Efficient Uncertainty Quantification in a Multiscale Model of Pulmonary Arterial and Venous Hemodynamics

Computational hemodynamics models are becoming increasingly useful in the management and prognosis of complex, multiscale pathologies, including those attributed to the development of pulmonary vascular disease. However, diseases like pulmonary hypertension are heterogeneous, and affect both the proximal arteries and veins as well as the microcirculation. Simulation tools and the data used for model calibration are also inherently uncertain, requiring a full analysis of the sensitivity and uncertainty attributed to model inputs and outputs. Thus, this study quantifies model sensitivity and output uncertainty in a multiscale, pulse-wave propagation model of pulmonary hemodynamics. Our pulmonary circuit model consists of fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite the sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. Our analyses provide uncertainty in blood pressure, flow, and wave propagation phenomenon, as well as wall shear stress and cyclic stretch, both of which are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal circulation.Comment: 10 Figures, 2 table

Viscoelastic Properties of Cardiovascular Tissues

The aims of this chapter are to review the current state of knowledge regarding the viscoelastic behavior of cardiovascular tissues. We begin with a brief, general discussion of measurement and modeling of cardiovascular tissue viscoelasticity. We then review known viscoelastic behavior of arteries, veins, capillaries, blood components, the heart, and lymphatics. For each tissue type, we highlight tissue-specific measurement methods, the cellular and extracellular components responsible for tissue viscoelasticity, and the clinical implications of energy loss due to viscoelasticity. We conclude with a summary and suggestions for future research

Persistent Vascular Collagen Accumulation Alters Hemodynamic Recovery from Chronic Hypoxia

Pulmonary arterial hypertension (PAH) is caused by narrowing and stiffening of the pulmonary arteries that increase pulmonary vascular impedance (PVZ). In particular, small arteries narrow and large arteries stiffen. Large pulmonary artery (PA) stiffness is the best current predictor of mortality from PAH. We have previously shown that collagen accumulation leads to extralobar PA stiffening at high strain (Ooi et al. 2010). We hypothesized that collagen accumulation would increase PVZ, including total pulmonary vascular resistance (Z0), characteristic impedance (ZC), pulse wave velocity (PWV) and index of global wave reflections (Pb/Pf), which contribute to increased right ventricular afterload. We tested this hypothesis by exposing mice unable to degrade type I collagen (Col1a1R/R) to 21 days of hypoxia (hypoxia), some of which were allowed to recover for 42 days (recovery). Littermate wild-type mice (Col1a1+/+) were used as controls. In response to hypoxia, mean PA pressure (mPAP) increased in both mouse genotypes with no changes in cardiac output (CO) or PA inner diameter (ID); as a consequence, Z0 (mPAP/CO) increased by ∼100% in both genotypes (pZC, PWV and Pb/Pf did not change. However, with recovery, ZC and PWV decreased in the Col1a1+/+ mice and remained unchanged in the Col1a1R/R mice. Z0 decreased with recovery in both genotypes. Microcomputed tomography measurements of large PAs did not show evidence of stiffness changes as a function of hypoxia exposure or genotype. We conclude that hypoxia-induced PA collagen accumulation does not affect the pulsatile components of pulmonary hemodynamics but that excessive collagen accumulation does prevent normal hemodynamic recovery, which may have important consequences for right ventricular function

Data‐enabled cognitive modeling: Validating student engineers’ fuzzy design‐based decision‐making in a virtual design problem

The ability of future engineering professionals to solve complex real‐world problems depends on their design education and training. Because engineers engage with open‐ended problems in which there are unknown parameters and multiple competing objectives, they engage in fuzzy decision‐making, a method of making decisions that takes into account inherent imprecisions and uncertainties in the real world. In the design‐based decision‐making field, few studies have applied fuzzy decision‐making models to actual decision‐making process data. Thus, in this study, we use datasets on student decision‐making processes to validate approximate fuzzy models of student decision‐making, which we call data‐enabled cognitive modeling. The results of this study (1) show that simulated design problems provide rich datasets that enable analysis of student design decision‐making and (2) validate models of student design cognition that can inform future design curricula and help educators understand how students think about design problems

Dobutamine stress MRI in pulmonary hypertension: relationships between stress pulmonary artery relative area change, RV performance, and 10-year survival

In pulmonary hypertension (PH), right ventricular (RV) performance determines survival. Pulmonary artery (PA) stiffening is an important biomechanical event in PH and also predicts survival based on the PA relative area change (RAC) measured at rest using magnetic resonance imaging (MRI). In this exploratory study, we sought to generate novel hypotheses regarding the influence of stress RAC on PH prognosis and the interaction between PA stiffening, RV performance and survival. Fifteen PH patients underwent dobutamine stress-MRI (ds-MRI) and right heart catheterization. RACREST, RACSTRESS, and ΔRAC (RAC STRESS – RAC REST) were correlated against resting invasive hemodynamics and ds-MRI data regarding RV performance and RV-PA coupling efficiency (n’vv [RV stroke volume/RV end-systolic volume]). The impact of RAC, RV data, and n’vv on ten-year survival were determined using Kaplan–Meier analysis. PH patients with a low ΔRAC (<−2.6%) had a worse long-term survival (log-rank P = 0.045, HR for death = 4.46 [95% CI = 1.08–24.5]) than those with ΔRAC ≥ −2.6%. Given the small sample, these data should be interpreted with caution; however, low ΔRAC was associated with an increase in stress diastolic PA area indicating proximal PA stiffening. Associations of borderline significance were observed between low RACSTRESS and low n’vvSTRESS, Δη’VV, and ΔRVEF. Further studies are required to validate the potential prognostic impact of ΔRAC and the biomechanics potentially connecting low ΔRAC to shorter survival. Such studies may facilitate development of novel PH therapies targeted to the proximal PA

