Mathematical models are essential tools to study how the cardiovascular system maintains homeostasis. The utility of such models is limited by the accuracy of their predictions, which can be determined by uncertainty quantification (UQ). A challenge associated with the use of UQ is that many published methods assume that the underlying model is identifiable (e.g. that a one-to-one mapping exists from the parameter space to the model output). In this study we present a novel workflow to calibrate a lumped-parameter model to left ventricular pressure and volume time series data. Key steps include using (1) literature and available data to determine nominal parameter values; (2) sensitivity analysis and subset selection to determine a set of identifiable parameters; (3) optimization to find a point estimate for identifiable parameters; and (4) frequentist and Bayesian UQ calculations to assess the predictive capability of the model. Our results show that it is possible to determine 5 identifiable model parameters that can be estimated to our experimental data from three rats, and that computed UQ intervals capture the measurement and model error.

Acrolein, an α,β-unsaturated aldehyde and a reactive product of lipid peroxidation, has been suggested as a key factor in neural post-traumatic secondary injury in SCI, mainly based on in vitro and ex vivo evidence. Here we demonstrate an increase of acrolein up to 300%; the elevation lasted at least two weeks in a rat SCI model. More importantly, hydralazine, a known acrolein scavenger can provide neuroprotection when applied systemically. Besides effectively reducing acrolein, hydralazine treatment also resulted in significant amelioration of tissue damage, motor deficits, and neuropathic pain. This effect was further supported by demonstrating the ability of hydralazine to reach spinal cord tissue at a therapeutic level following intraperitoneal application. This suggests that hydralazine is an effective neuroprotective agent not only in vitro, but in a live animal model of SCI as well. Finally, the role of acrolein in SCI was further validated by the fact that acrolein injection into the spinal cord caused significant SCI-like tissue damage and motor deficits. Taken together, available evidence strongly suggests a critical causal role of acrolein in the pathogenesis of spinal cord trauma. Since acrolein has been linked to a variety of illness and conditions, we believe that acrolein-scavenging measures have the potential to be expanded significantly ensuring a broad impact on human health.

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The relationship between regional variabilities in airflow (ventilation) and blood flow (perfusion) is a critical determinant of gas exchange efficiency in the lungs. Hypoxic pulmonary vasoconstriction is understood to be the primary active regulator of ventilation-perfusion matching, where upstream arterioles constrict to direct blood flow away from areas that have low oxygen supply. However, it is not understood how the integrated action of hypoxic pulmonary vasoconstriction affects oxygen transport at the system level. In this study we develop, and make functional predictions with a multi-scale multi-physics model of ventilation-perfusion matching governed by the mechanism of hypoxic pulmonary vasoconstriction. Our model consists of (a) morphometrically realistic 2D pulmonary vascular networks to the level of large arterioles and venules; (b) a tileable lumped-parameter model of vascular fluid and wall mechanics that accounts for the influence of alveolar pressure; (c) oxygen transport accounting for oxygen bound to hemoglobin and dissolved in plasma; and (d) a novel empirical model of hypoxic pulmonary vasoconstriction. Our model simulations predict that under the artificial test condition of a uniform ventilation distribution (1) hypoxic pulmonary vasoconstriction matches perfusion to ventilation; (2) hypoxic pulmonary vasoconstriction homogenizes regional alveolar-capillary oxygen flux; and (3) hypoxic pulmonary vasoconstriction increases whole-lobe oxygen uptake by improving ventilation-perfusion matching.

