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.

Blood pressure and blood flow variation during postural change from sitting to standing: model development and validation.

Short-term cardiovascular responses to postural change from sitting to standing involve complex interactions between the autonomic nervous system, which regulates blood pressure, and cerebral autoregulation, which maintains cerebral perfusion. We present a mathematical model that can predict dynamic changes in beat-to-beat arterial blood pressure and middle cerebral artery blood flow velocity during postural change from sitting to standing. Our cardiovascular model utilizes 11 compartments to describe blood pressure, blood flow, compliance, and resistance in the heart and systemic circulation. To include dynamics due to the pulsatile nature of blood pressure and blood flow, resistances in the large systemic arteries are modeled using nonlinear functions of pressure. A physiologically based submodel is used to describe effects of gravity on venous blood pooling during postural change. Two types of control mechanisms are included: 1) autonomic regulation mediated by sympathetic and parasympathetic responses, which affect heart rate, cardiac contractility, resistance, and compliance, and 2) autoregulation mediated by responses to local changes in myogenic tone, metabolic demand, and CO(2) concentration, which affect cerebrovascular resistance. Finally, we formulate an inverse least-squares problem to estimate parameters and demonstrate that our mathematical model is in agreement with physiological data from a young subject during postural change from sitting to standing.

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.

Estimation and identification of parameters in a lumped cerebrovascular model.

This study shows how sensitivity analysis and subset selection can be employed in a cardiovascular model to estimate total systemic resistance, cerebrovascular resistance, arterial compliance, and time for peak systolic ventricular pressure for healthy young and elderly subjects. These quantities are parameters in a simple lumped parameter model that predicts pressure and flow in the systemic circulation. The model is combined with experimental measurements of blood flow velocity from the middle cerebral artery and arterial finger blood pressure. To estimate the model parameters we use nonlinear optimization combined with sensitivity analysis and subset selection. Sensitivity analysis allows us to rank model parameters from the most to the least sensitive with respect to the output states (cerebral blood flow velocity and arterial blood pressure). Subset selection allows us to identify a set of independent candidate parameters that can be estimated given limited data. Analyses of output from both methods allow us to identify five independent sensitive parameters that can be estimated given the data. Results show that with the advance of age total systemic and cerebral resistances increase, that time for peak systolic ventricular pressure is increases, and that arterial compliance is reduced. Thus, the method discussed in this study provides a new methodology to extract clinical markers that cannot easily be assessed noninvasively.

Sensitivity analysis and model assessment: mathematical models for arterial blood flow and blood pressure.

The complexity of mathematical models describing the cardiovascular system has grown in recent years to more accurately account for physiological dynamics. To aid in model validation and design, classical deterministic sensitivity analysis is performed on the cardiovascular model first presented by Olufsen, Tran, Ottesen, Ellwein, Lipsitz and Novak (J Appl Physiol 99(4):1523-1537, 2005). This model uses 11 differential state equations with 52 parameters to predict arterial blood flow and blood pressure. The relative sensitivity solutions of the model state equations with respect to each of the parameters is calculated and a sensitivity ranking is created for each parameter. Parameters are separated into two groups: sensitive and insensitive parameters. Small changes in sensitive parameters have a large effect on the model solution while changes in insensitive parameters have a negligible effect. This analysis was successfully used to reduce the effective parameter space by more than half and the computation time by two thirds. Additionally, a simpler model was designed that retained the necessary features of the original model but with two-thirds of the state equations and half of the model parameters.