An integrated approach to patient-specific predictive modeling for single ventricle heart palliation

Computational Fluid Dynamic Assessment of Patients with Congenital Heart Disease from 3D Rotational Angiography

For congenital heart disease patients, multiple imaging modalities are needed to discern anatomy and functional information such as differential blood flow. During cardiac catheterization, 3D rotational angiography (3DRA) can provide CTA-like images, enabling anatomical information and intraprocedural guidance. We seek to establish whether unique aspects of this technique can also generate quantitative functional blood flow information. We propose that systematic integration of 3DRA imaging, catheter hemodynamic information, and computational fluid dynamics (CFD), can provide quantitative information regarding blood flow dynamics and energetics, without additional imaging or procedures. We report a single center retrospective feasibility study comprising four patients with 3DRA imaging and a complete set of hemodynamic data. 3DRA was processed and segmented to reconstruct vascular regions of interest (ROI), and a computational grid for CFD modeling of blood flow through the ROI was generated. Blood flow was simulated by integrating catheter hemodynamic data to devise boundary conditions at vascular ROI inlets and outlets. The 3DRA-based workflow successfully generated key computational outputs commonly used for cardiovascular applications, including flow patterns, distribution fractions, wall shear stress. Computational outputs obtained were as detailed and resolved as those obtained from more commonly used CT or MR angiography. Accuracy was confirmed by comparing computed flow distributions with measurements for 2 cases, showing less than 2.0% error from the measured data. Systematic integration of catheter hemodynamic information, 3DRA imaging, and CFD modeling, provides an effective and feasible alternative to obtain important quantitative blood flow information and visualization, without additional imaging.

Surgical Modulation of Pulmonary Artery Shear Stress: A Patient-Specific CFD Analysis of the Norwood Procedure

PURPOSR

This study created 3D CFD models of the Norwood procedure for hypoplastic left heart syndrome (HLHS) using standard angiography and echocardiogram data to investigate the impact of shunt characteristics on pulmonary artery (PA) hemodynamics. Leveraging routine clinical data offers advantages such as availability and cost-effectiveness without subjecting patients to additional invasive procedures.

METHODS

Patient-specific geometries of the intrathoracic arteries of two Norwood patients were generated from biplane cineangiograms. "Virtual surgery" was then performed to simulate the hemodynamics of alternative PA shunt configurations, including shunt type (modified Blalock-Thomas-Taussig shunt (mBTTS) vs. right ventricle-to-pulmonary artery shunt (RVPAS)), shunt diameter, and pulmonary artery anastomosis angle. Left-right pulmonary flow differential, Qp/Qs, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) were evaluated.

RESULTS

There was strong agreement between clinically measured data and CFD model output throughout the patient-specific models. Geometries with a RVPAS tended toward more balanced left-right pulmonary flow, lower Qp/Qs, and greater TAWSS and OSI than models with a mBTTS. For both shunt types, larger shunts resulted in a higher Qp/Qs and higher TAWSS, with minimal effect on OSI. Low TAWSS areas correlated with regions of low flow and changing the PA-shunt anastomosis angle to face toward low TAWSS regions increased TAWSS.

CONCLUSION

Excellent correlation between clinically measured and CFD model data shows that 3D CFD models of HLHS Norwood can be developed using standard angiography and echocardiographic data. The CFD analysis also revealed consistent changes in PA TAWSS, flow differential, and OSI as a function of shunt characteristics.

New Computational Approach to Shunt Design in Congenital Heart Palliation

Shunts are commonly used to redirect blood to pulmonary arteries in procedures that palliate congenital cardiovascular defects. Previous clinical studies and hemodynamic simulations reveal a critical role of shunt diameter in balancing flow to pulmonary versus systemic vessels, but the biomechanical process of creating the requisite anastomosis between the shunt and host vessel has received little attention. Here, we report a new Lagrange multiplier-based finite element approach that represents the shunt and host vessels as individual structures and predicts the anastomosis geometry and attachment force that result when the shunt is sutured at an incision in the host, followed by pressurization. Simulations suggest that anastomosis orifice opening increases markedly with increasing length of the host incision and moderately with increasing blood pressure. The host artery is further predicted to conform to common stiff synthetic shunts, whereas more compliant umbilical vessel shunts should conform to the host, with orifice area transitioning between these two extremes via a Hill-type function of shunt stiffness. Moreover, a direct relationship is expected between attachment forces and shunt stiffness. This new computational approach promises to aid in surgical planning for diverse vascular shunts by predicting in vivo pressurized geometries.

Hemodynamic Response to Device Titration in the Shunted Single Ventricle Circulation: A Patient Cohort Modeling Study

Clinical outcomes of ventricular assist device (VAD) support for shunted single ventricle patients trail the larger population due in part to the challenges in optimizing VAD support and balancing systemic and pulmonary circulations. We sought to understand the response to VAD titration in the shunted circulation using a lumped-parameter network modeling six patient-specific clinical cases. Hemodynamic data from six patients (mean body surface area = 0.30 m2) with a systemic-to-pulmonary shunt was used to construct simulated cases of heart failure and hemodynamic response to increasing VAD flow from 5 to 10 L/min/m2. With increasing VAD flow, the pulmonary arterial pressure stayed relatively constant in five patient cases and increased in one patient case. The mean VAD flow needed to attain an arterial-venous O2 saturation difference of 30% was 6.5 ± 1.2 L/min/m2, which is higher than that in the equivalent nonshunted scenario due to the partial diversion of flow to the pulmonary circulation. The hemodynamic responses to VAD support can vary significantly between specific patient cases; therefore hemodynamic modeling may help guide an individualized approach to perioperative VAD management in the shunted single-ventricle circulation and to understand the patients who may benefit the most from VAD support.

