Numerical simulation of blood flow and pressure drop in the pulmonary arterial and venous circulation

A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281–1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of ‘large’ arteries is connected to its corresponding terminal vein via a network of vessels representing the vascular bed of smaller arteries and veins. We develop and implement an algorithm to calculate the admittance of each vascular bed, using bifurcating structured trees and recursion. The structured-tree models take into account the geometry and material properties of the ‘smaller’ arteries and veins of radii ≥ 50 μ m. We study the effects on flow and pressure associated with three classes of pulmonary hypertension expressed via stiffening of larger and smaller vessels, and vascular rarefaction. The results of simulating these pathological conditions are in agreement with clinical observations, showing that the model has potential for assisting with diagnosis and treatment for circulatory diseases within the lung

Evaluation of a novel Y-shaped extracardiac Fontan baffle using computational fluid dynamics

ObjectivesThe objective of this work is to evaluate the hemodynamic performance of a new Y-graft modification of the extracardiac conduit Fontan operation. The performance of the Y-graft design is compared to two designs used in current practice: a t-junction connection of the venae cavae and an offset between the inferior and superior venae cavae.MethodsThe proposed design replaces the current tube grafts used to connect the inferior vena cava to the pulmonary arteries with a Y-shaped graft. Y-graft hemodynamics were evaluated at rest and during exercise with a patient-specific model from magnetic resonance imaging data together with computational fluid dynamics. Four clinically motivated performance measures were examined: Fontan pressures, energy efficiency, inferior vena cava flow distribution, and wall shear stress. Two variants of the Y-graft were evaluated: an “off-the-shelf” graft with 9-mm branches and an “area-preserving” graft with 12-mm branches.ResultsEnergy efficiency of the 12-mm Y-graft was higher than all other models at rest and during exercise, and the reduction in efficiency from rest to exercise was improved by 38%. Both Y-graft designs reduced superior vena cava pressures during exercise by as much as 5 mm Hg. The Y-graft more equally distributed the inferior vena cava flow to both lungs, whereas the offset design skewed 70% of the flow to the left lung. The 12-mm graft resulted in slightly larger regions of low wall shear stress than other models; however, minimum shear stress values were similar.ConclusionsThe area-preserving 12-mm Y-graft is a promising modification of the Fontan procedure that should be clinically evaluated. Further work is needed to correlate our performance metrics with clinical outcomes, including exercise intolerance, incidence of protein-losing enteropathy, and thrombus formation

In Vitro Multi Scale Models to Study the Early Stage Circulations for Single Ventricle Heart Diseases Palliations

