Multiscale model for pulmonary oxygen uptake and its application to quantify hypoxemia in hepatopulmonary syndrome

This paper presents a novel multiscale methodology for quantitative analysis of pulmonary gas exchange. The process of oxygen uptake in the lungs is a complex multiscale process, characterized by multiple time and length scales which are coupled nonlinearly through the processes of diffusion, convection and reaction, and the overall oxygen uptake is significantly influenced by the transport and reaction rate processes at the small-scales. Based on the separation of length scales, we characterize these disparate scales by three representative ones, namely micro (red blood cell), meso (capillary and alveolus) and macro (lung). We start with the fundamental convection-diffusion-reaction (CDR) equation that quantifies transport and reaction rates at each scale and apply spatial averaging techniques to reduce the dimensionality of these models. The resultant low-dimensional models embed each scale hierarchically within the other while retaining the important parameters of the small-scales in the averaged equations, and drastically reduce the computational efforts involved in solving them. We use our multiscale model for pulmonary gas exchange to quantify the oxygen uptake abnormalities in patients with hepatopulmonary syndrome (HPS), a disease which is characterized by coupled abnormalities in multiple length scales. Based on our multiscale modeling, we suggest a strategy to stratify patients with HPS into two categories--those who are oxygen-responsive and those who are oxygen non-responsive with intractable hypoxemia.     

Multiscale modeling of biomolecular systems: in serial and in parallel

Considerable progress has been recently achieved in the multiscale modeling of complex biological processes. Multiscale models have now investigated the structure and dynamics of lipid membranes, proteins, peptides and DNA over length and time scales ranging from the atomic to the macroscopic. Serial multiscale methods that parameterize low-resolution coarse-grained models with data from high-resolution models have studied long time or length scale phenomena that cannot be investigated with atomically detailed models. Parallel multiscale methods that directly couple high- and low-resolution models have efficiently explored slow structural transitions and the importance of long-wavelength fluctuations for biological molecules. The success of such models relies upon new theories and methods for constructing accurate multiscale bridges that transfer information between models with different resolutions.     

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.     

Multiscale modelling in biofluidynamics: application to reconstructive paediatric cardiac surgery

Multiscale computing is a challenging area even in biomechanics. Application of such a methodology to quantitatively compare postoperative hemodynamics in congenital heart diseases is very promising. In the treatment of hypoplastic left heart syndrome, which is a congenital heart disease where the left ventricle is missing or very small, the necessity to feed the pulmonary and systemic circulations is obtained with an interposition shunt. Two main options are available and differ from the sites of anastomoses: (i) the systemic-to-pulmonary conduit (Blalock-Taussig shunt known as the Norwood Operation (NO)) connecting the innominate artery (NO-BT) or the aorta (NO-CS) to the right pulmonary artery and (ii) the right ventricle to pulmonary artery shunt (known as Sano operation (SO)). The proposition that the SO is superior to the NO remains controversial. 3-D computer models of the NO (NO-BT and NO-CS) and SO were developed and investigated using the finite volume method. Conduits of 3, 3.5 and 4 mm were used in the NO models, whereas conduits of 4, 5 and 6 mm were used in the SO model. The hydraulic nets (lumped resistances, compliances, inertances and elastances) which represent the systemic, coronary and pulmonary circulations and the heart were identical in the two models. A multiscale approach was adopted to couple the 3-D models with the circulation net. Computer simulation results were compared with post-operative catheterization data. Results showed that (i) there is a good correlation between predicted and observed data: higher aortic diastolic pressure, decreased pulmonary arterial pressure, lower pulmonary-to-systemic flow ratio and higher coronary perfusion pressure in SO; (ii) there is a minimal regurgitant flow in the SO conduit. The close correlation between predicted and observed clinical data supports the use of mathematical modelling, with a mandatory multiscale approach, in the design and assessment of surgical procedures.     