Lumped parameter models for two-ventricle and healthy and failing extracardiac Fontan circulations

Fontan circulations are surgical strategies to treat infants born with single ventricle physiology. Clinical and mathematical definitions of Fontan failure are lacking, and understanding is needed of parameters indicative of declining physiologies. Our objective is to develop lumped parameter models of two-ventricle and single-ventricle circulations. These models, their mathematical formulations and a proof of existence of periodic solutions are presented. Sensitivity analyses are performed to identify key parameters. Systemic venous and systolic left ventricular compliances and systemic capillary and pulmonary venous resistances are identified as key parameters. Our models serve as a framework to study the differences between two-ventricle and single-ventricle physiologies and healthy and failing Fontan circulations.

Multiscale modeling of a modified Blalock-Taussig surgery in a patient-specific tetralogy of Fallot

Tetralogy of Fallot (TOF) is a congenital heart anomaly that causes a drastic reduction in the oxygen level. In this study, we coupled a lumped-parameter model with a patient-specific three-dimensional (3D) model which included a modified Blalock-Taussig (MBT) shunt. By forming a closed loop, we investigated the effects of certain parameters on the flow rates and the pressures at different locations of the developed network. A local sensitivity analysis on an initial zero-dimensional (0D) closed-loop model was conducted. The 0D lumped parameter (LP) model was then refined based on the results of the multiscale 0D-3D model and the local sensitivity analysis was repeated for the refined 0D model. It was shown that the maximum pressure of the pulmonary bed had the highest sensitivity of 94% to the diameter of MBT shunt. We observed that the existence of the flow in the shunt during the diastole caused an elevated wall shear stress (WSS) in the pulmonary artery. In this work, we calculated the flow velocity and pressure field in a 3D patient-specific aorta with an MBT shunt, and then we used the results to increase the accuracy of our LP model to simulate numerous 0D simulations in a significantly shorter time, which is potentially applicable for medical decision-making.

Differences in Pulmonary and Systemic Flow Measurements by Cardiac Magnetic Resonance vs Cardiac Catheterization and Relation to Collateral Flow in Single Ventricle Patients

Both cardiac magnetic resonance (CMR) and cardiac catheterization (cath) may assess patients with single ventricle physiology prior to stage II or Fontan palliation. However, development of significant aortopulmonary collaterals may invalidate assumptions of the Fick method. We compared CMR and cath flow measurements and evaluated the relation to collateral flow. This single-center study included all pre-stage II and pre-Fontan patients between 2010 and 2017 with CMR and cath within 1 month. Pulmonary (Qp) and systemic flow (Qs) by cath were calculated by Fick method. CMR Qp was calculated by total pulmonary venous flow, and Qs by total vena caval flow. Collateral flow by CMR was the difference of pulmonary vein and pulmonary artery flow. In 26 studies (16 pre-stage II and 10 pre-Fontan) in 21 patients, collateral flow was higher in pre-Fontan patients (1.8 ± 0.6 vs 0.9 ± 0.8 L/min/m², p = 0.01). Overall, CMR and cath had good agreement for Qs and Qp:Qs, with moderate correlation (r = 0.44, p = 0.02 for Qs, r = 0.48, p = 0.02 for Qp:Qs). In pre-Fontan but not in pre-stage II patients, CMR had higher Qp (mean difference - 1.71 L/min/m²) and Qp:Qs (mean difference - 0.36). The underestimation of cath Qp correlated with amount of collateral flow (r = - 0.47, p = 0.02). Neither cath nor CMR flow measurements correlated with outcomes in this small cohort. In conclusion, collaterals lead to systematically higher Qp and Qp:Qs measurements by CMR vs cath in single ventricle patients. Measurements may not be used interchangeably, with potential clinical significance in estimating pulmonary vascular resistance. Further study is necessary to evaluate possible relation to clinical outcomes.

Computational Modeling to Support Surgical Decision Making in Single Ventricle Physiology

Many of the advances in congenital heart surgery were built upon lessons and insights gained from model simulations. While animal and mock-circuit models have historically been the main arena to test new operative techniques and concepts, the recognition that complex cardiovascular anatomy and circulation can be modeled mathematically ushered a new era of collaboration between surgeons and engineers. In 1996, the computational age in congenital heart surgery began when investigators in London and Milan tapped the power of the computer to simulate the Fontan procedure and introduced operative improvements. Since then, computational modeling has led to numerous contributions in congenial heart surgery as continuing sophistication and advances in numerical and imaging methods furthered the ability to refine anatomic and physiologic details. Idealized generic models have given way to precise patient-specific simulations of the 3-dimensional anatomy, reconstructed circulation, affected hemodynamics, and altered physiology. Tools to perform virtual surgery, and predict flow dynamic and circulatory results, have been developed for some of the most complex defects, such as those requiring single ventricle palliation. In today's quest for personalized medicine and precision care, computational modeling's role to assist surgical planning in complex congenital heart surgery will continue to grow and evolve. With ever closer collaboration between surgeons and engineers, and clear understanding of modeling limitations, computational simulations can be a valuable adjunct to support preoperative surgical decision making.

Numerical Simulation of the Effect of Pulmonary Vascular Resistance on the Hemodynamics of Reoperation After Failure of One and a Half Ventricle Repair

OBJECTIVE

The one and a half ventricle repair (1.5VR) is a common clinical choice for patients with right heart dysfunction. Considering the influence of blood circulation failure and reoperation in urgent need, this essay aims to explore the hemodynamic effects of different pulmonary vascular resistance (PVR) values on reoperation after 1.5VR failure.

METHODS

The lumped parameter model (LPM) was used to simulate the reoperation, including the return biventricular repair (2VR), ligation of azygos vein (1.5VR') and return single ventricular repair (1.0VR). Firstly, the debugging parameters were used to simulate the hemodynamics of 2VR. Secondly, the value of PVR was changed from one to four times while the other parameters remained unchanged. Finally, 15 cardiac cycles were simulated and the 15th result was obtained. In this work, the left and right ventricular stroke work and their sum (Plv, Prv, Ptotal), the left and right ventricular ejection fraction (LVEF, RVEF), the mean Cardiac Output (mCO) and the mean pressure and flow-rate ratio of superior and inferior vena cava (mPsvc\mPivc and mQsvc\mQivc), respectively, were used to describe the hemodynamics of reoperation.