Impaired Myofilament Contraction Drives Right Ventricular Failure Secondary to Pressure Overload: Model Simulations, Experimental Validation, and Treatment Predictions

Introduction: Pulmonary hypertension (PH) causes pressure overload leading to right ventricular failure (RVF). Myocardial structure and myocyte mechanics are altered in RVF but the direct impact of these cellular level factors on organ level function remain unclear. A computational model of the cardiovascular system that integrates cellular function into whole organ function has recently been developed. This model is a useful tool for investigating how changes in myocyte structure and mechanics contribute to organ function. We use this model to determine how measured changes in myocyte and myocardial mechanics contribute to RVF at the organ level and predict the impact of myocyte-targeted therapy.Methods: A multiscale computational framework was tuned to model PH due to bleomycin exposure in mice. Pressure overload was modeled by increasing the pulmonary vascular resistance (PVR) and decreasing pulmonary artery compliance (CPA). Myocardial fibrosis and the impairment of myocyte maximum force generation (Fmax) were simulated by increasing the collagen content (↑PVR + ↓CPA + fibrosis) and decreasing Fmax (↑PVR + ↓CPA + fibrosis + ↓Fmax). A61603 (A6), a selective α1A-subtype adrenergic receptor agonist, shown to improve Fmax was simulated to explore targeting myocyte generated Fmax in PH.Results: Increased afterload (RV systolic pressure and arterial elastance) in simulations matched experimental results for bleomycin exposure. Pressure overload alone (↑PVR + ↓CPA) caused decreased RV ejection fraction (EF) similar to experimental findings but preservation of cardiac output (CO). Myocardial fibrosis in the setting of pressure overload (↑PVR + ↓PAC + fibrosis) had minimal impact compared to pressure overload alone. Including impaired myocyte function (↑PVR + ↓PAC + fibrosis + ↓Fmax) reduced CO, similar to experiment, and impaired EF. Simulations predicted that A6 treatment preserves EF and CO despite maintained RV pressure overload.Conclusion: Multiscale computational modeling enabled prediction of the contribution of cellular level changes to whole organ function. Impaired Fmax is a key feature that directly contributes to RVF. Simulations further demonstrate the therapeutic benefit of targeting Fmax, which warrants additional study. Future work should incorporate growth and remodeling into the computational model to enable prediction of the multiscale drivers of the transition from dysfunction to failure

Exercise-Induced Changes in Pulmonary Artery Stiffness in Pulmonary Hypertension

Background: Pulmonary hypertension causes pulmonary artery (PA) stiffening, which overloads the right ventricle (RV). Since symptoms of pulmonary hypertension (PH) are exacerbated by exercise, exercise-induced PA stiffening is relevant to cardiopulmonary status. Here, we sought to demonstrate the feasibility of using magnetic resonance imaging (MRI) for non-invasive assessment of exercise-induced changes in PA stiffness in patients with PH.Methods: MRI was performed on 7 PH patients and 8 age-matched control subjects at rest and during exercise stress. Main pulmonary artery (MPA) relative area change (RAC) and pulse wave velocity (PWV) were measured from 2D-PC images. Invasive right heart catheterization (RHC) was performed on 5 of the PH patients in conjunction with exercise stress to measure MPA pressures and stiffness index (β).Results: Heart rate and cardiac index (CI) were significantly increased with exercise in both groups. In controls, RAC decreased from 0.27 ± 0.05 at rest to 0.22 ± 0.06 with exercise (P < 0.05); a modest increase in PWV was not significant (P = 0.06). In PH patients, RAC decreased from 0.15 ± 0.02 to 0.11 ± 0.01 (P < 0.05) and PWV and β increased from 3.9 ± 0.54 m/s and 1.86 ± 0.12 at rest to 5.75 ± 0.70 m/s and 3.25 ± 0.26 with exercise (P < 0.05 for both), respectively. These results confirm increased MPA stiffness with exercise stress in both groups and the non-invasive metrics of MPA stiffness correlated well with β. Finally, as assessed by PWV but not RAC, PA stiffness of PH patients increased more than that of controls for comparable levels of moderate exercise.Conclusion: These results demonstrate the feasibility of using MRI for non-invasive assessment of exercise-induced changes in MPA stiffness in a small, heterogeneous group of PH patients in a research context. Similar measurements in a larger cohort are required to investigate differences between PWV and RAC for estimation of MPA stiffness

Validation of an arterial constitutive model accounting for collagen content and crosslinking

During the progression of pulmonary hypertension (PH), proximal pulmonary arteries (PAs) increase in both thickness and stiffness. Collagen, a component of the extracellular matrix, is mainly responsible for these changes via increased collagen fiber amount (or content) and crosslinking. We sought to differentiate the effects of collagen content and cross-linking on mouse PA mechanical changes using a constitutive model with parameters derived from experiments in which collagen content and cross-linking were decoupled during hypoxic pulmonary hypertension (HPH). We employed an eight-chain orthotropic element model to characterize collagen’s mechanical behavior and an isotropic neo-Hookean form to represent elastin. Our results showed a strong correlation between the material parameter related to collagen content and measured collagen content (R2 = 0.82, P < 0.0001) and a moderate correlation between the material parameter related to collagen crosslinking and measured crosslinking (R2 = 0.24, P = 0.06). There was no significant change in either the material parameter related to elastin or the measured elastin content from histology. The model-predicted pressure at which collagen begins to engage was ∼25 mmHg, which is consistent with experimental observations. We conclude that this model may allow us to predict changes in the arterial extracellular matrix from measured mechanical behavior in PH patients, which may provide insight into prognoses and the effects of therapy