Single ventricle physiology can result from various congenital heart defects in which the patient has only one functional ventricle. Hypoplastic left heart syndrome refers to patients born with an underdeveloped left ventricle. A three stage palliation strategy is applied over the first several years of life to establish a viable circulation path using the one functioning ventricle. Results of the first stage Norwood procedure on neonates with hypoplastic left heart syndrome are unsatisfactory with high morbidities and mortalities primarily due to high ventricle load and other complications. An early second stage Bidirectional Glenn (BDG) procedure is not a suitable option for neonates due to their high pulmonary vascular resistance (PVR), which limits pulmonary blood flow. Realistic experimental models of these circulations are not well established and would be useful for studying the physiological response to surgical decisions on the distribution of flows to the various territories, so as to predict clinical hemodynamics and guide clinical planning. These would serve well to study novel intervention strategies and the effects of known complications at the local and systems-level. This study proved the hypothesis that it is possible to model accurately the first and second stage palliation circulations using multi-scale in vitro circulation models and to use these models to test novel surgical strategies while including the effects of possible complications. A multi-scale mock circulatory system (MCS), which couples a lumped parameter network model (LPN) of the neonatal circulation with an anatomically accurate three-dimensional model of the surgical anastomosis site, was built to simulate the hemodynamic performance of both the Stage 1 and Stage 2 circulations. A pediatric ventricular assist device was used as the single ventricle and a respiration model was applied to the Stage 2 circulation system. Resulting parameters measured were pressure and flow rates within the various territories, and systemic oxygen delivery (OD) were calculated. The Stage 1 and Stage 2 systems were validated by direct comparisons of time-based and mean pressures and flow rates between the experimental measurements, available clinical recordings and/or CFD simulations. Regression and correlation analyses and unpaired t-tests showed that there was excellent agreement between the clinical and experimental time-based results as measured throughout the circulations (0.60 \u3c R^2 \u3c 0.99; p \u3e 0.05, r.m.s error\u3c 5%). A novel, potentially alternative surgical strategy for the initial palliation, was proposed and was tested, called the assisted bidirectional Glenn (ABG) procedure. The approach taps the higher potential energy of the systemic circulation through a systemic to caval shunt with nozzle to increase pulmonary blood flow and oxygen delivery within a superior cavopulmonary connection. Experimental model was validated against a numerical model (0.65 \u3c sigma \u3c 0.97; p \u3e 0.05). The tested results demonstrated the ABG had two main advantages over the Norwood circulation. First, the flow through the ABG shunt is a fraction of the pulmonary flow, reducing the volume overload on the single ventricle and improving systemic and coronary perfusion. Second, the ABG should provide a more stable source of pulmonary flow, which should reduce thrombotic risk or intimal thickening over an mBT shunt. A study to examine the ejector pump effect was conducted. Two parameters were investigated: (1) the superior vena cava (SVC) and pulmonary artery (PA) pressure difference; and (2) the SVC and PA pressure difference relative to PA flow rate. Results validated the hypothesis that an ejector pump advantage can be adopted in a superior cavo-pulmonary circulation, where the low-energy pulmonary blood flow can be assisted by an additional source of high energy flow from the systemic circulation. But the ejector pump effect produced by the current nozzle designs was not strong. Parametric study includes nozzle size, placement, and nozzle shape was conducted. Results shown that nozzle to shunt diameter ratio had the most important effects on the ABG performance. As β increased, pulmonary artery flow rate and systemic oxygen delivery increased. A suggested β value falls between 0.48 and 0.72. The study showed that a bigger β produced a smaller resistance value. The shape of the nozzle did not change the resistance value. The effects of shunt angle, nozzle placement and nozzle shape on the ABG circulation were not statistical significant. The aortic coarctation study showed that the aortic coarctation could have an effect on the ABG circulation. The coarctation index (CoI) around 0.5 was found to be the transition point between no effects (CoI \u3e 0.5) and discernible effects on the ABG circulation. These effects include changes in pulmonary to systemic flow distribution. In summary, this research verified and validated an in vitro mock circulatory system (MCS) for Stage 1 and Stage 2 circulations. The system was used to assess a novel conceptual surgery option named the ABG. Parametric studies were conducted to give guidance on designing the important element for the ABG: the shunt (nozzle) connecting the SVC and systemic circulation. The performance of the ABG under one unhealthy condition, namely, aortic coarctation was assessed

In-Vitro and In-Silico Investigations of Alternative Surgical Techniques for Single Ventricular Disease

Single ventricle (SV) anomalies account for one-fourth of all cases of congenital Heart disease. The conventional second and third stage i.e. Comprehensive stage II and Fontan procedure of the existing three-staged surgical approach serving as a palliative treatment for this anomaly, entails multiple complications and achieves a survival rate of 50%. Hence, to reduce the morbidity and mortality rate associated with the second and third stages of the existing palliative procedure, the novel alternative techniques called “Hybrid Comprehensive Stage II” (HCSII), and a “Self-powered Fontan circulation” have been proposed. The goal of this research is to conduct in-vitro investigations to validate computational and clinical findings on these proposed novel surgical techniques. The research involves the development of a benchtop study of HCSII and self-powered Fontan circulation

MULTI-SCALE MODELING OF THE FONTAN CIRCULATION USING A MOCK CIRCULATORY SYSTEM

The Fontan circulation is the result of a series of operations performed to save the lives of children born with univentricular circulations. The Fontan procedure achieves venous return to the pulmonary circulation without a ventricular power source. The load on the heart is reduced to normal, and these patients can lead a normal life into adulthood, although late complications continue to prevent normal lifespan. A unique feature of the Fontan circulation is the dependency of inferior vena cava flow on respiration. The Fontan circulation has been modeled experimentally using an adjustable mock circulatory system, which for the first time includes the influence of respiration. A multi-scale model based on a realistic, 3D patient-specific test section coupled with a lumped parameter model tuned to patient-specific parameters is used to simulate the pressure and flow found in the Fontan circulation. For the first time, the clinically observed respiratory effects in TCPC venous physiology were successfully simulated in an experimental model, where venous flow increased during inspiration and decreased during expiration. Clinically observed hepatic vein flow reversal was also seen in the model. This reverse flow was accentuated when the pulmonary vascular resistance was increased on the venous side

