arXiv subjects

Charles Puelz

Publications and source records attributed to Charles Puelz.

17 recordsLinked to original sources

arXiv2025

A One Dimensional (1D) Computational Fluid Dynamics Study of Fontan-Associated Liver Disease (FALD)

Fontan-Associated Liver Disease (FALD) is a disorder arising from hemodynamic changes and venous congestion in the liver. This disease is prominent in patients with hypoplastic left heart syndrome (HLHS). Although HLHS patients typically survive into adulthood, they have reduced cardiac output due to their univentricular physiology (i.e., a Fontan circuit). As a result, they have insufficient blood delivery to the liver. In comparison, patients with double outlet right ventricle (DORV), also having a univentricular circuit, have lower incidence of FALD. In this study, we use a patient-specific, one-dimensional computational fluid dynamics (1D-CFD) model to predict hemodynamics in the liver of an HLHS patient and compare predictions with an age- and size-matched DORV control patient. Additionally, we simulate FALD conditions in the HLHS patient to predict hemodynamic changes across various stages of disease progression. Our results show that the HLHS patient has a higher portal venous pressure compared to the DORV patient. This difference is exacerbated as FALD conditions progress. The wall shear stress (WSS) is also higher than normal for the HLHS patient, suggesting vascular remodeling. WSS decreases slightly under FALD conditions, consistent with the development of portal hypertension. Perfusion analysis gives insight into regions of liver tissue at risk for fibrosis development, showing increasing pressures and reduced flow throughout the liver tissue fed by the portal vein under FALD conditions. Our results provide insight into the specific hemodynamic changes in Fontan circulation that can cause FALD.

physics.med-ph↗

arXiv2025

Deformable Registration of MRA and 4D Flow Images to Facilitate Accurate Estimation of Flow Properties within Blood Vessels

A method is presented for the registration of MRA and 4D Flow images, with the goal of calculating blood flow properties using both modalities simultaneously. In particular, the method produces an alignment of segmentations of vessel networks, from MRA images, with the blood velocity field within those networks, from the corresponding 4D Flow images. The alignment procedure is driven by the registration of centerlines of vessels extracted from the two modalities. Our approach is robust to noise, small deformations, and partial omissions of vessel surfaces and/or blood velocities. The alignment procedure is tested on 7 patient data sets acquired at Texas Children's Hospital. The quality of the resulting alignment is assessed by (i) an illustration of the aligned and unaligned surface segmentations for a sample patient, (ii) histograms of distances between centerline networks, and (iii) graphs of estimated blood flow. For each of the 7 analyzed data sets, medians of the distance histograms decreased an average of 83.5%, and the estimated blood flow increased significantly as a result of the alignment procedure.

q-bio.QM↗

arXiv2024

Parameter selection and optimization of a computational network model of blood flow in single-ventricle patients

Hypoplastic left heart syndrome (HLHS) is a congenital heart disease responsible for 23% of infant cardiac deaths each year. HLHS patients are born with an underdeveloped left heart, requiring several surgeries to reconstruct the aorta and create a single ventricle circuit known as the Fontan circulation. While survival into early adulthood is becoming more common, Fontan patients suffer from reduced cardiac output, putting them at risk for a multitude of complications. These patients are monitored using chest and neck MRI imaging, but these scans do not capture energy loss, pressure, wave intensity, or hemodynamics beyond the imaged region. This study develops a framework for predicting these missing features by combining imaging data and computational fluid dynamics (CFD) models. Predicted features from models of HLHS patients are compared to those from control patients with a double outlet right ventricle (DORV). We use parameter inference to render the model patient-specific. In the calibrated model, we predict pressure, flow, wave-intensity (WI), and wall shear stress (WSS). Results reveal that HLHS patients have higher vascular stiffness and lower compliance than DORV patients, resulting in lower WSS and higher WI in the ascending aorta and increased WSS and decreased WI in the descending aorta.