RESULTS

With the change of PVR from one to four times, the values of Plv, Prv, Ptotal, LVEF, and RVEF gradually decreased. The change rate of Plv, Ptotal and LVEF of 1.0VR were the largest in the three kinds of reoperation. The change rate of Prv of 1.5VR' was larger than that of 2VR, but it was the opposite for their EF change rate. The mCO of 2VR, 1.5VR', and 1.0VR decreased by 18.53%, 37.58%, and 48.07%, respectively. The mPsvc\mPivc of 1.5VR' increased from 3.76 to 6.77 and the mQsvc\mQivc decreased from 0.55 to 0.36, while the mPsvc\mPivc and mQsvc\mQivc of 2VR and 1.0VR remained 1 and 0.67, respectively. The peak value of the tricuspid flow-rate (Qti) waveform of 2VR and 1.5VR' changed from "E peak" to "A peak."

CONCLUSION

The numerical results demonstrate the highly reoperation-dependent hemodynamic consequences and their responses to variations in PVR. Comprehensive analysis of EF, mCO and ventricular stroke work indicates that PVR has a greater impact on 1.5VR' and 1.0VR. Therefore, we suggest that the selection strategy of reoperation should focus on PVR.

Dobutamine stress testing in patients with Fontan circulation augmented by biomechanical modeling

Understanding (patho)physiological phenomena and mechanisms of failure in patients with Fontan circulation-a surgically established circulation for patients born with a functionally single ventricle-remains challenging due to the complex hemodynamics and high inter-patient variations in anatomy and function. In this work, we present a biomechanical model of the heart and circulation to augment the diagnostic evaluation of Fontan patients with early-stage heart failure. The proposed framework employs a reduced-order model of heart coupled with a simplified circulation including venous return, creating a closed-loop system. We deploy this framework to augment the information from data obtained during combined cardiac catheterization and magnetic resonance exams (XMR), performed at rest and during dobutamine stress in 9 children with Fontan circulation and 2 biventricular controls. We demonstrate that our modeling framework enables patient-specific investigation of myocardial stiffness, contractility at rest, contractile reserve during stress and changes in vascular resistance. Hereby, the model allows to identify key factors underlying the pathophysiological response to stress in these patients. In addition, the rapid personalization of the model to patient data and fast simulation of cardiac cycles make our framework directly applicable in a clinical workflow. We conclude that the proposed modeling framework is a valuable addition to the current clinical diagnostic XMR exam that helps to explain patient-specific stress hemodynamics and can identify potential mechanisms of failure in patients with Fontan circulation.

Factors Affecting Cardiovascular Physiology in Cardiothoracic Surgery: Implications for Lumped-Parameter Modeling

Cardiothoracic surgeries are complex procedures during which the patient cardiovascular physiology is constantly changing due to various factors. Physiological changes begin with the induction of anesthesia, whose effects remain active into the postoperative period. Depending on the surgery, patients may require the use of cardiopulmonary bypass and cardioplegia, both of which affect postoperative physiology such as cardiac index and vascular resistance. Complications may arise due to adverse reactions to the surgery, causing hemodynamic instability. In response, fluid resuscitation and/or vasoactive agents with varying effects may be used in the intraoperative or postoperative periods to improve patient hemodynamics. These factors have important implications for lumped-parameter computational models which aim to assist surgical planning and medical device evaluation. Patient-specific models are typically tuned based on patient clinical data which may be asynchronously acquired through invasive techniques such as catheterization, during which the patient may be under the effects of drugs such as anesthesia. Due to the limited clinical data available and the inability to foresee short-term physiological regulation, models often retain preoperative parameters for postoperative predictions; however, without accounting for the physiologic changes that may occur during surgical procedures, the accuracy of these predictive models remains limited. Understanding and incorporating the effects of these factors in cardiovascular models will improve the model fidelity and predictive capabilities.

Multiscale Modeling of Superior Cavopulmonary Circulation: Hemi-Fontan and Bidirectional Glenn Are Equivalent

Superior cavopulmonary circulation (SCPC) can be achieved by either the Hemi-Fontan (hF) or Bidirectional Glenn (bG) connection. Debate remains as to which results in best hemodynamic results. Adopting patient-specific multiscale computational modeling, we examined both the local dynamics and global physiology to determine if surgical choice can lead to different hemodynamic outcomes. Six patients (age: 3-6 months) underwent cardiac magnetic resonance imaging and catheterization prior to SCPC surgery. For each patient: (1) a finite 3-dimensional (3D) volume model of the preoperative anatomy was constructed to include detailed definition of the distal branch pulmonary arteries, (2) virtual hF and bG operations were performed to create 2 SCPC 3D models, and (3) a specific lumped network representing each patient's entire cardiovascular circulation was developed from clinical data. Using a previously validated multiscale algorithm that couples the 3D models with lumped network, both local flow dynamics, that is, power loss, and global systemic physiology can be quantified. In 2 patients whose preoperative imaging demonstrated significant left pulmonary artery (LPA) stenosis, we performed virtual pulmonary arterioplasty to assess its effect. In one patient, the hF model showed higher power loss (107%) than the bG, while in 3, the power losses were higher in the bG models (18-35%). In the remaining 2 patients, the power loss differences were minor. Despite these variations, for all patients, there were no significant differences between the hF and bG models in hemodynamic or physiological outcomes, including cardiac output, superior vena cava pressure, right-left pulmonary flow distribution, and systemic oxygen delivery. In the 2 patients with LPA stenosis, arterioplasty led to better LPA flow (5-8%) while halving the power loss, but without important improvements in SVC pressure or cardiac output. Despite power loss differences, both hF and bG result in similar SCPC hemodynamics and physiology outcome. This suggests that for SCPC, the pre-existing patient-specific physiology and condition, such as pulmonary vascular resistance, are more deterministic in the hemodynamic performance than the type of surgical palliation. Multiscale modeling can be a decision-assist tool to assess whether an extensive LPA reconstruction is needed at the time of SCPC for LPA stenosis.

