A Thermodynamically Consistent, Microscopically-Based, Model of the Rheology of Aggregating Particles Suspensions.

In this work, we outline the development of a thermodynamically consistent microscopic model for a suspension of aggregating particles under arbitrary, inertia-less deformation. As a proof-of-concept, we show how the combination of a simplified population-balance-based description of the aggregating particle microstructure along with the use of the single-generator bracket description of nonequilibrium thermodynamics, which leads naturally to the formulation of the model equations. Notable elements of the model are a lognormal distribution for the aggregate size population, a population balance-based model of the aggregation and breakup processes and a conformation tensor-based viscoelastic description of the elastic network of the particle aggregates. The resulting example model is evaluated in steady and transient shear forces and elongational flows and shown to offer predictions that are consistent with observed rheological behavior of typical systems of aggregating particles. Additionally, an expression for the total entropy production is also provided that allows one to judge the thermodynamic consistency and to evaluate the importance of the various dissipative phenomena involved in given flow processes.

A comparative study of blood rheology across species.

Recent advances in hemorheology are extended to study blood rheology across species, which has important clinical implications particularly in intravenous drug scaleup as drugs undergoing clinical trials are first tested in animals. Some of the first hemorheological measurements from seven different species under both steady and transient shear conditions are presented and modeled using a rheological model developed and validated on human blood rheology fit to 20 different donors. Despite similar physiological properties across the blood samples from different species, significant differences are observed, particularly at low shear rates. Blood from species that form rouleaux exhibit a yield-like behavior and enhanced viscoelasticity at low shear rates, while blood from species without rouleaux exhibit nearly Newtonian behavior at similar shear rates. Viscoelasticity due to blood cell deformation is evident for all species at high shear rates. Novel, unidirectional large amplitude oscillatory shear measurements differentiate species. Using the newly acquired data in combination with previous literature data, a new allometric scaling relation is suggested for the low-shear blood viscosity for various mammalian evolutionary orders. Using an established model for arterial branching across species, it is conjectured that the observed hemorheological scaling across species is driven by maintaining a constant wall shear stress in arterial vessels.

Recent advances in blood rheology: a review.

Due to the potential impact on the diagnosis and treatment of various cardiovascular diseases, work on the rheology of blood has significantly expanded in the last decade, both experimentally and theoretically. Experimentally, blood has been confirmed to demonstrate a variety of non-Newtonian rheological characteristics, including pseudoplasticity, viscoelasticity, and thixotropy. New rheological experiments and the development of more controlled experimental protocols on more extensive, broadly physiologically characterized, human blood samples demonstrate the sensitivity of aspects of hemorheology to several physiological factors. For example, at high shear rates the red blood cells elastically deform, imparting viscoelasticity, while at low shear rates, they form "rouleaux" structures that impart additional, thixotropic behavior. In addition to the advances in experimental methods and validated data sets, significant advances have also been made in both microscopic simulations and macroscopic, continuum, modeling, as well as novel, multiscale approaches. We outline and evaluate the most promising of these recent developments. Although we primarily focus on human blood rheology, we also discuss recent observations on variations observed across some animal species that provide some indication on evolutionary effects.

Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease Part II: Extension for Variable Metabolic Rates.

Recently, we developed a systems engineering model of the human cardiorespiratory system [Kurian et al. ACS Omega2023, 8 (23), 20524-20535. DOI: 10.1021/acsomega.3c00854] based on existing models of physiological processes and adapted it for chronic obstructive pulmonary disease (COPD)-an inflammatory lung disease with multiple manifestations and one of the leading causes of death in the world. This control engineering-based model is extended here to allow for variable metabolic rates established at different levels of physical activity. This required several changes to the original model: the model of the controller was enhanced to include the feedforward loop that is responsible for cardiorespiratory control under varying metabolic rates (activity level, characterized as metabolic equivalent of the task-Rm-and normalized to one at rest). In addition, a few refinements were made to the cardiorespiratory mechanics, primarily to introduce physiological processes that were not modeled earlier but became important at high metabolic rates. The extended model is verified by analyzing the impact of exercise (Rm > 1) on the cardiorespiratory system of healthy individuals. We further formally justify our previously proposed adaptation of the model for COPD patients through sensitivity analysis and refine the parameter tuning through the use of a parallel tempering stochastic global optimization method. The extended model successfully replicates experimentally observed abnormalities in COPD-the drop in arterial oxygen tension and dynamic hyperinflation under high metabolic rates-without being explicitly trained on any related data. It also supports the prospects of remote patient monitoring in COPD.

Systems Engineering Approach to Modeling and Analysis of Chronic Obstructive Pulmonary Disease.

