows showed close agreement with the analytical LP model (p < 0.05). The ratio of the flow rates occurring during inspiration to expiration were within the clinical range of values reported elsewhere. The approach used to set up and control the model was effective and provided reasonable comparisons with clinical data.

Control of Respiration-Driven Retrograde Flow in the Subdiaphragmatic Venous Return of the Fontan Circulation

Respiration influences the subdiaphragmatic venous return in the total cavopulmonary connection (TCPC) of the Fontan circulation whereby both the inferior vena cava (IVC) and hepatic vein flows can experience retrograde motion. Controlling retrograde flows could improve patient outcomes. Using a patient-specific model within a Fontan mock circulatory system with respiration, we inserted a valve into the IVC to examine its effects on local hemodynamics while varying retrograde volumes by changing vascular impedances. A bovine valved conduit reduced IVC retrograde flow to within 3% of antegrade flow in all cases. The valve closed only under conditions supporting retrograde flow and its effects on local hemodynamics increased with larger retrograde volume. Liver and TCPC pressures improved only when the valve leaflets were closed whereas cycle-averaged pressures improved only slightly (<1 mm Hg). Increased pulmonary vascular resistance raised mean circulation pressures, but the valve functioned and cardiac output improved and stabilized. Power loss across the TCPC improved by 12%–15% (p < 0.05) with a valve. The effectiveness of valve therapy is dependent on patient vascular impedance.

In vitro study of the norwood palliation: A patient-specific mock circulatory system

The aim of this study was to build a mock circulatory system replicating in vitro the hemodynamics following the Norwood procedure and testing patient-specific anatomies focusing on the effect of aortic coarctation. Three anatomies were reconstructed from magnetic resonance images and rapid prototyped with transparent rigid resin. The models presented varying degrees of coarctation (none, moderate, and severe). A Blalock-Taussing (BT) shunt was modeled in all phantoms, which were inserted into a mock circulation. The single ventricle was simulated using a Berlin Heart driven with a PC-controlled piston. Resistive and compliant elements were implemented, creating a lumped parameter network. Pressure was measured at three locations: the transverse aortic arch, just after the aortic isthmus, and further downstream in the thoracic aorta. Volume distribution was derived from the instantaneous flow measurements at three outlets: upper body, lower body, and BT shunt. The combination of three-dimensional (3D) detailed anatomy and lumped parameter network effectively renders the circuit a multiscale in vitro model that successfully reproduces physiologic pressure signals. The pressure results highlight the larger pressure drop caused by coarctation and show the effect of pressure recovery. Results also suggest a reduction of flow to the lower body with increasing severity of coarctation, to the advantage of upper body and pulmonary circulation.

How successful is successful? Aortic arch shape after successful aortic coarctation repair correlates with left ventricular function

Objectives: Even after successful aortic coarctation repair, there remains a significant incidence of late systemic hypertension and other morbidities. Independently of residual obstruction, aortic arch morphology alone may affect cardiac function and outcome. We sought to uncover the relationship of arch 3‐dimensional shape features with functional data obtained from cardiac magnetic resonance scans. Methods: Three‐dimensional aortic arch shape models of 53 patients (mean age, 22.3 ± 5.6 years) 12 to 38 years after aortic coarctation repair were reconstructed from cardiac magnetic resonance data. A novel validated statistical shape analysis method computed a 3‐dimensional mean anatomic shape of all aortic arches and calculated deformation vectors of the mean shape toward each patients arch anatomy. From these deformations, 3‐dimensional shape features most related to left ventricular ejection fraction, indexed left ventricular end‐diastolic volume, indexed left ventricular mass, and resting systolic blood pressure were extracted from the deformation vectors via partial least‐squares regression. Results: Distinct arch shape features correlated significantly with left ventricular ejection fraction (r = 0.42, P = .024), indexed left ventricular end‐diastolic volume (r = 0.65, P < .001), and indexed left ventricular mass (r = 0.44, P = .014). Lower left ventricular ejection fraction, larger indexed left ventricular end‐diastolic volume, and increased indexed left ventricular mass were identified with an aortic arch shape that has an elongated ascending aorta with a high arch height‐to‐width ratio, a relatively short proximal transverse arch, and a relatively dilated descending aorta. High blood pressure seemed to be linked to gothic arch shape features, but this did not achieve statistical significance. Conclusions: Independently of hemodynamically important arch obstruction or residual aortic coarctation, specific aortic arch shape features late after successful aortic coarctation repair seem to be associated with worse left ventricular function. Analyzing 3‐dimensional shape information via statistical shape modeling can be an adjunct to long‐term risk assessment in patients after aortic coarctation repair.

