Use of mathematical modeling to compare and predict hemodynamic effects between hybrid and surgical Norwood palliations for hypoplastic left heart syndrome.

BACKGROUND: Combining bilateral pulmonary artery banding with arterial duct stenting, the hybrid approach achieves stage 1 palliation for hypoplastic left heart syndrome with different flow characteristics than those after the surgical Norwood procedures. Accordingly, we used computational modeling to assess some of these differences, including influence on systemic and cerebral oxygen deliveries. METHODS AND RESULTS: A 3-dimensional computational model of hybrid palliation was developed by the finite volume method, along with models of the Norwood operation with a modified Blalock-Tausig or right ventricle-to-pulmonary artery shunt. Hybrid circulation was modeled with a 7-mm ductal stent and bilateral pulmonary artery banding to a 2-mm diameter. A 3.5-mm conduit was used in the Blalock-Tausig shunt model, whereas a 5-mm conduit was used in the right ventricle-to-pulmonary artery shunt model. Coupled to all the models was an identical hydraulic network that described the entire circulatory system based on pre-stage 2 hemodynamics. This clinically validated multiscale approach predicts flow dynamics, as well as global cardiac output, mixed venous oxygen saturation, and systemic and cerebral oxygen delivery. Compared with either of the Norwood models, the hybrid palliation had higher pulmonary-to-systemic flow ratio and lower cardiac output. Total systemic oxygen delivery was markedly reduced in the hybrid palliation (Blalock-Tausig shunt 591, right ventricle-to-pulmonary artery shunt 640, and hybrid 475 mL · min(-1) · m(-2)). Cerebral oxygen delivery was similarly lower in the hybrid palliation. CONCLUSIONS: These computational results suggest that the hybrid approach may provide inferior systemic and cerebral oxygen deliveries compared with either of the 2 surgical Norwood procedures before stage 2 palliation.

Patient-specific computational models to support interventional procedures: a case study of complex aortic re-coarctation.

AIMS: We report the application of patient-specific computational models to plan the treatment of complex aortic re-coarctation (rCoA) with a proximal aberrant right subclavian artery in a patient who had previously undergone bare metal stenting. METHODS AND RESULTS: Clinically acquired images were used to set up patient-specific computational models for finite element (FE) and fluid dynamics (CFD) analyses. The 3D geometry was reconstructed from computed tomography and echocardiography images. Computer-generated deployment of a CP covered stent (NuMED, Hopkinton, NY, USA) at different diameters was tested using FE simulations. CFD analyses based on preoperative magnetic resonance flow measurements allowed assessment of rCoA pressure relief and right subclavian artery perfusion in the different scenarios. The simulations suggested an expansion diameter for the CP stent (8 zigs, length=28 mm) of between 16 and 18 mm to relieve the obstruction, cover the aneurysm and maintain satisfactory flow to the right subclavian artery. Following the modelling study, a 16 mm CP covered stent was successfully implanted. CONCLUSIONS: Patient-specific models can be successfully used to plan re-stenting of complex rCoA, showing the benefits of integrating computational techniques into patient management.

Using 4D Cardiovascular Magnetic Resonance Imaging to Validate Computational Fluid Dynamics: A Case Study.

Computational fluid dynamics (CFD) can have a complementary predictive role alongside the exquisite visualization capabilities of 4D cardiovascular magnetic resonance (CMR) imaging. In order to exploit these capabilities (e.g., for decision-making), it is necessary to validate computational models against real world data. In this study, we sought to acquire 4D CMR flow data in a controllable, experimental setup and use these data to validate a corresponding computational model. We applied this paradigm to a case of congenital heart disease, namely, transposition of the great arteries (TGA) repaired with arterial switch operation. For this purpose, a mock circulatory loop compatible with the CMR environment was constructed and two detailed aortic 3D models (i.e., one TGA case and one normal aortic anatomy) were tested under realistic hemodynamic conditions, acquiring 4D CMR flow. The same 3D domains were used for multi-scale CFD simulations, whereby the remainder of the mock circulatory system was appropriately summarized with a lumped parameter network. Boundary conditions of the simulations mirrored those measured in vitro. Results showed a very good quantitative agreement between experimental and computational models in terms of pressure (overall maximum % error = 4.4% aortic pressure in the control anatomy) and flow distribution data (overall maximum % error = 3.6% at the subclavian artery outlet of the TGA model). Very good qualitative agreement could also be appreciated in terms of streamlines, throughout the cardiac cycle. Additionally, velocity vectors in the ascending aorta revealed less symmetrical flow in the TGA model, which also exhibited higher wall shear stress in the anterior ascending aorta.

