Laura Ellwein

Computational Simulations for Aortic Coarctation: Representative Results From a Sampling of Patients

Treatments for coarctation of the aorta (CoA) can alleviate blood pressure (BP) gradients (Δ), but long-term morbidity still exists that can be explained by altered indices of hemodynamics and biomechanics. We introduce a technique to increase our understanding of these indices for CoA under resting and nonresting conditions, quantify their contribution to morbidity, and evaluate treatment options. Patient-specific computational fluid dynamics (CFD) models were created from imaging and BP data for one normal and four CoA patients (moderate native CoA: Δ12 mmHg, severe native CoA: Δ25 mmHg and postoperative end-to-end and end-to-side patients: Δ0 mmHg). Simulations incorporated vessel deformation, downstream vascular resistance and compliance. Indices including cyclic strain, time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) were quantified. Simulations replicated resting BP and blood flow data. BP during simulated exercise for the normal patient matched reported values. Greatest exercise-induced increases in systolic BP and mean and peak ΔBP occurred for the moderate native CoA patient (SBP: 115 to 154 mmHg; mean and peak ΔBP: 31 and 73 mmHg). Cyclic strain was elevated proximal to the coarctation for native CoA patients, but reduced throughout the aorta after treatment. A greater percentage of vessels was exposed to subnormal TAWSS or elevated OSI for CoA patients. Local patterns of these indices reported to correlate with atherosclerosis in normal patients were accentuated by CoA. These results apply CFD to a range of CoA patients for the first time and provide the foundation for future progress in this area.

INCLUDING AORTIC VALVE MORPHOLOGY IN COMPUTATIONAL FLUID DYNAMICS SIMULATIONS: INITIAL FINDINGS AND APPLICATION TO AORTIC COARCTATION

Computational fluid dynamics (CFD) simulations quantifying thoracic aortic flow patterns have not included disturbances from the aortic valve (AoV). 80% of patients with aortic coarctation (CoA) have a bicuspid aortic valve (BAV) which may cause adverse flow patterns contributing to morbidity. Our objectives were to develop a method to account for the AoV in CFD simulations, and quantify its impact on local hemodynamics. The method developed facilitates segmentation of the AoV, spatiotemporal interpolation of segments, and anatomic positioning of segments at the CFD model inlet. The AoV was included in CFD model examples of a normal (tricuspid AoV) and a post-surgical CoA patient (BAV). Velocity, turbulent kinetic energy (TKE), time-averaged wall shear stress (TAWSS), and oscillatory shear index (OSI) results were compared to equivalent simulations using a plug inlet profile. The plug inlet greatly underestimated TKE for both examples. TAWSS differences extended throughout the thoracic aorta for the CoA BAV, but were limited to the arch for the normal example. OSI differences existed mainly in the ascending aorta for both cases. The impact of AoV can now be included with CFD simulations to identify regions of deleterious hemodynamics thereby advancing simulations of the thoracic aorta one step closer to reality.

Patient-specific modeling of cardiovascular and respiratory dynamics during hypercapnia.

This study develops a lumped cardiovascular-respiratory system-level model that incorporates patient-specific data to predict cardiorespiratory response to hypercapnia (increased CO(2) partial pressure) for a patient with congestive heart failure (CHF). In particular, the study focuses on predicting cerebral CO(2) reactivity, which can be defined as the ability of vessels in the cerebral vasculature to expand or contract in response CO(2) induced challenges. It is difficult to characterize cerebral CO(2) reactivity directly from measurements, since no methods exist to dynamically measure vasomotion of vessels in the cerebral vasculature. In this study we show how mathematical modeling can be combined with available data to predict cerebral CO(2) reactivity via dynamic predictions of cerebral vascular resistance, which can be directly related to vasomotion of vessels in the cerebral vasculature. To this end we have developed a coupled cardiovascular and respiratory model that predicts blood pressure, flow, and concentration of gasses (CO(2) and O(2)) in the systemic, cerebral, and pulmonary arteries and veins. Cerebral vascular resistance is incorporated via a model parameter separating cerebral arteries and veins. The model was adapted to a specific patient using parameter estimation combined with sensitivity analysis and subset selection. These techniques allowed estimation of cerebral vascular resistance along with other cardiovascular and respiratory parameters. Parameter estimation was carried out during eucapnia (breathing room air), first for the cardiovascular model and then for the respiratory model. Then, hypercapnia was introduced by increasing inspired CO(2) partial pressure. During eucapnia, seven cardiovascular parameters and four respiratory parameters was be identified and estimated, including cerebral and systemic resistance. During the transition from eucapnia to hypercapnia, the model predicted a drop in cerebral vascular resistance consistent with cerebral vasodilation.

Image-based quantification of 3D morphology for bifurcations in the left coronary artery: Application to stent design

Improved strategies for stent‐based treatment of coronary artery disease at bifurcations require a greater understanding of artery morphology.

Immersive visualization for enhanced computational fluid dynamics analysis.

Modern biomedical computer simulations produce spatiotemporal results that are often viewed at a single point in time on standard 2D displays. An immersive visualization environment (IVE) with 3D stereoscopic capability can mitigate some shortcomings of 2D displays via improved depth cues and active movement to further appreciate the spatial localization of imaging data with temporal computational fluid dynamics (CFD) results. We present a semi-automatic workflow for the import, processing, rendering, and stereoscopic visualization of high resolution, patient-specific imaging data, and CFD results in an IVE. Versatility of the workflow is highlighted with current clinical sequelae known to be influenced by adverse hemodynamics to illustrate potential clinical utility.