Mixed impact of torsion on LV hemodynamics: A CFD study based on the Chimera technique

Image-based patient-specific Computational Fluid Dynamics (CFD) models of the Left Ventricle (LV) can be used to quantify hemodynamics-based biomarkers that can support the clinicians in the early diagnosis, follow-up and treatment planning of patients, beyond the capabilities of the current imaging modalities. We propose a workflow to build patient-specific CFD models of the LV with moving boundaries based on the Chimera technique to overcome the convergence issues previously encountered by means of the Arbitrarian Lagrangian Eulerian approach. The workflow was tested while investigating whether the torsional motion has an impact on LV fluid dynamics. Starting from 3D cine MRI scans of a healthy volunteer, six cardiac cycles were simulated in three CFD LV models: with no, physiological, and exaggerated torsion. The Chimera technique was robust in handling the impulsive motion of the LV endocardium, allowing to notice cycle-to-cycle variations in every simulated case. Torsion affected slightly velocity, vorticity, WSS. It did not affect energy loss and induced a double-sided effect in terms of residence time: the particles ejected in one beat decreased, whereas the motility of the particles remaining in the LV was affected only in the exaggerated torsion case, indicating that implementation of torsion can be discarded in case of physiological levels. Nonetheless, caution is warranted when interpreting these results given the absence of the mitral valve, the papillary muscles, and the trabeculae. The effects of the mitral valve will be evaluated within an Fluid Structure Interaction simulation framework as further development of the current model.

Application of Patient-Specific Computational Fluid Dynamics in Coronary and Intra-Cardiac Flow Simulations: Challenges and Opportunities

The emergence of new cardiac diagnostics and therapeutics of the heart has given rise to the challenging field of virtual design and testing of technologies in a patient-specific environment. Given the recent advances in medical imaging, computational power and mathematical algorithms, patient-specific cardiac models can be produced from cardiac images faster, and more efficiently than ever before. The emergence of patient-specific computational fluid dynamics (CFD) has paved the way for the new field of computer-aided diagnostics. This article provides a review of CFD methods, challenges and opportunities in coronary and intra-cardiac flow simulations. It includes a review of market products and clinical trials. Key components of patient-specific CFD are covered briefly which include image segmentation, geometry reconstruction, mesh generation, fluid-structure interaction, and solver techniques.

Patient-Specific Cardiovascular Computational Modeling: Diversity of Personalization and Challenges

Patient-specific computer models have been developed representing a variety of aspects of the cardiovascular system spanning the disciplines of electrophysiology, electromechanics, solid mechanics, and fluid dynamics. These physiological mechanistic models predict macroscopic phenomena such as electrical impulse propagation and contraction throughout the entire heart as well as flow and pressure dynamics occurring in the ventricular chambers, aorta, and coronary arteries during each heartbeat. Such models have been used to study a variety of clinical scenarios including aortic aneurysms, coronary stenosis, cardiac valvular disease, left ventricular assist devices, cardiac resynchronization therapy, ablation therapy, and risk stratification. After decades of research, these models are beginning to be incorporated into clinical practice directly via marketed devices and indirectly by improving our understanding of the underlying mechanisms of health and disease within a clinical context.

Fontan Surgical Planning: Previous Accomplishments, Current Challenges, and Future Directions

The ultimate goal of Fontan surgical planning is to provide additional insights into the clinical decision-making process. In its current state, surgical planning offers an accurate hemodynamic assessment of the pre-operative condition, provides anatomical constraints for potential surgical options, and produces decent post-operative predictions if boundary conditions are similar enough between the pre-operative and post-operative states. Moving forward, validation with post-operative data is a necessary step in order to assess the accuracy of surgical planning and determine which methodological improvements are needed. Future efforts to automate the surgical planning process will reduce the individual expertise needed and encourage use in the clinic by clinicians. As post-operative physiologic predictions improve, Fontan surgical planning will become an more effective tool to accurately model patient-specific hemodynamics.

Lumped parameter model for hemodynamic simulation of congenital heart diseases

The recent development of computer technology has made it possible to simulate the hemodynamics of congenital heart diseases on a desktop computer. However, multi-scale modeling of the cardiovascular system based on computed tomographic and magnetic resonance images still requires long simulation times. The lumped parameter model is potentially beneficial for real-time bedside simulation of congenital heart diseases. In this review, we introduce the basics of the lumped parameter model (time-varying elastance chamber model combined with modified Windkessel vasculature model) and illustrate its usage in hemodynamic simulation of congenital heart diseases using examples such as hypoplastic left heart syndrome and Fontan circulation. We also discuss the advantages of the lumped parameter model and the problems for clinical use.