Chronic obstructive pulmonary disease (COPD) is a progressive lung disease characterized by airflow limitation. This study develops a systems engineering framework for representing important mechanistic details of COPD in a model of the cardiorespiratory system. In this model, we present the cardiorespiratory system as an integrated biological control system responsible for regulating breathing. Four engineering control system components are considered: sensor, controller, actuator, and the process itself. Knowledge of human anatomy and physiology is used to develop appropriate mechanistic mathematical models for each component. Following a systematic analysis of the computational model, we identify three physiological parameters associated with reproducing clinical manifestations of COPD: changes in the forced expiratory volume, lung volumes, and pulmonary hypertension. We quantify the changes in these parameters (airway resistance, lung elastance, and pulmonary resistance) as the ones that result in a systemic response that is diagnostic of COPD. A multivariate analysis of the simulation results reveals that the changes in airway resistance have a broad impact on the human cardiorespiratory system and that the pulmonary circuit is stressed beyond normal under hypoxic environments in most COPD patients.

Effects of ex vivo aging and storage temperature on blood viscosity.

BACKGROUND: Research on hemorheology is driven in part by its significance in blood diseases and the possible use of hemorheology as a diagnostic tool. However, existing data on blood rheology are limited largely to measurements of steady shear behavior often with varying measurement protocols and insufficient characterization of the physiology. OBJECTIVE: The effects of ex vivo aging and environmental conditions on blood viscosity are investigated to improve standards for hemorheology measurements. METHODS: Measurements on the viscosity of blood from nine healthy donors are obtained and the physiological state of the blood determined. Steady and transient shear measurements are reported as a function of time from withdrawal. The effect of transportation temperature is also assessed. RESULTS: Blood transported at 4 °C may exhibit anomalous viscosity variations for short to intermediate times, as opposed to blood transported at room temperature. A time of approximately 3.0 hours was identified as the maximum time after the initial test that accurate rheological tests can be conducted on blood samples. CONCLUSIONS: Measurement protocol and time limit guidelines are established for conducting accurate rheological measurements on blood.

Application of 1D blood flow models of the human arterial network to differential pressure predictions.

A new application of 1D models of the human arterial network is proposed. We take advantage of the sensitivity of the models predictions for the pressure profiles within the main aorta to key model parameter values. We propose to use the patterns in the predicted differences from a base case as a way to infer to the most probable changes in the parameter values. We demonstrate this application using an impedance model that we have recently developed (Johnson, 2010). The input model parameters are all physiologically related, such as the geometric dimensions of large arteries, various blood properties, vessel elasticity, etc. and can therefore be patient specific. As a base case, nominal values from the literature are used. The necessary information to characterize the smaller arteries, arterioles, and capillaries is taken from a physical scaling model (West, 1999). Model predictions for the effective impedance of the human arterial system closely agree with experimental data available in the literature. The predictions for the pressure wave development along the main arteries are also found in qualitative agreement with previous published results. The model has been further validated against our own measured pressure data in the carotid and radial arteries, obtained from healthy individuals. Upon changes in the value of key model parameters, we show that the differences seen in the pressure profiles correspond to qualitatively different patterns for different parameters. This suggests the possibility of using the model in interpreting multiple pressure data of healthy/diseased individuals.

Continuum formulation of the Scheutjens-Fleer lattice statistical theory for homopolymer adsorption from solution.

Homopolymer adsorption from a dilute solution on an interacting (attractive) surface under static equilibrium conditions is studied in the framework of a Hamiltonian model. The model makes use of the density of chain ends n(1,e) and utilizes the concept of the propagator G describing conformational probabilities to locally define the polymer segment density or volume fraction phi; both n(1,e) and phi enter into the expression for the system free energy. The propagator G obeys the Edwards diffusion equation for walks in a self-consistent potential field. The equilibrium distribution of chain ends and, consequently, of chain conformational probabilities is found by minimizing the system free energy. This results in a set of model equations that constitute the exact continuum-space analog of the Scheutjens-Fleer (SF) lattice statistical theory for the adsorption of interacting chains. Since for distances too close to the surface the continuum formulation breaks down, the continuum model is here employed to describe the probability of chain configurations only for distances z greater than 2l, where l denotes the segment length, from the surface; instead, for distances z < or = 2l, the SF lattice model is utilized. Through this novel formulation, the lattice solution at z = 2l provides the boundary condition for the continuum model. The resulting hybrid (lattice for distances z < or = 2l, continuum for distances z > 2l) model is solved numerically through an efficient implementation of the pseudospectral collocation method. Representative results obtained with the new model and a direct application of the SF lattice model are extensively compared with each other and, in all cases studied, are found to be practically identical.