Patients with sickle cell anemia (SCD) and pulmonary hypertension (PH) have a significantly increased risk of sudden death compared to patients with SCD alone. Sickled red blood cells (RBCs) are stiffer, more dense, more frequently undergo hemolysis, and have a sixfold shorter lifespan compared to normal RBCs. Here, we sought to investigate the impact of increased RBC stiffness, independent of other SCD-related biological and mechanical RBC abnormalities, on the hemodynamic changes that ultimately cause PH and increase mortality in SCD. To do so, pulmonary vascular impedance (PVZ) measures were recorded in control C57BL6 mice before and after ∼50 μ l of blood (Hct = 45%) was extracted and replaced with an equal volume of blood containing either untreated RBCs or RBCs chemically stiffened with glutaraldehyde (Hct = 45%). Chemically stiffened RBCs increased mean pulmonary artery pressure (mPAP) (13.5 ± 0.6 mmHg at baseline to 23.2 ± 0.7 mmHg after the third injection), pulmonary vascular resistance (PVR) (1.23 ± 0.11 mmHg*min/ml at baseline to 2.24 ± 0.14 mmHg*min/ml after the third injection), and wave reflections (0.31 ± 0.02 at baseline to 0.43 ± 0.03 after the third injection). Chemically stiffened RBCs also decreased cardiac output, but did not change hematocrit, blood viscosity, pulmonary arterial compliance, or heart rate. The main finding of this study is that increased RBC stiffness alone affects pulmonary pulsatile hemodynamics, which suggests that RBC stiffness plays an important role in the development of PH in patients with SCD.

The present study, through finite element simulations, shows the geometric effects of a bioinspired solid on pressure and impulse mitigation for an elastic, plastic, and viscoelastic material. Because of the bioinspired geometries, stress wave mitigation became apparent in a nonintuitive manner such that potential real-world applications in human protective gear designs are realizable. In nature, there are several toroidal designs that are employed for mitigating stress waves; examples include the hyoid bone on the back of a woodpecker's jaw that extends around the skull to its nose and a ram's horn. This study evaluates four different geometries with the same length and same initial cross-sectional diameter at the impact location in three-dimensional finite element analyses. The geometries in increasing complexity were the following: (1) a round cylinder, (2) a round cylinder that was tapered to a point, (3) a round cylinder that was spiraled in a two dimensional plane, and (4) a round cylinder that was tapered and spiraled in a two-dimensional plane. The results show that the tapered spiral geometry mitigated the greatest amount of pressure and impulse (approximately 98% mitigation) when compared to the cylinder regardless of material type (elastic, plastic, and viscoelastic) and regardless of input pressure signature. The specimen taper effectively mitigated the stress wave as a result of uniaxial deformational processes and an induced shear that arose from its geometry. Due to the decreasing cross-sectional area arising from the taper, the local uniaxial and shear stresses increased along the specimen length. The spiral induced even greater shear stresses that help mitigate the stress wave and also induced transverse displacements at the tip such that minimal wave reflections occurred. This phenomenon arose although only longitudinal waves were introduced as the initial boundary condition (BC). In nature, when shearing occurs within or between materials (friction), dissipation usually results helping the mitigation of the stress wave and is illustrated in this study with the taper and spiral geometries. The combined taper and spiral optimized stress wave mitigation in terms of the pressure and impulse; thus providing insight into the ram's horn design and woodpecker hyoid designs found in nature.

Computational hemodynamic models of the cardiovascular system are often limited to finite segments of the system and therefore need well-controlled inlet and outlet boundary conditions. Classical boundary conditions are measured total pressure or flow rate imposed at the inlet and impedances of RLR, RLC, or LR filters at the outlet. We present a new approach based on an unidirectional propagative approach (UPA) to model the inlet/outlet boundary conditions on the axisymmetric Navier–Stokes equations. This condition is equivalent to a nonreflecting boundary condition in a fluid–structure interaction model of an axisymmetric artery. First we compare the UPA to the best impedance filter (RLC). Second, we apply this approach to a physiological situation, i.e., the presence of a stented segment into a coronary artery. In that case a reflection index is defined which quantifies the amount of pressure waves reflected upon the singularity.

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.

A two-dimensional axi-symmetric numerical model is constructed of the spinal cord, consisting of elastic cord tissue surrounded by aqueous cerebrospinal fluid, in turn surrounded by elastic dura. The geometric and elastic parameters are simplified but of realistic order, compared with existing measurements. A distal reflecting site models scar tissue formed by earlier trauma to the cord, which is commonly associated with syrinx formation. Transients equivalent to both arterial pulsation and percussive coughing are used to excite wave propagation. Propagation is investigated in this model and one with a central canal down the middle of the cord tissue, and in further idealized versions of it, including a model with no cord, one with a rigid cord, one with a rigid dura, and a double-length untapered variant of the rigid-dura model. Analytical predictions for axial and radial wave-speeds in these different situations are compared with, and used to explain, the numerical outcomes. We find that the anatomic circumstances of the spinal cerebrospinal fluid cavity probably do not allow for significant wave steepening phenomena. The results indicate that wave propagation in the real cord is set by the elastic properties of both the cord tissue and the confining dura mater, fat, and bone. The central canal does not influence the wave propagation significantly.