Virtual medicine: Utilization of the advanced cardiac imaging patient avatar for procedural planning and facilitation

Advances in imaging technology have led to a paradigm shift from planning of cardiovascular procedures and surgeries requiring the actual patient in a "brick and mortar" hospital to utilization of the digitalized patient in the virtual hospital. Cardiovascular computed tomographic angiography (CCTA) and cardiovascular magnetic resonance (CMR) digitalized 3-D patient representation of individual patient anatomy and physiology serves as an avatar allowing for virtual delineation of the most optimal approaches to cardiovascular procedures and surgeries prior to actual hospitalization. Pre-hospitalization reconstruction and analysis of anatomy and pathophysiology previously only accessible during the actual procedure could potentially limit the intrinsic risks related to time in the operating room, cardiac procedural laboratory and overall hospital environment. Although applications are specific to areas of cardiovascular specialty focus, there are unifying themes related to the utilization of technologies. The virtual patient avatar computer can also be used for procedural planning, computational modeling of anatomy, simulation of predicted therapeutic result, printing of 3-D models, and augmentation of real time procedural performance. Examples of the above techniques are at various stages of development for application to the spectrum of cardiovascular disease processes, including percutaneous, surgical and hybrid minimally invasive interventions. A multidisciplinary approach within medicine and engineering is necessary for creation of robust algorithms for maximal utilization of the virtual patient avatar in the digital medical center. Utilization of the virtual advanced cardiac imaging patient avatar will play an important role in the virtual health care system. Although there has been a rapid proliferation of early data, advanced imaging applications require further assessment and validation of accuracy, reproducibility, standardization, safety, efficacy, quality, cost effectiveness, and overall value to medical care.

Inverse problems in reduced order models of cardiovascular haemodynamics: aspects of data assimilation and heart rate variability

Inverse problems in cardiovascular modelling have become increasingly important to assess each patient individually. These problems entail estimation of patient-specific model parameters from uncertain measurements acquired in the clinic. In recent years, the method of data assimilation, especially the unscented Kalman filter, has gained popularity to address computational efficiency and uncertainty consideration in such problems. This work highlights and presents solutions to several challenges of this method pertinent to models of cardiovascular haemodynamics. These include methods to (i) avoid ill-conditioning of the covariance matrix, (ii) handle a variety of measurement types, (iii) include a variety of prior knowledge in the method, and (iv) incorporate measurements acquired at different heart rates, a common situation in the clinic where the patient state differs according to the clinical situation. Results are presented for two patient-specific cases of congenital heart disease. To illustrate and validate data assimilation with measurements at different heart rates, the results are presented on a synthetic dataset and on a patient-specific case with heart valve regurgitation. It is shown that the new method significantly improves the agreement between model predictions and measurements. The developed methods can be readily applied to other pathophysiologies and extended to dynamical systems which exhibit different responses under different sets of known parameters or different sets of inputs (such as forcing/excitation frequencies).

An effective model of cerebrovascular pressure reactivity and blood flow autoregulation

Understanding cerebral blood flow dynamics is crucial for the care of patients at risk of poor cerebral perfusion. We describe an effective model of cerebral hemodynamics designed to reveal important macroscopic features of cerebral blood flow without having to resolve the detailed microvasculature of the brain. Based on principles of fluid and elastic dynamics and vascular pressure-reactivity, the model quantifies the physical means by which the vasculature executes autoregulatory reflexes. We demonstrate that the frequency response of the proposed model matches experimental measurements and explains the influence of mechanical factors on the autoregulatory performance. Analysis of the model indicates the existence of an optimal mean arterial pressure which minimizes the sensitivity of the flow to changes in perfusion pressure across the frequency spectrum of physiological oscillations. We highlight the simplicity of the model and its potential to improve monitoring of brain perfusion via real-time computational simulations of cerebro- and cardio-vascular interventions.

Simulation of aortopulmonary collateral flow in Fontan patients for use in prediction of interventional outcomes

PURPOSE

Patients with complex congenital heart disease may need to be converted to a Fontan circulation with systemic venous return surgically connected to the pulmonary circulation. These patients frequently form aortopulmonary collaterals (APC), that is arterial inflows to the pulmonary artery vascular tree. The aim of this study was to develop a method to calculate the effect of APC on the pulmonary flow distribution based on magnetic resonance imaging (MRI) measurements and computational fluid dynamics simulations in order to enable prediction of interventional outcomes in Fontan patients.

METHODS

Patient-specific models of 11 patients were constructed in a 3D-design software based on MRI segmentations. APC flow was quantified as the difference between pulmonary venous flow and pulmonary artery flow, measured by MRI. A method was developed to include the modulating effect of the APC flow by calculating the patient-specific relative pulmonary vascular resistance. Simulations, including interventions with a Y-graft replacement and a stent dilatation, were validated against MRI results.

RESULTS

The bias between simulated and MRI-measured fraction of blood to the left lung was 2·9 ± 5·3%. Including the effects of the APC flow in the simulation (n = 6) reduced simulation error from 9·8 ± 7·0% to 5·2 ± 6·3%. Preliminary findings in two patients show that the effect of surgical and catheter interventions could be predicted using the demonstrated methods.

CONCLUSIONS

The work demonstrates a novel method to include APC flow in predictive simulations of Fontan hemodynamics. APC flow was found to have a significant contribution to the pulmonary flow distribution in Fontan patients.

Tetralogy of Fallot Surgical Repair: Shunt Configurations, Ductus Arteriosus and the Circle of Willis

In this study, hemodynamic performance of three novel shunt configurations that are considered for the surgical repair of tetralogy of Fallot (TOF) disease are investigated in detail. Clinical experience suggests that the shunt location, connecting angle, and its diameter can influence the post-operative physiology and the neurodevelopment of the neonatal patient. An experimentally validated second order computational fluid dynamics (CFD) solver and a parametric neonatal diseased great artery model that incorporates the ductus arteriosus (DA) and the full patient-specific circle of Willis (CoW) are employed. Standard truncated resistance CFD boundary conditions are compared with the full cerebral arterial system, which resulted 21, -13, and 37% difference in flow rate at the brachiocephalic, left carotid, and subclavian arteries, respectively. Flow splits at the aortic arch and cerebral arteries are calculated and found to change with shunt configuration significantly for TOF disease. The central direct shunt (direct shunt) has pulmonary flow 5% higher than central oblique shunt (oblique shunt) and 23% higher than modified Blalock Taussig shunt (RPA shunt) while the DA is closed. Maximum wall shear stress (WSS) in the direct shunt configuration is 9 and 60% higher than that of the oblique and RPA shunts, respectively. Patent DA, significantly eliminated the pulmonary flow control function of the shunt repair. These results suggests that, due to the higher flow rates at the pulmonary arteries, the direct shunt, rather than the central oblique, or right pulmonary artery shunts could be preferred by the surgeon. This extended model introduced new hemodynamic performance indices for the cerebral circulation that can correlate with the post-operative neurodevelopment quality of the patient.