Bifurcation study of blood flow control in the kidney

Renal blood flow is maintained within a narrow window by a set of intrinsic autoregulatory mechanisms. Here, a mathematical model of renal hemodynamics control in the rat kidney is used to understand the interactions between two major renal autoregulatory mechanisms: the myogenic response and tubuloglomerular feedback. A bifurcation analysis of the model equations is performed to assess the effects of the delay and sensitivity of the feedback system and the time constants governing the response of vessel diameter and smooth muscle tone. The results of the bifurcation analysis are verified using numerical simulations of the full nonlinear model. Both the analytical and numerical results predict the generation of limit cycle oscillations under certain physiologically relevant conditions, as observed in vivo.

Modeling Blood Flow Control in the Kidney

A mathematical model of renal hemodynamics is developed in this study to investigate autoregulation in the rat kidney under physiological and pathophysiological conditions. The model simulates the blood supply to a nephron via the afferent arteriole, the filtration of blood through the glomerulus, and the transport of water and ions in the thick ascending limb of the short loop of Henle. The afferent arteriole exhibits the myogenic response, which induces changes in vascular smooth muscle tone in response to hydrostatic pressure variations. Chloride transport is simulated along the thick ascending limb, and the concentration of chloride at the macula densa provides the signal for the constriction or dilation of the afferent arteriole via tubuloglomerular feedback (TGF). With this configuration, the model predicts a stable glomerular filtration rate within a physiological range of perfusion pressure (60–180 mmHg). The contribution of TGF to overall blood flow autoregulation in the kidney is significant only within a narrow band of perfusion pressure values. Simulations of renal autoregulation under conditions of diabetes mellitus yield a > 60% increase in glomerular filtration rate, due in large part to the impairment of the voltage-gated Ca2+ channels of the afferent arteriole smooth muscle cells.

Modeling cardio-respiratory system response to inhaled CO 2 in patients with congestive heart failure

In this paper we examine a cardiovascular-respiratory model of mid-level complexity designed to predict the dynamics of end-tidal carbon dioxide (CO2) and cerebral blood flow velocity in response to a CO2 challenge. Respiratory problems often emerge as heart function diminishes in congestive heart failure patients. To assess system function, various tests can be performed including inhalation of a higher than normal CO2 level. CO2 is a key quantity firstly because any perturbation in system CO2 quickly influences ventilation (oxygen perturbations need to be more severe). Secondly, the CO2 response gain has been associated with respiratory system control instability. Thirdly, CO2 in a short time impacts the degree of cerebral vascular constriction, allowing for the assessment of cerebral vasculature function. The presented model can be used to study key system characteristics including cerebral vessel CO2 reactivity and ventilatory feedback factors influencing ventilatory stability in patients with congestive heart failure. Accurate modeling of the dynamics of system response to CO2 challenge, in conjunction with robust parameter identification of key system parameters, can help in assessing patient system status.

Use of NIRS data as boundary conditions for CFD simulations (PMID27376865)

This Excel file contains the following 4 worksheets that allow researchers to confirm, extend and apply the findings from PMID 27376865: Worksheet 1 - Windkessel parameters from Table 1 of the paper; Worksheet 2 - A blood flow distribution calculator that uses NIRS data as input; Worksheet 3 - Ensemble-averaged (n=6) blood flow waveforms in the ascending aorta under resting blood flow conditions and three levels of exercise; Worksheet 4 - A waveform creator that automatically generates ascending aortic blood flow waveforms during rest and exercise using cardiac output and heart rate data from any patient.

Quantification of thoracic aorta blood flow by magnetic resonance imaging during supine cycling exercise of increasing intensity

Background Cardiac magnetic resonance imaging (MRI) may be used for the diagnosis and follow-up of diseases affecting the thoracic aorta (TA). Typically, patients are imaged at rest. Quantifying TA blood flow distribution during activity may improve understanding of disease impact by assessing possible factors contributing to exercise intolerance. Blood flow quantification during exercise MRI, though, has heretofore been complicated by prolonged MRI scan times, motion artifact, and gradient field inhomogeneities. We developed a protocol for phase-contrast (PC) MRI flow quantification in the TA and head and neck arteries during three-tiered supine cycling submaximal exercise. Methods PC-MRI was acquired in the ascending aorta (AAo) and innominate (IA), left common carotid (LCCA), and left subclavian (LSA) arteries using a 1.5T Siemens MAGNETOM ® Symphony magnet. Six healthy volunteers (28±2 years) were imaged during rest and supine pedaling of an MRI-compatible cycle to reach 130%, 150%, and 170% of resting heart rate (HR130 ,H R150 ,H R170). Scan parameters balanced image quality with acquisition time, accounting for subject positioning in the magnet and motion from pedaling. Time-resolved volumetric blood flow was calculated from PC-MRI data and estimated in the descending aorta (dAo). Flow quantification included cardiac index from AAo flow, arterial normalized mean flow (NMF,L/min/m 2 ) and flow distribution (FD,% of AAo flow). Significance of flow quantification between HRs and rest was tested post-hoc with Student’s t-test. Results Cardiac index increased linearly (r 2 =0.99) from 3.1±0.3 to 5.2±0.3 L/min/m 2 from rest to HR170 (p<0.05). HR increased to 111±5.9 bpm and workload to 38±9 watts at HR170. In the dAo, NMF increased linearly with respect to HR (r 2 =0.99) by 46%, 72%, and 93% with significance at all levels (Table 1). The IA showed significant increase in NMF of 39% at HR170 compared to rest. Increases in NMF