Comparative In Vitro Study of Bileaflet and Tilting Disk Valve Behavior in the Pulmonary Position

A study of mechanical heart valve behavior in the pulmonary position as a function of pulmonary vascular resistance is reported for the St. Jude Medical bileaflet (SJMB) valve and the MedicalCV Omnicarbon (OTD) tilting disk valve. Tests were conducted in a pulmonic mock circulatory system and impedance was varied in terms of system pulmonary vascular resistance (PVR). An impedance spectrum was found using instantaneous pulmonary artery pressure and flow rate curves. Both valves fully opened and closed at and above a nominal PVR of 3.0 mmHg/L/min. The SJMB valve was prone to leaflet bounce at closure, but otherwise completely closed, at settings above and below this nominal setting. At PVR values at and below 2.0 mmHg/L/min, the SJMB valve exhibited two types of leaflet aberrant behavior: single leaflet only closure while the other leaflet fluttered, and incomplete closure where both leaflets flutter but neither remain fully closed. The OTD valve fully opened and closed to a PVR value of 1.6 mmHg/L/min. At lower values, the valve did not close. Valves designed for the left heart can show aberrant behavior under normal conditions as pulmonary valves.

A study of the dynamic response of a local heat flux probe

A study of the transient and frequency response of a heat flux probe is reported. The probe consists of a metallic film sensor deposited onto a substrate and covered by a thin protective coating. This study considers the case of constant sensor temperature operation with the probe mounted in an isothermal wall and one probe surface exposed to a convecting environment. A two-dimensional numerical analysis of the probe subjected to both step change and periodic boundary conditions is presented. The effect of probe design on temporal and frequency response and probe sensitivity is demonstrated.

Modeling single ventricle physiology: review of engineering tools to study first stage palliation of hypoplastic left heart syndrome

First stage palliation of hypoplastic left heart syndrome, i.e., the Norwood operation, results in a complex physiological arrangement, involving different shunting options (modified Blalock-Taussig, RV-PA conduit, central shunt from the ascending aorta) and enlargement of the hypoplastic ascending aorta. Engineering techniques, both computational and experimental, can aid in the understanding of the Norwood physiology and their correct implementation can potentially lead to refinement of the decision-making process, by means of patient-specific simulations. This paper presents some of the available tools that can corroborate clinical evidence by providing detailed insight into the fluid dynamics of the Norwood circulation as well as alternative surgical scenarios (i.e., virtual surgery). Patient-specific anatomies can be manufactured by means of rapid prototyping and such models can be inserted in experimental set-ups (mock circulatory loops) that can provide a valuable source of validation data as well as hydrodynamic information. Such models can be tuned to respond to differing the patient physiologies. Experimental set-ups can also be compatible with visualization techniques, like particle image velocimetry and cardiovascular magnetic resonance, further adding to the knowledge of the local fluid dynamics. Multi-scale computational models include detailed three-dimensional (3D) anatomical information coupled to a lumped parameter network representing the remainder of the circulation. These models output both overall hemodynamic parameters while also enabling to investigate the local fluid dynamics of the aortic arch or the shunt. As an alternative, pure lumped parameter models can also be employed to model Stage 1 palliation, taking advantage of a much lower computational cost, albeit missing the 3D anatomical component. Finally, analytical techniques, such as wave intensity analysis, can be employed to study the Norwood physiology, providing a mechanistic perspective on the ventriculo-arterial coupling for this specific surgical scenario.