Patient-specific parameter estimation in single-ventricle lumped circulation models under uncertainty

Computational models of cardiovascular physiology can inform clinical decision-making, providing a physically consistent framework to assess vascular pressures and flow distributions, and aiding in treatment planning. In particular, lumped parameter network (LPN) models that make an analogy to electrical circuits offer a fast and surprisingly realistic method to reproduce the circulatory physiology. The complexity of LPN models can vary significantly to account, for example, for cardiac and valve function, respiration, autoregulation, and time-dependent hemodynamics. More complex models provide insight into detailed physiological mechanisms, but their utility is maximized if one can quickly identify patient specific parameters. The clinical utility of LPN models with many parameters will be greatly enhanced by automated parameter identification, particularly if parameter tuning can match non-invasively obtained clinical data. We present a framework for automated tuning of 0D lumped model parameters to match clinical data. We demonstrate the utility of this framework through application to single ventricle pediatric patients with Norwood physiology. Through a combination of local identifiability, Bayesian estimation and maximum a posteriori simplex optimization, we show the ability to automatically determine physiologically consistent point estimates of the parameters and to quantify uncertainty induced by errors and assumptions in the collected clinical data. We show that multi-level estimation, that is, updating the parameter prior information through sub-model analysis, can lead to a significant reduction in the parameter marginal posterior variance. We first consider virtual patient conditions, with clinical targets generated through model solutions, and second application to a cohort of four single-ventricle patients with Norwood physiology. Copyright © 2016 John Wiley & Sons, Ltd.

Blood flow in the cerebral venous system: modeling and simulation

The development of a software platform incorporating all aspects, from medical imaging data, through three-dimensional reconstruction and suitable meshing, up to simulation of blood flow in patient-specific geometries, is a crucial challenge in biomedical engineering. In the present study, a fully three-dimensional blood flow simulation is carried out through a complete rigid macrovascular circuit, namely the intracranial venous network, instead of a reduced order simulation and partial vascular network. The biomechanical modeling step is carefully analyzed and leads to the description of the flow governed by the dimensionless Navier-Stokes equations for an incompressible viscous fluid. The equations are then numerically solved with a free finite element software using five meshes of a realistic geometry obtained from medical images to prove the feasibility of the pipeline. Some features of the intracranial venous circuit in the supine position such as asymmetric behavior in merging regions are discussed.

Two-dimensional intraventricular flow pattern visualization using the image-based computational fluid dynamics

The image-based computational fluid dynamics (IB-CFD) technique, as the combination of medical images and the CFD method, is utilized in this research to analyze the left ventricle (LV) hemodynamics. The research primarily aims to propose a semi-automated technique utilizing some freely available and commercial software packages in order to simulate the LV hemodynamics using the IB-CFD technique. In this research, moreover, two different physiological time-resolved 2D models of a patient-specific LV with two different types of aortic and mitral valves, including the orifice-type valves and integrated with rigid leaflets, are adopted to visualize the process of developing intraventricular vortex formation and propagation. The blood flow pattern over the whole cardiac cycle of two models is also compared to investigate the effect of utilizing different valve types in the process of the intraventricular vortex formation. Numerical findings indicate that the model with integrated valves can predict more complex intraventricular flow that can match better the physiological flow pattern in comparison to the orifice-type model.

Computational modelling for congenital heart disease: how far are we from clinical translation?

Computational models of congenital heart disease (CHD) have become increasingly sophisticated over the last 20 years. They can provide an insight into complex flow phenomena, allow for testing devices into patient-specific anatomies (pre-CHD or post-CHD repair) and generate predictive data. This has been applied to different CHD scenarios, including patients with single ventricle, tetralogy of Fallot, aortic coarctation and transposition of the great arteries. Patient-specific simulations have been shown to be informative for preprocedural planning in complex cases, allowing for virtual stent deployment. Novel techniques such as statistical shape modelling can further aid in the morphological assessment of CHD, risk stratification of patients and possible identification of new ‘shape biomarkers’. Cardiovascular statistical shape models can provide valuable insights into phenomena such as ventricular growth in tetralogy of Fallot, or morphological aortic arch differences in repaired coarctation. In a constant move towards more realistic simulations, models can also account for multiscale phenomena (eg, thrombus formation) and importantly include measures of uncertainty (ie, CIs around simulation results). While their potential to aid understanding of CHD, surgical/procedural decision-making and personalisation of treatments is undeniable, important elements are still lacking prior to clinical translation of computational models in the field of CHD, that is, large validation studies, cost-effectiveness evaluation and establishing possible improvements in patient outcomes.