q-bio.QM↗

arXiv2024

Computational framework for the generation of one-dimensional vascular models accounting for uncertainty in networks extracted from medical images

Patient-specific computational modeling is a popular, non-invasive method to answer medical questions. Medical images are used to extract geometric domains necessary to create these models, providing a predictive tool for clinicians. However, in vivo imaging is subject to uncertainty, impacting vessel dimensions essential to the mathematical modeling process. While there are numerous programs available to provide information about vessel length, radii, and position, there is currently no exact way to determine and calibrate these features. This raises the question, if we are building patient-specific models based on uncertain measurements, how accurate are the geometries we extract and how can we best represent a patient's vasculature? In this study, we develop a novel framework to determine vessel dimensions using change points. We explore the impact of uncertainty in the network extraction process on hemodynamics by varying vessel dimensions and segmenting the same images multiple times. Our analyses reveal that image segmentation, network size, and minor changes in radius and length have significant impacts on pressure and flow dynamics in rapidly branching structures and tapering vessels. Accordingly, we conclude that it is critical to understand how uncertainty in network geometry propagates to fluid dynamics, especially in clinical applications.

q-bio.TO↗

arXiv2024

Fluid-structure interaction simulations for the prediction of fractional flow reserve in pediatric patients with anomalous aortic origin of a coronary artery

Computer simulations of blood flow in patients with anomalous aortic origin of a coronary artery (AAOCA) have the promise to provide insight into this complex disease. They provide an in-silico experimental platform to explore possible mechanisms of myocardial ischemia, a potentially deadly complication for patients with this defect. This paper focuses on the question of model calibration for fluid-structure interaction models of pediatric AAOCA patients. Imaging and cardiac catheterization data provide partial information for model construction and calibration. However, parameters for downstream boundary conditions needed for these models are difficult to estimate. Further, important model predictions, like fractional flow reserve (FFR), are sensitive to these parameters. We describe an approach to calibrate downstream boundary condition parameters to clinical measurements of resting FFR. The calibrated models are then used to predict FFR at stress, an invasively measured quantity that can be used in the clinical evaluation of these patients. We find reasonable agreement between the model predicted and clinically measured FFR at stress, indicating the credibility of this modeling framework for predicting hemodynamics of pediatric AAOCA patients. This approach could lead to important clinical applications since it may serve as a tool for risk stratifying children with AAOCA.

q-bio.TO↗

arXiv2023

Simulating Cardiac Fluid Dynamics in the Human Heart

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart's microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed; instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients.

q-bio.TO↗

arXiv2022

Optimal fenestration of the Fontan circulation

In this paper, we develop a pulsatile compartmental model of the Fontan circulation and use it to explore the effects of a fenestration added to this physiology. A fenestration is a shunt between the systemic and pulmonary veins that is added either at the time of Fontan conversion or at a later time for the treatment of complications. This shunt increases cardiac output and decreases systemic venous pressure. However, these hemodynamic benefits are achieved at the expense of a decrease in the arterial oxygen saturation. The model developed this paper incorporates fenestration size as a parameter and describes both blood flow and oxygen transport. It is calibrated to clinical data from Fontan patients, and we use it to study the impact of a fenestration on several hemodynamic variables. In certain scenarios corresponding to high-risk Fontan physiology, we demonstrate the existence of an optimal fenestration size that maximizes oxygen delivery to the systemic tissues.