The influence of systemic-to-pulmonary arterial shunts and peripheral vasculatures in univentricular circulations: Focus on coronary perfusion and aortic arch hemodynamics through computational multi-domain modeling

Initial palliation for univentricular hearts can be achieved via a systemic-to-pulmonary shunt (SPS). SPS configurations differ depending on the proximal anastomosis location, which might lead to dissimilar coronary and upper body perfusions. Mathematical modeling can be used to explore the local and global hemodynamic effects of the SPSs. In literature there are few patient-specific models of SPS that specifically address the influence of both the local and peripheral vasculature. In this study, multi-domain models of univentricular circulations were developed to investigate local hemodynamics and flow distribution in the presence of two shunt configurations. We also analyzed the relative impact of local and peripheral vascular resistances on coronary perfusion and flows through the upper aortic branches.A two-step approach was followed. First, two patient-specific models were based on clinical data collected from univentricular patients having different shunts and peripheral vasculatures. Each model coupled a three-dimensional representation of SPS, aortic arch (AA) and pulmonary arteries, with a lumped parameter model (LPM) of peripheral vasculature closing the circulatory loop. Then, two additional models of hypothetical subjects were created by coupling each customized LPM with the other patient’s three-dimensional anatomy.Flow rates and pressures predicted by the patient-specific models revealed overall agreement with clinical data. Differences in the local hemodynamics were seen during diastole between the two models. Varying the three-dimensional models, while keeping an identical LPM, led to comparable flow distribution through the AA, suggesting that peripheral vasculatures have a dominant effect on local hemodynamics with respect to the shunt configuration.     

Acute adaptations of the coronary circulation to exercise

Coronary blood flow is tightly coupled to myocardial oxygen consumption to maintain a consistently high level of myocardial oxygen extraction. This tight coupling has been proposed to depend on periarteriolar, oxygen tension, signals released from cardiomyocytes (adenosine acting on K _ATP ⁺ channels), and/or the endothelium (prostanoids, nitric oxide, endothelin [ET]) and autonomic influences (catecholamines), but the contribution of each of these regulatory pathways and their interactions are still incompletely understood. Until recently, experimental studies into the regulation of coronary blood flow during exercise were principally performed in the dog. We have performed several studies on the regulation of vasomotor tone in coronary resistance vessels in chronically instrumented exercising swine. These studies have shown that the coronary resistance vessels in swine lack significant α-adrenergic control, but that these vessels are subject to β-adrenergic feed-forward control during exercise, which is aided by a parasympathetic withdrawal. In addition, withdrawal of an ET-mediated vasoconstrictor influence also contributes to exercise-induced coronary vasodilation. Coronary blood flow regulation by endothelial and metabolic vasodilator pathways contributes to resting vasomotor tone regulation but does not appear to contribute to the exercise-induced coronary vasodilation. Furthermore, blockade of one vasodilator pathway is not compensated by an increased contribution of the other vasodilator mechanisms, suggesting that porcine coronary vasomotor control by endothelial and metabolic factors occurs in a linear additive rather than a nonlinear synergistic fashion.     

Multiscale modeling of cellular actin filaments: from atomistic molecular to coarse-grained dynamics

In this article, we present a computational multiscale model for the characterization of subcellular proteins. The model is encoded inside a simulation tool that builds coarse-grained (CG) force fields from atomistic simulations. Equilibrium molecular dynamics simulations on an all-atom model of the actin filament are performed. Then, using the statistical distribution of the distances between pairs of selected groups of atoms at the output of the MD simulations, the force field is parameterized using the Boltzmann inversion approach. This CG force field is further used to characterize the dynamics of the protein via Brownian dynamics simulations. This combination of methods into a single computational tool flow enables the simulation of actin filaments with length up to 400 nm, extending the time and length scales compared to state-of-the-art approaches. Moreover, the proposed multiscale modeling approach allows to investigate the relationship between atomistic structure and changes on the overall dynamics and mechanics of the filament and can be easily (i) extended to the characterization of other subcellular structures and (ii) used to investigate the cellular effects of molecular alterations due to pathological conditions.     