The importance and priority of specific micro-structural and mechanical design parameters must be established to effectively engineer scaffolds (biomaterials) that mimic the extracellular matrix (ECM) environment of cells and have clinical applications as tissue substitutes. In this study, three-dimensional (3-D) matrices were prepared from type I collagen, the predominant compositional and structural component of connective tissue ECMs, and structural-mechanical relationships were studied. Polymerization conditions, including collagen concentration (0.3–3 mg/mL) and pH (6–9), were varied to obtain matrices of collagen fibrils with different microstructures. Confocal reflection microscopy was used to assess specific micro-structural features (e.g., diameter and length) and organization of component fibrils in 3-D. Microstructural analyses revealed that changes in collagen concentration affected fibril density while maintaining a relatively constant fibril diameter. On the other hand, both fibril length and diameter were affected by the pH of the polymerization reaction. Mechanically, all matrices exhibited a similar stress-strain curve with identifiable “toe,” “linear,” and “failure” regions. However, the linear modulus and failure stress increased with collagen concentration and were correlated with an increase in fibril density. Additionally, both the linear modulus and failure stress showed an increase with pH, which was related to an increased fibril length and a decreased fibril diameter. The tensile mechanical properties of the collagen matrices also showed strain rate dependence. Such fundamental information regarding the 3-D microstructural-mechanical properties of the ECM and its component molecules are important to our overall understanding of cell-ECM interactions (e.g., mechanotransduction) and the development of novel strategies for tissue repair and replacement.

A corrected derivation is provided for the relationship between the impulse response of a wave tube termination and pressure signals measured at two different locations within the tube. This derivation yields exactly the same final result as was reported previously by Louis et al. (1993), despite the omission of the active source term in that earlier derivation. This technique has become the basis of an important medical diagnostic technology. This report revises and corrects the earlier theory upon which that technology rests.

Oscillatory flow of a Newtonian fluid in an elastic tube, which is a model of blood flow in arteries, is analyzed in this paper. For a rigid tube, the steady flow field can be described by Poiseuille’s law and the unsteady flow field by Womersley’s solution. These are the linearized solutions for flow in elastic tubes. To evaluate the importance of nonlinear effects, a perturbation solution is developed realizing that the amplitude of arterial wall movement is small (typically 5–10 percent of the diameter). The nonlinear effects on the amplitude of the wall shear rate, on the amplitude of the pressure gradient, and on the mean velocity profile have been considered. Nonlinear effects on the oscillatory components depend on Womersley’s unsteadiness parameter (α), the ratio between the mean and amplitude of the flow rate, the diameter variation, and the phase difference between the diameter variation and the flow rate (φ) which is indicative of the degree of wave reflection. On the other hand, the mean velocity profile is found to be dependent on the steady-streaming Reynolds number, R s . When R s is small, the mean velocity profile is parabolic (1 − ξ 2 ); however, when R s is large, the velocity profile is distorted by the nonlinear effect and can be described by sin(πξ 2 ). The increase of the amplitude and reduction of the mean of wall shear rate as π changes from 0 to −90 deg suggests an indirect mechanism for the role of hypertension in arterial disease: hypertension → increased wave reflection → wall shear stress is reduced and more oscillatory.

This report deals with noninvasive imaging of airway geometry based upon information contained in acoustic reflections measured at the mouth. Here we describe a new theoretical approach that enables development of a new miniaturized apparatus. Unlike the single-transducer systems used currently, this new strategy is based upon a two-transducer system that is a variant of that suggested originally by Shroeder (1967). We have developed, implemented, and tested computational algorithms necessary to reconstruct airway dimensions from acoustic reflection data using this two-transducer strategy.

Oscillatory and pulsatile flows of Newtonian fluids in straight elastic tubes are simulated numerically with the aid of Ling and Atabek’s “local flow” assumption for the nonlinear convective acceleration terms. For the first time, a theoretical assessment of the local flow assumption is presented, and the range of validity of the assumption is estimated by comparison with perturbation solutions of the complete flow problem. Subsequent simulations with the local flow model indicate that the flow field and associated wall shear stress are extremely sensitive to the phase angle between oscillatory pressure and flow waves (impedance phase angle). This phase angle, which is a measure of the wave reflection present in the system, is known to be altered by arterial disease (e.g., hypertension) and vasoactive drugs. Thus, the paper elucidates a mechanism by which subtle changes in systemic hemodynamics (i.e., phase angles) can markedly influence local wall shear stress values.