q-bio.TO↗

arXiv2022

A computational study of aortic reconstruction in single ventricle patients

Patients with hypoplastic left heart syndrome (HLHS) are born with an underdeveloped left heart. They typically receive a sequence of surgeries that result in a single ventricle physiology called the Fontan circulation. While these patients usually survive into early adulthood, they are at risk for medical complications, partially due to their lower than normal cardiac output, which leads to insufficient cerebral and gut perfusion. While clinical imaging data can provide detailed insight into cardiovascular function within the imaged region, it is difficult to use this data for assessing deficiencies in the rest of the body and for deriving blood pressure dynamics. Data from patients used in this paper include three dimensional, magnetic resonance angiograms (MRA), time-resolved phase contrast cardiac magnetic resonance images (4D-MRI) and sphygmomanometer blood pressure measurements. The 4D-MRI images provide detailed insight into velocity and flow in vessels within the imaged region, but they cannot predict flow in the rest of the body, nor do they provide values of blood pressure. To remedy these limitations, this study combines the MRA, 4D-MRI, and pressure data with 1D fluid dynamics models to predict hemodynamics in the major systemic arteries, including the cerebral and gut vasculature. To study effects post-surgery we compare simulations for an HLHS patient with simulations for a matched control patient that has double outlet right ventricle (DORV) physiology with a native aorta. Our results show that the HLHS patient has hypertensive pressures in the brain as well as reduced flow to the gut. Wave-intensity analysis suggests that the HLHS patient has irregular circulatory function during light upright exercise conditions and that predicted wall-shear stresses are lower than normal, suggesting the HLHS patient may have hypertension.

math.DS↗

arXiv2021

Computer simulation of surgical interventions for the treatment of refractory pulmonary hypertension

This paper describes computer models of three interventions used for treating refractory pulmonary hypertension (RPH). These procedures create either an atrial septal defect, a ventricular septal defect, or, in the case of a Potts shunt, a patent ductus arteriosus. The aim in all three cases is to generate a right-to-left shunt, allowing for either pressure or volume unloading of the right side of the heart in the setting of right ventricular failure, while maintaining cardiac output. These shunts are created, however, at the expense of introducing de-oxygenated blood into the systemic circulation, thereby lowering the systemic arterial oxygen saturation. The models developed in this paper are based on compartmental descriptions of human hemodynamics and oxygen transport. An important parameter included in our models is the cross-sectional area of the surgically created defect. Numerical simulations are performed to compare different interventions and various shunt sizes and to assess their impact on hemodynamic variables and oxygen saturations. We also create a model for exercise and use it to study exercise tolerance in simulated pre-intervention and post-intervention RPH patients.

q-bio.TO↗

arXiv2020

Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation

This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data. We also show that the algebraic delay equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters.

math.DS↗

arXiv2019

A reduced model for solute transport in compliant blood vessels with arbitrary axial velocity profile

We derive a reduced model of solute transport in blood based on the center manifold theory. The derivation is carried out on a convection diffusion equation with general axial and radial velocity profiles in a blood vessel of varying cross section. We couple the resulting one dimensional equation to a reduced model for blood flow in a compliant vessel. In the special case of a no--slip axial velocity profile, we study the dependence of the diffusion coefficient and corresponding numerical solutions on the shape of the profile.

physics.flu-dyn↗

arXiv2019

A sharp interface method for an immersed viscoelastic solid

The immersed boundary-finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are discontinuities in the pressure and viscous stress at fluid-structure interfaces. The standard immersed boundary approach, which connects the Lagrangian and Eulerian variables via integral transforms with regularized Dirac delta function kernels, smooths out these discontinuities, which generally leads to low order accuracy. This paper describes an approach to accurately resolve pressure discontinuities for these types of formulations, in which the solid may undergo large deformations. Our strategy is to decompose the physical pressure field into a sum of two pressure-like fields, one defined on the entire computational domain, which includes both the fluid and solid subregions, and one defined only on the solid subregion. Each of these fields is continuous on its domain of definition, which enables high accuracy via standard discretization methods without sacrificing sharp resolution of the pressure discontinuity. Numerical tests demonstrate that this method improves rates of convergence for displacements, velocities, stresses, and pressures, as compared to the conventional IBFE method. Further, it produces much smaller errors at reasonable numbers of degrees of freedom. The performance of this method is tested on several cases with analytic solutions, a nontrivial benchmark problem of incompressible solid mechanics, and an example involving a thick, actively contracting torus.

math.NA↗

arXiv2019

A physiological model of the inflammatory-thermal-pain-cardiovascular interactions during a pathogen challenge