Role of short-term cardiovascular regulation in heart period variability: a modeling study

A mathematical model of short-term cardiovascular regulation is used to investigate how heart period variability reflects the action of the autonomic regulatory mechanisms (vagal and sympathetic). The model includes the pulsating heart, the systemic (splanchnic and extrasplanchnic) and pulmonary circulation, the mechanical effect of respiration on venous return, two groups of receptors (arterial baroreceptors and lung stretch receptors), the sympathetic and vagal efferent branches, and a very low-frequency (LF) vasomotor noise. All model parameters were given on the basis of physiological data from the literature. We used data from humans whenever possible, whereas parameters for the regulation loops are derived from dog experiments. The model, with basal parameter values, produces a heart period power spectrum with two distinct peaks [a high frequency (HF) peak at the respiratory rate and a LF peak at approximately 0.1 Hz]. Sensitivity analysis on the mechanism gains suggests that the HF peak is mainly affected by the vagal mechanism, whereas the LF peak is increased by a high sympathetic gain and reduced by a high vagal gain. Moreover, the LF peak depends significantly on the reactivity of resistance vessels and is affected by noise, amplified by the sympathetic control loop at its resonance frequency. The model may represent a new tool to study alterations in the heart period spectrum on the basis of quantitative physiological hypotheses.     

Multiscale simulations of protein folding: application to formation of secondary structures

A multiscale simulation method of protein folding is proposed, using atomic representation of protein and solvent, combing genetic algorithms to determine the key protein structures from a global view, with molecular dynamic simulations to reveal the local folding pathways, thus providing an integrated landscape of protein folding. The method is found to be superior to previously investigated global search algorithms or dynamic simulations alone. For secondary structure formation of a selected peptide, RN24, the structures and dynamics produced by this method agree well with corresponding experimental results. Three most populated conformations are observed, including hairpin, β-sheet and α-helix. The energetic barriers separating these three structures are comparable to the kinetic energy of the atoms of the peptide, implying that the transition between these states can be easily triggered by kinetic perturbations, mainly through electrostatic interactions between charged atoms. Transitions between α-helix and β-sheet should jump over at least two energy barriers and may stay in the energetic trap of hairpin. It is proposed that the structure of proteins should be jointly governed by thermodynamic and dynamic factors; free energy is not the exclusive dominant for stability of proteins.     

Multiscale modeling of tumor growth and angiogenesis: Evaluation of tumor-targeted therapy

The dynamics of tumor growth and associated events cover multiple time and spatial scales, generally including extracellular, cellular and intracellular modifications. The main goal of this study is to model the biological and physical behavior of tumor evolution in presence of normal healthy tissue, considering a variety of events involved in the process. These include hyper and hypoactivation of signaling pathways during tumor growth, vessels’ growth, intratumoral vascularization and competition of cancer cells with healthy host tissue. The work addresses two distinctive phases in tumor development—the avascular and vascular phases—and in each stage two cases are considered—with and without normal healthy cells. The tumor growth rate increases considerably as closed vessel loops (anastomoses) form around the tumor cells resulting from tumor induced vascularization. When taking into account the host tissue around the tumor, the results show that competition between normal cells and cancer cells leads to the formation of a hypoxic tumor core within a relatively short period of time. Moreover, a dense intratumoral vascular network is formed throughout the entire lesion as a sign of a high malignancy grade, which is consistent with reported experimental data for several types of solid carcinomas. In comparison with other mathematical models of tumor development, in this work we introduce a multiscale simulation that models the cellular interactions and cell behavior as a consequence of the activation of oncogenes and deactivation of gene signaling pathways within each cell. Simulating a therapy that blocks relevant signaling pathways results in the prevention of further tumor growth and leads to an expressive decrease in its size (82% in the simulation).