Ventilation‐Perfusion (V/Q) matching is a critical determinant of efficient gas exchange in the pulmonary circulation. The regulatory mechanisms that control V/Q matching under normal and pathological scenarios are incompletely understood. In this study we present the derivation and validation of a multi‐scale computer model of hemodynamics and gas exchange accounting for the fractal‐like pattern of pulmonary vascular branching, mechanical coupling of blood‐tissue interactions, gas exchange, hemoglobin biochemistry, and vasoregulatory mechanisms. By simulating the regional distribution of V/Q ratios, this model serves as an in‐silico platform to test and refine hypotheses regarding the contributions of vasoregulatory mechanisms to regional perfusion and V/Q matching in the lung. Figure 1 depicts the various model “blocks” and how they are interconnected. The complete model is formulated as an algebraically constrained system of ordinary and partial differential equations and is parameterized to represent function in an adult Sprague Dawley rat. Block (A) illustrates the whole‐lung vascular network model. The network geometry is generated by a space‐filling algorithm and is validated by comparing anatomical predications (length, radius, and connectivity) to morphometric data (from existing literature). Block (B) shows how the mechanics of each vessel segment is represented as a lumped system. Mechanics are validated by comparing model predictions to macro‐scale pressure‐flow relationships and pulmonary artery pressure waveforms (from existing literature and our own in vivo studies). Block (C) depicts a representative gas exchange unit. Block (D) portrays oxygen‐sensitive vasoregulatory mechanisms that have been implicated in the maintenance of pulmonary vasomotor tone. Model simulations illustrate that perfusion heterogeneity is governed by the geometry of the vascular tree, and local interaction between alveolar and vascular pressures. Moreover, conducted vascular responses (hypoxic pulmonary vasoconstriction, and the hypoxia‐mediated/mechanically‐transduced release of ATP from red blood cells) modulate the redistribution of blood flow in response to pathological insults such as a pulmonary embolism. Taken together, our results suggest that more homogenous blood flow distributions increase the bulk oxygen content entering the systemic circulation.Support or Funding InformationNIH/NINDS R01 NS087147NIH/NHLBI R01 HL127151This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

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CD39 (ENTPD1 - ectonucleoside triphosphate diphosphohydrolase 1) is a membrane-tethered ectonucleotidase that hydrolyzes extracellular ATP to ADP and ADP to AMP. This enzyme is expressed in a variety of cell types and tissues and has broadly been recognized within vascular tissue to have a protective role in converting “danger” ligands (ATP) into neutral or “protective” ligands (AMP, adenosine). In this study, we investigate the enzyme kinetics of CD39 using a Michaelis-Menten modeling framework. We show how the unique situation of having a reaction product also serving as a substrate (ADP) complicates the determination of the governing kinetic parameters. Model simulations using values for the kinetic parameters reported in the literature do not align with corresponding time-series data. This dissonance is explained by CD39 kinetic parameters previously being determined by graphical/linearization methods, which have been shown to distort the underlying error structure and lead to inaccurate parameter estimates. Modern methods of estimating these kinetic parameters using non-linear least squares is still challenging due to unidentifiable parameter interactions. We propose a workflow to accurately determine these parameters by isolating the ADPase and ATPase reactions and estimating the respective ADPase parameters and ATPase parameters with independent data sets. Theoretically, this ensures all kinetic parameters are identifiable and reliable for future prospective model simulations involving CD39. These kinds of mathematical models can be used to understand how circulating purinergic nucleotides affect disease etiology and potentially inform the development of corresponding therapies.

A major determinant of how efficient the lungs can transport oxygen into the bloodstream is the regional matching of airflow and blood flow – referred to as ventilation‐perfusion (V/Q) matching. It is appreciated that the mechanisms governing V/Q matching play pathophysiological roles in the etiology of disease states such as acute pulmonary embolism and atelectasis. Yet how physiological V/Q matching is achieved remains poorly understood. This study aims to investigate how V and Q together govern oxygen transport and theoretically determine the optimal ratio of air and blood flow to maximize oxygen uptake. Clinical V/Q ratios are regionally measured by the ratio of 2 distinct contrast agents that are inhaled and infused. In other words, clinical V/Q ratio measurements are not a ratio of flow rates—they are ratio of contrast agent signals. To understand how the ratio of flow rates affect oxygen uptake, we derive and analyze series of progressively more sophisticated models of V/Q matching: Model A is a simple linear compartmental formulation; Model B accounts for the effect of nonlinear hemoglobin on oxygen solubility; Model C accounts for the spatial profile of a pulmonary capillary; and Model D accounts for both hemoglobin and spatial transport. Each model is analyzed using linear stability analysis. The results of our analysis conflict with the intuition that a V/Q ratio (of flow rates) equal to 1 maximizes oxygen uptake. We find that for each of the four models analyzed, optimal oxygen delivery is typically associated with a V/Q ratio greater than 1. Moreover, we observe that oxygen uptake is not only dependent upon the V/Q ratio, but the magnitude of air and blood flow – with increasing blood flow, even larger increases in air flow are required to maintain a given level of oxygen in the bloodstream. Thus our analysis reveals a non‐linear relationship between optimal air and blood flow rates, V/Q ratios, and oxygenation. This non‐linearity is consistent with cardiac output and ventilation data measured in humans over a range of cardiovascular exercise intensities.