An iterative method of calculating propagation parameters at harmonics of heart rate for a uniform vascular segment from a combination of four arterial waveform measurements is presented. Measurements of blood pressure, vascular diameter, and blood flow-rate may be combined arbitrarily provided only that at least one measurement of pressure and one of flow-rate be included; the requirement of four measurements implies at least two measurement sites along the vessel. The analysis is thus a generalization of those associated with previous methods of determining propagation parameters, allowing for instance relaxation of the requirement of equal spacing in the three-point method. Results are presented for the propagation of an impulse along a rubber tube when the measurements are pressure at two sites, flowrate and diameter.

Blood flow in human brachial arteries, compressed by a pneumatic cuff for blood pressure measurement, is examined using several different noninvasive techniques. From the experimental results it is shown that, when arterial pressure distal to the cuff is always lower than cuff pressure, flow in the artery under the cuff becomes supercritical near the cuff downstream margin and no reflection occurs there and the reflected wave from the peripheral vascular system of the arm does not propagate beyond the cuff downstream margin. Therefore an unsteady transition from supercritical to subcritical flow occurs near the cuff downstream margin. When the peak value of distal arterial pressure exceeds cuff pressure, a reflection occurs near the cuff downstream margin. The reflection becomes stronger corresponding to decrement of the cuff pressure and the whole artery segment under the cuff inflates fully at systole. At diastole, however, the artery segment under the cuff does not collapse completely and, hence, the phenomenon becomes that of pressure wave propagation in a partially collapsed artery segment.

The development of a one-dimensional numerical (finite-difference) model of the arterial network surrounding the circle of Willis is described based on the full Navier-Stokes and conservation of mass equations generalized for distensible vessels. The present model assumes an elastic wall defined by a logarithmic pressure-area relation obtained from the literature. The viscous term in the momentum equation is evaluated using the slope of a Karman-Pohlhausen velocity profile at the vessel boundary. The afferent vessels (two carotids and two vertebrals) are forced with a canine physiologic pressure signature corresponding to an aortic site. The network associated with each main efferent artery of the circle is represented by a single vessel containing an appropriate amount of resistance so that the mean flow through the system is distributed in accordance with the weight of brain irrigated by each vessel as determined from a steady flow model of the same network. This resistance is placed a quarter wave-length downstream from the heart to insure proper reflection from the terminations, where the quarter wavelength is determined using the frequency corresponding to the first minimum on an input impedance-frequency diagram obtained at the heart. Computer results are given as time histories of pressure and flow at any model nodal point starting from initial conditions of null flow and constant pressure throughout the model. Variations in these pressure and flow distributions caused by the introduction of pathologic situations into the model illustrate the efficacy of the simulation and of the circle in equalizing and redistributing flows in abnormal situations.

A simple model is presented to analyze the effect of stenoses of different severities in a long elastic tube or artery on the pressure and flow-rate wave forms incident upon them. Wave propagation in the undisturbed tube is taken to be linear; nonlinearity arises from the quadratic dependence of stenosis pressure drop on flow rate. Before the model can be applied in practice, important physiological questions must be answered; e.g.: (a) Can the incident wave form and mean proximal pressure be regarded as given input? (b) Is the mean flow rate given, or does the peripheral resistance remain constant? Results are given on the assumption that the answer to (a) is yes. The principal conclusion is that the input impedance spectrum of a stenosed artery depends strongly on the incident waveform, as well as on the severity of the stenosis and on the distance from it at which measurements are made. There is good qualitative agreement with the results of experiments and of other models.

Filling of a thin-walled, highly compliant tube in a partially collapsed condition is studied. The theory, based on one-dimensional flow, takes account of friction, longitudinal tension, and the highly nonlinear pressure-area law for the tube. Various aspects of filling behavior are revealed by alternative calculations using: (i) the method of characteristics; (ii) numerical integration of the continuity, momentum, and tube-law equations; and (iii) a crude but simple lumped-element capacitance-inertance-resistance model. Varied phenomena appear. At high Reynolds number, these include dispersive wave trains associated with circumferential bending stiffness and longitudinal tension, nonlinear changes of wave form, development of highly asymmetrical wave reflections, and sloshing. At low Reynolds number, the area changes with time in a diffusivelike manner. The experiments exhibited the dispersive phenomena predicted by the theory.

An inference of the summed cross-sectional area of the airway network of the lung as a function of distance from the airway opening can be obtained noninvasively by inversion of high-frequency reflection response data with the Ware-Aki algorithm. This method is critically evaluated. The response of branching models of the complete tracheo-bronchial tree are simulated and inverted to produce an area versus distance inference. The models incorporate branching asymmetry, nonrigid walls, and a viscous gas. Direct comparison of the area inference with the anatomic area of the model indicates that the inference is markedly influenced by nonrigidity of the airway walls and branching asymmetry, and that the inference does not possess a simple anatomic correlate. Empirical uses of the inference method are not precluded.