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

Non-invasive hemodynamic monitoring by electrical impedance tomography

The monitoring of central hemodynamic parameters such as cardiac output (CO) and pulmonary artery pressure (PAP) is of paramount clinical importance to assess the health status of the cardiovascular system. However, their measurement requires the insertion of a pulmonary artery catheter, a highly invasive procedure associated with non-negligible morbidity and mortality rates. In this thesis, we investigated the clinical potential of electrical impedance tomography (EIT) - a radiation-free medical imaging technique - as a non-invasive alternative for the measurement of CO and PAP. In a first phase, we investigated the potential of EIT for the measurement of CO. This measurement is implicitly based on the hypothesis that the EIT heart signal (the ventricular component of the EIT signals) is induced by ventricular blood volume changes. This hypothesis has never been formally investigated, and the exact origins of the EIT heart signal remain subject to interpretation. Therefore, using a model, we investigated the genesis of this signal by identifying its various sources and their respective contributions. The results revealed that the EIT heart signal is dominated by cardioballistic effects (heart motion). However, although of prominently cardioballistic origin, the amplitude of the signal has shown to be strongly correlated to stroke volume (r = 0.996, p < 0.001; error of 0.57 +/- 2.19 mL). We explained these observations by the quasi-incompressibility of myocardial tissue and blood. We further identified several factors and conditions susceptible to affect the accuracy of the measurement. Finally, we investigated the influence of the EIT sensor belt position on the measured heart signal. We observed that small belt displacements - likely to occur in clinical settings during patient handling - can induce errors of up to 30 mL on stroke volume estimation. In a second phase, we investigated the feasibility of a novel method for the non-invasive measurement of PAP by EIT. The method is based on the physiological relation linking the PAP to the velocity of propagation of the pressure waves in the pulmonary arteries. We hypothesized that the variations of this velocity, and therefore of the PAP, could be measured by EIT. In a bioimpedance model of the human thorax, we demonstrated the feasibility of our method in various types of pulmonary hypertensive disorders. Our EIT-derived parameter has shown to be particularly well-suited for predicting early changes in pulmonary hemodynamics due to its physiological link with arterial compliance. Finally, we validated experimentally our method in 14 subjects undergoing hypoxia-induced PAP changes. Significant correlation coefficients (range: [0.70, 0.98], average: 0.89) and small standard errors of the estimate (range: [0.9, 6.3] mmHg, average: 2.4 mmHg) were found between our EIT-derived systolic PAP and reference systolic PAP values obtained by Doppler echocardiography. In conclusion, there is a promising outlook for EIT in non-invasive hemodynamic monitoring. Our observations provide novel insights for the interpretation and understanding of EIT heart signals, and detail the physiological and metrological requirements for an accurate measurement of CO by EIT. Our novel PAP monitoring method, validated in vivo, allows a reliable tracking of PAP changes, thereby paving the way towards the development of a new branch of non-invasive hemodynamic monitors based on the use of EIT

Simulating the pulse wave in the human pulmonary circulation

This thesis deals with the development and application of an existing [169] non-linear, one-dimensional mathematical and computational model of pulse wave propagation in the human pulmonary circulation with an aim to improve our ability to predict blood pressure and flow in the pulmonary arteries and veins and enhance our understanding of haemodynamic changes occurring during health and disease. The existing model by Vaughan [169] is developed in two ways, firstly by improving the descriptions of venous geometry, values of physiological parameters, inflow and outflow boundary conditions, and then by extending the model to predict pressure drop across the pulmonary vascular beds. The arteries and veins are treated as thin, homogeneous elastic tubes, and blood as a viscous, homogeneous and incompressible fluid. The non-linear effects of pulse wave propagation are predicted in the large arteries and veins, solving the governing equations by means of two-step Lax-Wendroff scheme. For an accurate haemodynamic prediction, the effects of downstream vasculature are incorporated through dynamic structured-tree matching conditions by linking the arterial and venous pressures and flows. For each blood vessel in the structured trees, linearised governing equations are solved analytically. The modelling capability is enhanced by imposing four out flow conditions at the orifices of four large veins opening in the left atrium. Considering the fundamental differences between pulmonary and systemic compliance behaviour, a revised compliance parameter value is used to obtain improved predictions of the pulmonary pressure pulse. The model is applied to various hypotheses of pulmonary hypertension to analyse the haemodynamic disorders linked with the causes of the pulmonary hypertension. The prescribed flow-rate boundary condition at the system inlet limits the occurrence of any changes in the flow patterns due to the hypertension, so a new pressure boundary condition, simulating remodelling of the heart or ventricular dysfunction, is imposed to study the effects of the hypertension on the volume flow-rate. To better understand the microcirculatory characteristic in the pulmonary circulation, under normal and diseased conditions, the model is further extended to predict the mean pressure drop across the pulmonary arterioles and venules by treating the connected structure trees not only as boundary conditions but also an active fluid dynamical part of the model. A more insightful interpretation of the results is provided by separating the pulse waveforms into incident and reflected components using Wave Intensity Analysis. Finally, the model is applied to assess the effectiveness of commonly used techniques to estimate local pulse wave velocity in the pulmonary arteries. This thesis is a step forward in understanding the performance of the pulmonary circulation and its behaviour in response to various anatomical and physiological changes in health and disease. Moreover, despite having room for further developments and validation, the model has the ability to simulate physiologically relevant pulse waveforms at a reasonable computational cost and therefore has a prospect of clinical application in the long run