Heart blood flow simulation: a perspective review

Cardiovascular disease (CVD), the leading cause of death today, incorporates a wide range of cardiovascular system malfunctions that affect heart functionality. It is believed that the hemodynamic loads exerted on the cardiovascular system, the left ventricle (LV) in particular, are the leading cause of CVD initiation and propagation. Moreover, it is believed that the diagnosis and prognosis of CVD at an early stage could reduce its high mortality and morbidity rate. Therefore, a set of robust clinical cardiovascular assessment tools has been introduced to compute the cardiovascular hemodynamics in order to provide useful insights to physicians to recognize indicators leading to CVD and also to aid the diagnosis of CVD. Recently, a combination of computational fluid dynamics (CFD) and different medical imaging tools, image-based CFD (IB-CFD), has been widely employed for cardiovascular functional assessment by providing reliable hemodynamic parameters. Even though the capability of CFD to provide reliable flow dynamics in general fluid mechanics problems has been widely demonstrated for many years, up to now, the clinical implications of the IB-CFD patient-specific LVs have not been applicable due to its limitations and complications. In this paper, we review investigations conducted to numerically simulate patient-specific human LV over the past 15 years using IB-CFD methods. Firstly, we divide different studies according to the different LV types (physiological and different pathological conditions) that have been chosen to reconstruct the geometry, and then discuss their contributions, methodologies, limitations, and findings. In this regard, we have studied CFD simulations of intraventricular flows and related cardiology insights, for (i) Physiological patient-specific LV models, (ii) Pathological heart patient-specific models, including myocardial infarction, dilated cardiomyopathy, hypertrophic cardiomyopathy and hypoplastic left heart syndrome. Finally, we discuss the current stage of the IB-CFD LV simulations in order to mimic realistic hemodynamics of patient-specific LVs. We can conclude that heart flow simulation is on the right track for developing into a useful clinical tool for heart function assessment, by (i) incorporating most of heart structures' (such as heart valves) operations, and (ii) providing useful diagnostic indices based hemodynamic parameters, for routine adoption in clinical usage.

On a sparse pressure-flow rate condensation of rigid circulation models

Cardiovascular simulation has shown potential value in clinical decision-making, providing a framework to assess changes in hemodynamics produced by physiological and surgical alterations. State-of-the-art predictions are provided by deterministic multiscale numerical approaches coupling 3D finite element Navier Stokes simulations to lumped parameter circulation models governed by ODEs. Development of next-generation stochastic multiscale models whose parameters can be learned from available clinical data under uncertainty constitutes a research challenge made more difficult by the high computational cost typically associated with the solution of these models. We present a methodology for constructing reduced representations that condense the behavior of 3D anatomical models using outlet pressure-flow polynomial surrogates, based on multiscale model solutions spanning several heart cycles. Relevance vector machine regression is compared with maximum likelihood estimation, showing that sparse pressure/flow rate approximations offer superior performance in producing working surrogate models to be included in lumped circulation networks. Sensitivities of outlets flow rates are also quantified through a Sobol׳ decomposition of their total variance encoded in the orthogonal polynomial expansion. Finally, we show that augmented lumped parameter models including the proposed surrogates accurately reproduce the response of multiscale models they were derived from. In particular, results are presented for models of the coronary circulation with closed loop boundary conditions and the abdominal aorta with open loop boundary conditions.

Patient-Specific Simulations Reveal Significant Differences in Mechanical Stimuli in Venous and Arterial Coronary Grafts

Mechanical stimuli are key to understanding disease progression and clinically observed differences in failure rates between arterial and venous grafts following coronary artery bypass graft surgery. We quantify biologically relevant mechanical stimuli, not available from standard imaging, in patient-specific simulations incorporating non-invasive clinical data. We couple CFD with closed-loop circulatory physiology models to quantify biologically relevant indices, including wall shear, oscillatory shear, and wall strain. We account for vessel-specific material properties in simulating vessel wall deformation. Wall shear was significantly lower (p = 0.014*) and atheroprone area significantly higher (p = 0.040*) in venous compared to arterial grafts. Wall strain in venous grafts was significantly lower (p = 0.003*) than in arterial grafts while no significant difference was observed in oscillatory shear index. Simulations demonstrate significant differences in mechanical stimuli acting on venous vs. arterial grafts, in line with clinically observed graft failure rates, offering a promising avenue for stratifying patients at risk for graft failure.

Data assimilation and modelling of patient-specific single-ventricle physiology with and without valve regurgitation

A closed-loop lumped parameter model of blood circulation is considered for single-ventricle shunt physiology. Its parameters are estimated by an inverse problem based on patient-specific haemodynamics measurements. As opposed to a black-box approach, maximizing the number of parameters that are related to physically measurable quantities motivates the present model. Heart chambers are described by a single-fibre mechanics model, and valve function is modelled with smooth opening and closure. A model for valve prolapse leading to valve regurgitation is proposed. The method of data assimilation, in particular the unscented Kalman filter, is used to estimate the model parameters from time-varying clinical measurements. This method takes into account both the uncertainty in prior knowledge related to the parameters and the uncertainty associated with the clinical measurements. Two patient-specific cases - one without regurgitation and one with atrioventricular valve regurgitation - are presented. Pulmonary and systemic circulation parameters are successfully estimated, without assumptions on their relationships. Parameters governing the behaviour of heart chambers and valves are either fixed based on biomechanics, or estimated. Results of the inverse problem are validated qualitatively through clinical measurements or clinical estimates that were not included in the parameter estimation procedure. The model and the estimation method are shown to successfully capture patient-specific clinical observations, even with regurgitation, such as the double peaked nature of valvular flows and anomalies in electrocardiogram readings. Lastly, biomechanical implications of the results are discussed.

Patient-Specific Surgical Planning, Where Do We Stand? The Example of the Fontan Procedure

The Fontan surgery for single ventricle heart defects is a typical example of a clinical intervention in which patient-specific computational modeling can improve patient outcome: with the functional heterogeneity of the presenting patients, which precludes generic solutions, and the clear influence of the surgically-created Fontan connection on hemodynamics, it is acknowledged that individualized computational optimization of the post-operative hemodynamics can be of clinical value. A large body of literature has thus emerged seeking to provide clinically relevant answers and innovative solutions, with an increasing emphasis on patient-specific approaches. In this review we discuss the benefits and challenges of patient-specific simulations for the Fontan surgery, reviewing state of the art solutions and avenues for future development. We first discuss the clinical impact of patient-specific simulations, notably how they have contributed to our understanding of the link between Fontan hemodynamics and patient outcome. This is followed by a survey of methodologies for capturing patient-specific hemodynamics, with an emphasis on the challenges of defining patient-specific boundary conditions and their extension for prediction of post-operative outcome. We conclude with insights into potential future directions, noting that one of the most pressing issues might be the validation of the predictive capabilities of the developed framework.