Measurement of in vitro and in vivo stent geometry and deformation by means of 3D imaging and stereo-photogrammetry.

PURPOSE: To quantify variability of in vitro and in vivo measurement of 3D device geometry using 3D and biplanar imaging. METHODS: Comparison of stent reconstruction is reported for in vitro coronary stent deployment (using micro-CT and optical stereo-photogrammetry) and in vivo pulmonary valve stent deformation (using 4DCT and biplanar fluoroscopy). Coronary stent strut length and inter-strut angle were compared in the fully deployed configuration. Local (inter-strut angle) and global (dog-boning ratio) measures of stent deformation were reported during stent deployment. Pulmonary valve stent geometry was assessed throughout the cardiac cycle by reconstruction of stent geometry and measurement of stent diameter. RESULTS: Good agreement was obtained between methods for assessment of coronary stent geometry with maximum disagreement of +/- 0.03 mm (length) and +/- 3 degrees (angle). The stent underwent large, non-uniform, local deformations during balloon inflation, which did not always correlate with changes in stent diameter. Three-dimensional reconstruction of the pulmonary valve stent was feasible for all frames of the fluoroscopy and for 4DCT images, with good correlation between the diameters calculated from the two methods. The largest compression of the stent during the cardiac cycle was 6.98% measured from fluoroscopy and 7.92% from 4DCT, both in the most distal ring. CONCLUSIONS: Quantitative assessment of stent geometry reconstructed from biplanar imaging methods in vitro and in vivo has shown good agreement with geometry reconstructed from 3D techniques. As a result of their short image acquisition time, biplanar methods may have significant advantages in the measurement of dynamic 3D stent deformation.

Uncertainty assessment of imaging techniques for the 3D reconstruction of stent geometry.

This paper presents a quantitative assessment of uncertainty for the 3D reconstruction of stents. This study investigates a CP stent (Numed, USA) used in congenital heart disease applications with a focus on the variance in measurements of stent geometry. The stent was mounted on a model of patient implantation site geometry, reconstructed from magnetic resonance images, and imaged using micro-computed tomography (CT), conventional CT, biplane fluoroscopy and optical stereo-photogrammetry. Image data were post-processed to retrieve the 3D stent geometry. Stent strut length, separation angle and cell asymmetry were derived and repeatability was assessed for each technique along with variation in relation to µCT data, assumed to represent the gold standard. The results demonstrate the performance of biplanar reconstruction methods is comparable with volumetric CT scans in evaluating 3D stent geometry. Uncertainty on the evaluation of strut length, separation angle and cell asymmetry using biplanar fluoroscopy is of the order ±0.2mm, 3° and 0.03, respectively. These results support the use of biplanar fluoroscopy for in vivo measurement of 3D stent geometry and provide quantitative assessment of uncertainty in the measurement of geometric parameters.

Geometrical and stress analysis of factors associated with stent fracture after melody percutaneous pulmonary valve implantation.