MR image based measurement, modelling and diagnostic interpretation of pressure and flow in the pulmonary arteries: applications in pulmonary hypertension

Pulmonary hypertension (PH) is a clinical condition characterised by an increased mean pulmonary arterial pressure (mPAP) of over 25 mmHg measured, at rest, by right heart catheterisation (RHC). RHC is currently considered the gold standard for diagnosis, follow-up and measurement of response to treatment. Although the severe complications and mortality risk associated with the invasive procedure are reduced when it is performed in a specialist centre, finding non-invasive PH diagnosis methods is highly desirable. Non-invasive, non-ionising imaging techniques, based on magnetic resonance imaging (MRI) and on echocardiography, have been integrated into the clinical routine as means for PH assessment. Although the imaging techniques can provide valuable information supporting the PH diagnosis, accurately identifying patients with PH based upon images alone remains challenging. Computationally based models can bring additional insights into the haemodynamic changes occurring under the manifestation of PH. The primary hypothesis of this thesis is that that the physiological status of the pulmonary circulation can be inferred using solely non-invasive flow and anatomy measurements of the pulmonary arteries, measured by MRI and interpreted by 0D and 1D mathematical models. The aim was to implement a series of simple mathematical models, taking the inputs from MRI measurements, and to evaluate their potential to support the non-invasive diagnosis and monitoring of PH. The principal objective was to develop a tool that can readily be translated into the clinic, requiring minimum operator input and time and returning meaningful and accurate results. Two mathematical models, a 3 element Windkessel model and a 1D model of an axisymmetric straight elastic tube for wave reflections were implemented and clinically tested on a cohort of healthy volunteers and of patients who were clinically investigated for PH. The latter group contained some who were normotensive, and those with PH were stratified according to severity. A 2D semi-automatic image segmentation workflow was developed to provide patient specific, simultaneous flow and anatomy measurements of the main pulmonary artery (MPA) as input to the mathematical models. Several diagnostic indices are proposed, and of these distal resistance (Rd), total vascular compliance (C) and the ratio of reflected to total wave power (Wb/Wtot) showed statistically significant differences between the analysed groups, with good accuracy in PH classification. A machine learning classifier using the derived computational metrics and several other PH metrics computed from MRI images of the MPA and of the right ventricle alone, proposed in the literature as PH surrogate markers, was trained and validated with leave-one-out cross-validation to improve the accuracy of non-invasive PH diagnosis. The results accurately classified 92% of the patients, and furthermore the misclassified 8% were patients with mPAP close to the 25 mmHg (at RHC) threshold (within the range of clinical uncertainty). The individual analysis of all PH surrogate markers emphasised that wave reflection quantification, although with lower diagnosis accuracy (75%) than the machine learning model embedding multiple markers, has the potential to distinguish between multiple PH categories. A finite element method (FEM) based model to solve a 1D pulmonary arterial tree linear system, has been implemented to contribute further to the accurate, non-invasive assessment of pulmonary hypertension. The diagnostic protocols, including the analysis work flow, developed and reported in this PhD thesis can be integrated into the clinical process, with the potential to reduce the need for RHC by maximising the use of available MRI data