A multiscale model for the study of cardiac biomechanics in single-ventricle surgeries: a clinical case

Complex congenital heart disease characterized by the underdevelopment of one ventricular chamber (single ventricle (SV) circulation) is normally treated with a three-stage surgical repair. This study aims at developing a multiscale computational framework able to couple a patient-specific three-dimensional finite-element model of the SV to a patient-specific lumped parameter (LP) model of the whole circulation, in a closed-loop fashion. A sequential approach was carried out: (i) cardiocirculatory parameters were estimated by using a fully LP model; (ii) ventricular material parameters and unloaded geometry were identified by means of the stand-alone, three-dimensional model of the SV; and (iii) the three-dimensional model of SV was coupled to the LP model of the circulation, thus closing the loop and creating a multiscale model. Once the patient-specific multiscale model was set using pre-operative clinical data, the virtual surgery was performed, and the post-operative conditions were simulated. This approach allows the analysis of local information on ventricular function as well as global parameters of the cardiovascular system. This methodology is generally applicable to patients suffering from SV disease for surgical planning at different stages of treatment. As an example, a clinical case from stage 1 to stage 2 is considered here.

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.

Hemodynamic effects of left pulmonary artery stenosis after superior cavopulmonary connection: a patient-specific multiscale modeling study

OBJECTIVE

Currently, no quantitative guidelines have been established for treatment of left pulmonary artery (LPA) stenosis. This study aims to quantify the effects of LPA stenosis on postoperative hemodynamics for single-ventricle patients undergoing stage II superior cavopulmonary connection (SCPC) surgery, using a multiscale computational approach.

METHODS

Image data from 6 patients were segmented to produce 3-dimensional models of the pulmonary arteries before stage II surgery. Pressure and flow measurements were used to tune a 0-dimensional model of the entire circulation. Postoperative geometries were generated through stage II virtual surgery; varying degrees of LPA stenosis were applied using mesh morphing and hemodynamics assessed through coupled 0-3-dimensional simulations. To relate metrics of stenosis to clinical classifications, pediatric cardiologists and surgeons ranked the degrees of stenosis in the models. The effects of LPA stenosis were assessed based on left-to-right pulmonary artery flow split ratios, mean pressure drop across the stenosis, cardiac pressure-volume loops, and other clinically relevant parameters.

RESULTS

Stenosis of >65% of the vessel diameter was required to produce a right pulmonary artery:LPA flow split <30%, and/or a mean pressure drop of >3.0 mm Hg, defined as clinically significant changes.

CONCLUSIONS

The effects of <65% stenosis on SCPC hemodynamics and physiology were minor and may not justify the increased complexity of adding LPA arterioplasty to the SCPC operation. However, in the longer term, pulmonary augmentation may affect outcomes of the Fontan completion surgery, as pulmonary artery distortion is a risk factor that may influence stage III physiology.

Surgical planning of the total cavopulmonary connection: robustness analysis

In surgical planning of the Fontan connection for single ventricle physiologies, there can be differences between the proposed and implemented options. Here, we developed a surgical planning framework that help determine the best performing option and ensures that the results will be comparable if there are slight geometrical variations. Eight patients with different underlying anatomies were evaluated in this study; surgical variations were created for each connection by changing either angle, offset or baffle diameter. Computational fluid dynamics were performed and the energy efficiency (indexed power loss-iPL) and hepatic flow distribution (HFD) computed. Differences with the original connection were evaluated: iPL was not considerably affected by the changes in geometry. For HFD, the single superior vena cava (SVC) connections presented less variability compared to the other anatomies. The Y-graft connection was the most robust overall, while the extra-cardiac connections showed dependency to offset. Bilateral SVC and interrupted inferior vena cava with azygous continuation showed high variability in HFD. We have developed a framework to assess the robustness of a surgical option for the TCPC; this will be useful to assess the most complex cases where pre-surgery planning could be most beneficial to ensure an efficient and robust hemodynamic performance.

Using of porous portion to simulate pulmonary resistance in the computational fluid dynamic models of Fontan connection

In this study, we performed computational fluid dynamic (CFD) simulations in a patient-specific three-dimensional extracardiac conduit Fontan connection. The pulmonary resistance was incorporated in the CFD model by connecting porous portions in the left and right pulmonary arteries. The pressure in the common atrium was set as boundary conditions at the outlets of the pulmonary arteries. The flow rate in the innominate veins and the inferior vena cava (IVC) was set as inflow boundary conditions. Furthermore, the inflow rate of IVC was increased to 2 and 3 times of that measured to perform another two simulations and the resistance provided by the porous portions was compared among these three conditions. We found out that the pulmonary resistance set as porous portion in the CFD models remains relatively steady despite the change of the inflow rate. We concluded that, in the CFD simulations for the Fontan connections, porous portion could be used to represent pulmonary resistance steadily. The pulmonary resistance and pressure in the common atrium could be acquired directly by clinical examination. The employment of porous portion together with pressure in the common atrium in the CFD model could facilitate and accurate the set of outlet boundary conditions especially for those actual pulmonary flow splits was unpredictable such as virtual operative designs related CFD simulations.

Computational fluid dynamics models and congenital heart diseases

Mathematical modeling is a powerful tool to investigate hemodynamics of the circulatory system. With improving imaging techniques and detailed clinical investigations, it is now possible to construct patient-specific models of reconstructive surgeries for the treatment of congenital heart diseases. These models can help clinicians to better understand the hemodynamic behavior of different surgical options for a treated patient. This review outlines recent advances in mathematical modeling in congenital heart diseases, the discoveries and limitations these models present, and future directions that are on the horizon.