Uncontrolled, excessive production of pro-inflammatory mediators from immune cells and traumatized tissues can cause systemic inflammatory issues like sepsis, one of the ten leading causes of death in the United States and one of the three leading causes of death in the intensive care unit. Understanding the effects of inflammation on the autonomic control system can improve a patient's chance of recovery after an inflammatory event such as surgery. Though the effects of the autonomic response on the inflammatory system are well defined, there remains a gap in understanding the reverse response. Specifically, the impact of the inflammatory response on the autonomic control system remains unknown. In this study, we investigate hypothesized interactions of the inflammatory system with the thermal and cardiovascular regulatory systems in response to an endotoxin challenge using mathematical modeling. We calibrate the model to data from two independent studies: a) of the inflammatory response in healthy young men and b) a comparative study of the inflammatory response between mice and humans. Simulation analysis is used to explore how the model responds to pathological input and treatment, specifically antibiotics, antipyretics, vasopressors, and combination therapy. Our findings show that multimodal treatment that simultaneously targets both the pathogen and the infection symptoms gives the most favorable recovery outcome.

q-bio.TO↗

arXiv2017

A priori error estimates of Adams-Bashforth discontinuous Galerkin methods for scalar nonlinear conservation laws

In this paper we show theoretical convergence of a second-order Adams-Bashforth discontinuous Galerkin method for approximating smooth solutions to scalar nonlinear conservation laws with E-fluxes. A priori error estimates are also derived for a first-order forward Euler discontinuous Galerkin method. Rates are optimal in time and suboptimal in space; they are valid under a CFL condition.

math.NA↗

arXiv2016

Comparison of reduced models for blood flow using Runge-Kutta discontinuous Galerkin methods

One-dimensional blood flow models take the general form of nonlinear hyperbolic systems but differ greatly in their formulation. One class of models considers the physically conserved quantities of mass and momentum, while another class describes mass and velocity. Further, the averaging process employed in the model derivation requires the specification of the axial velocity profile; this choice differentiates models within each class. Discrepancies among differing models have yet to be investigated. In this paper, we systematically compare several reduced models of blood flow for physiologically relevant vessel parameters, network topology, and boundary data. The models are discretized by a class of Runge-Kutta discontinuous Galerkin methods.

physics.flu-dyn↗

arXiv2015

Numerical method of characteristics for one-dimensional blood flow

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by computationally intensive methods like finite elements and discontinuous Galerkin, while some recent applications require more efficient approaches (e.g. for real-time clinical decision support, phenomena occurring over multiple cardiac cycles, iterative solutions to optimization/inverse problems, and uncertainty quantification). Further, the high speed of pressure waves in blood vessels greatly restricts the time step needed for stability in explicit schemes. We address both cost and stability by presenting an efficient and unconditionally stable method for approximating solutions to diagonal nonlinear hyperbolic systems. Theoretical analysis of the algorithm is given along with a comparison of our method to a discontinuous Galerkin implementation. Lastly, we demonstrate the utility of the proposed method by implementing it on small and large arterial networks of vessels whose elastic and geometrical parameters are physiologically relevant.

physics.comp-ph↗

arXiv2014

Spectral Approximation for Quasiperiodic Jacobi Operators

Quasiperiodic Jacobi operators arise as mathematical models of quasicrystals and in more general studies of structures exhibiting aperiodic order. The spectra of these self-adjoint operators can be quite exotic, such as Cantor sets, and their fine properties yield insight into associated dynamical systems. Quasiperiodic operators can be approximated by periodic ones, the spectra of which can be computed via two finite dimensional eigenvalue problems. Since long periods are necessary to get detailed approximations, both computational efficiency and numerical accuracy become a concern. We describe a simple method for numerically computing the spectrum of a period-$K$ Jacobi operator in $O(K^2)$ operations, and use it to investigate the spectra of Schrödinger operators with Fibonacci, period doubling, and Thue-Morse potentials.

math.SP↗