BACKGROUND: Patients treated with the Melody device (Medtronic) for percutaneous pulmonary valve implantation experience stent fractures in ≈25% of the cases. The aim of this study is to identify the risk factors associated with fracture using 3-dimensional (3D) analyses. METHODS AND RESULTS: In situ 3D shape of the Melody stent was reconstructed from 42 patients using procedural biplane fluoroscopy images, after balloon inflation, at systole and diastole. Four geometric parameters at systole and their variation during balloon deflation and cardiac cycles were measured to describe the 3D strut, cell, section, and stent configuration. Furthermore, patient-specific computer simulations were set up to replicate the history of stent deformations for each patient. Maximum and minimum principal stresses resulting from these analyses were monitored during balloon deflation and cardiac cycle. Univariate logistic regression analyses of 21 geometric parameters and of 4 stress parameters respectively, identified the decreased stent circularity after balloon deflation (odds ratio 0.98; 95% confidence interval, 0.96-0.99; P=0.006) and large compressive stresses during balloon deflation (odds ratio, 0.98; 0.96-0.997; P=0.03), as associated with the risk of fracture. In a multivariable logistic regression model, the 2 covariates identified on univariate analysis (1 geometric and 1 stress) were found to be independently associated with the risk of fracture. The resultant statistical model correctly identified fracture/no fracture in 93% of patients. CONCLUSIONS: Changes in stent section shape after balloon deflation are important variables influencing fracture. This methodology could help design tailored follow-up for patients after percutaneous pulmonary valve implantation.

Effects of pulmonary artery banding and retrograde aortic arch obstruction on the hybrid palliation of hypoplastic left heart syndrome.

OBJECTIVES: The hybrid approach achieves stage 1 palliation of hypoplastic left heart syndrome with flow and physiologic characteristics that are different from those of the surgical Norwood circulations. In addition to having branch pulmonary arterial banding regulating the balance between pulmonary and systemic blood flows, coronary and cerebral perfusion are dependent on retrograde flow through the native aortic arch when aortic atresia is present. Accordingly, we used computational modeling to assess the effects of pulmonary artery banding diameter and retrograde aortic arch hypoplasia or obstruction on the hybrid stage 1 circulation, including the influence on systemic and cerebral oxygen deliveries. METHODS: A computational modeling technique was used to couple a 3-dimensional geometry of the hybrid palliation with a hydraulic network of the entire circulation based on pre-stage 2 hemodynamics. This validated multiscale approach predicts clinically relevant outcomes, such as flow, pressure, ejection fraction, and oxygen delivery. Simulations with pulmonary artery banding varying between 1.5 and 3.5 mm were performed. To examine the effects of retrograde aortic arch hypoplasia and obstruction, models of differing aortic arch diameter (2-5 mm) and isthmus coarctation (2.5-5 mm) were studied. RESULTS: Banding the branch pulmonary arteries to 2 mm led to pulmonary and systemic blood flows closest to 1:1 and produced the highest mixed venous saturation and systemic oxygen delivery. Both cerebral and coronary perfusion decreased markedly when the retrograde aortic arch or the coarctation was less than 3 mm in diameter. Moreover, flow reversal in the carotid arteries was observed during diastole in all models. CONCLUSIONS: These computational simulations of the stage 1 hybrid palliation for hypoplastic left heart syndrome with aortic atresia suggest that small differences in the degree of branch pulmonary arterial banding can result in significant changes in the overall performance of the hybrid palliation. Furthermore, retrograde aortic arch hypoplasia or obstruction can lead to suboptimal cerebral and coronary perfusion. Precise pulmonary artery banding may be important to optimize interstage physiology in patients undergoing the hybrid approach, and pre-interventional imaging of the aortic arch and isthmus should be performed to rule out potential for post-procedural suboptimal cerebral and coronary perfusion.

Virtual and real bench testing of a new percutaneous valve device: a case study.

AIMS: To validate patient-specific computational testing of a second-generation device for percutaneous pulmonary valve implantation (PPVI), against realistic in vitro data. METHODS AND RESULTS: Tests were initially carried out in a simple loading mode, performing a compliance test on a rapid prototyped cylinder. This model was reproduced computationally and validated against the experimental data. A second-generation PPVI stent-graft, with no valve mounted, was then deployed in a simplified cylindrical geometry, measuring its displacement when subjected to a pressure pulse. Experimental and computational measurements were in good agreement. Finally, having selected a patient regarded as unsuitable for first-generation PPVI, but potentially suitable for a second-generation device, the stent-graft was studied in the rapidly prototyped patient-specific right ventricular outflow tract (RVOT). Stent positioning and radial displacements with pulsatile flow were observed in a mock circuit using fluoroscopy imaging. Stent deformation and anchoring were measured both in vitro and computationally. Both tests indicated that the stent was well anchored in the RVOT, especially in the distal position, and its central region was rounded, ensuring, were a valve present, optimal valve function. CONCLUSION: We suggest that an experimentally validated computational model can be used for preclinical device characterisation and patient selection.

Finite element strategies to satisfy clinical and engineering requirements in the field of percutaneous valves.

Finite element (FE) modelling can be a very resourceful tool in the field of cardiovascular devices. To ensure result reliability, FE models must be validated experimentally against physical data. Their clinical application (e.g., patients' suitability, morphological evaluation) also requires fast simulation process and access to results, while engineering applications need highly accurate results. This study shows how FE models with different mesh discretisations can suit clinical and engineering requirements for studying a novel device designed for percutaneous valve implantation. Following sensitivity analysis and experimental characterisation of the materials, the stent-graft was first studied in a simplified geometry (i.e., compliant cylinder) and validated against in vitro data, and then in a patient-specific implantation site (i.e., distensible right ventricular outflow tract). Different meshing strategies using solid, beam and shell elements were tested. Results showed excellent agreement between computational and experimental data in the simplified implantation site. Beam elements were found to be convenient for clinical applications, providing reliable results in less than one hour in a patient-specific anatomical model. Solid elements remain the FE choice for engineering applications, albeit more computationally expensive (>100 times). This work also showed how information on device mechanical behaviour differs when acquired in a simplified model as opposed to a patient-specific model.

Multiscale models of the hybrid palliation for hypoplastic left heart syndrome.

A less-invasive procedure that combines interventional stent placement in the ductus arteriosus and surgical banding of the branch pulmonary arteries has been recently introduced in the treatment of the hypoplastic left heart syndrome (HLHS). The hemodynamic behaviour of this hybrid approach has not been examined before in a mathematical model. In this study, a mathematical model of the hybrid procedure for HLHS is described, applying a multiscale approach that couples 3D models of the area of the surgical operation and lumped parameter models of the remaining circulation. The effects of various degrees of pulmonary banding and different stent sizes inserted in the ductus arteriosus on pulmonary-systemic flow ratio, cardiac output and oxygen delivery were assessed. Computational results suggest that balanced systemic and pulmonary blood flow and optimal systemic oxygen delivery are sensitive to the degree of pulmonary arterial banding and not to the size of the ductal stent.

Boundary conditions of patient-specific fluid dynamics modelling of cavopulmonary connections: possible adaptation of pulmonary resistances results in a critical issue for a virtual surgical planning.

Cavopulmonary connections are surgical procedures used to treat a variety of complex congenital cardiac defects. Virtual pre-operative planning based on in silico patient-specific modelling might become a powerful tool in the surgical decision-making process. For this purpose, three-dimensional models can be easily developed from medical imaging data to investigate individual haemodynamics. However, the definition of patient-specific boundary conditions is still a crucial issue. The present study describes an approach to evaluate the vascular impedance of the right and left lungs on the basis of pre-operative clinical data and numerical simulations. Computational fluid dynamics techniques are applied to a patient with a bidirectional cavopulmonary anastomosis, who later underwent a total cavopulmonary connection (TCPC). Multi-scale models describing the surgical region and the lungs are adopted, while the flow rates measured in the venae cavae are used at the model inlets. Pre-operative and post-operative conditions are investigated; namely, TCPC haemodynamics, which are predicted using patient-specific pre-operative boundary conditions, indicates that the pre-operative balanced lung resistances are not compatible with the TCPC measured flows, suggesting that the pulmonary vascular impedances changed individually after the surgery. These modifications might be the consequence of adaptation to the altered pulmonary blood flows.