435 research outputs found
On the Deformation of a Hyperelastic Tube Due to Steady Viscous Flow Within
In this chapter, we analyze the steady-state microscale fluid--structure
interaction (FSI) between a generalized Newtonian fluid and a hyperelastic
tube. Physiological flows, especially in hemodynamics, serve as primary
examples of such FSI phenomena. The small scale of the physical system renders
the flow field, under the power-law rheological model, amenable to a
closed-form solution using the lubrication approximation. On the other hand,
negligible shear stresses on the walls of a long vessel allow the structure to
be treated as a pressure vessel. The constitutive equation for the microtube is
prescribed via the strain energy functional for an incompressible, isotropic
Mooney--Rivlin material. We employ both the thin- and thick-walled formulations
of the pressure vessel theory, and derive the static relation between the
pressure load and the deformation of the structure. We harness the latter to
determine the flow rate--pressure drop relationship for non-Newtonian flow in
thin- and thick-walled soft hyperelastic microtubes. Through illustrative
examples, we discuss how a hyperelastic tube supports the same pressure load as
a linearly elastic tube with smaller deformation, thus requiring a higher
pressure drop across itself to maintain a fixed flow rate.Comment: 19 pages, 3 figures, Springer book class; v2: minor revisions, final
form of invited contribution to the Springer volume entitled "Dynamical
Processes in Generalized Continua and Structures" (in honour of Academician
D.I. Indeitsev), eds. H. Altenbach, A. Belyaev, V. A. Eremeyev, A. Krivtsov
and A. V. Porubo
Fluid-structure interaction in blood flow capturing non-zero longitudinal structure displacement
We present a new model and a novel loosely coupled partitioned numerical
scheme modeling fluid-structure interaction (FSI) in blood flow allowing
non-zero longitudinal displacement. Arterial walls are modeled by a {linearly
viscoelastic, cylindrical Koiter shell model capturing both radial and
longitudinal displacement}. Fluid flow is modeled by the Navier-Stokes
equations for an incompressible, viscous fluid. The two are fully coupled via
kinematic and dynamic coupling conditions. Our numerical scheme is based on a
new modified Lie operator splitting that decouples the fluid and structure
sub-problems in a way that leads to a loosely coupled scheme which is
{unconditionally} stable. This was achieved by a clever use of the kinematic
coupling condition at the fluid and structure sub-problems, leading to an
implicit coupling between the fluid and structure velocities. The proposed
scheme is a modification of the recently introduced "kinematically coupled
scheme" for which the newly proposed modified Lie splitting significantly
increases the accuracy. The performance and accuracy of the scheme were studied
on a couple of instructive examples including a comparison with a monolithic
scheme. It was shown that the accuracy of our scheme was comparable to that of
the monolithic scheme, while our scheme retains all the main advantages of
partitioned schemes, such as modularity, simple implementation, and low
computational costs
Arterial Pulse Waveform under the watch of Left Ventricular Ejection time: A physiological outlook
The behavior of arterial pulse waves was studied in connection with time interval at different phases of propagation. The essence of the study was to have a clue about the incidence of the time of pulse wave propagation on cardio-vascular parameters. Model analysis shows that arterial waveforms behave like solitons. It was seen, from the soliton solution of the arterial pulse waveform, that time interval between the phases of propagation, which corresponds with left ventricular ejection time (LVET), could supply some information about apparent pathogenesis. Keywords: pressure; waveform; soliton; incompressible; mathematical; physiology
Mathematical analysis of blood flow model through channels with flexible walls
A simplified mathematical model of blood flow through flexible arteries is developed and analyzed. The resulting system of non-linear, non-homogeneous PDE\u27s is analyzed numerically using the Richtmyer Lax-Wendroff method. Numerical and theoretical results show excellent agreement suggesting that in physiologically relevant situations shocks only develop outside the domain of interest. These results suggest that when the model assumptions are satisfied the model provides sufficient regularity to yield a physically reasonable representation of flow through a flexible artery. We conclude with a discussion of future directions for this model
Advancements in blood rheology and hemodynamics simulation with a brief history
Blood rheology is a complex field of study that investigates blood flow behavior, vital for understanding its role in physiological and pathological conditions. This article delves into various rheological models that describe blood behavior, ranging from Generalized Newtonian models to more sophisticated thixotropic and elastoviscoplastic models. One such model, the Horner-Armstrong-Wagner-Beris (HAWB) model, offers valuable insights into the dynamic interplay of reversible and irreversible phenomena in blood flow. Recent advancements, such as the mHAWB framework, provide enhanced accuracy and versatility in modeling blood rheology, holding great potential for diagnostic and therapeutic applications. Moreover, microscopic and mesoscopic simulations have paved the way for deeper insights into blood behavior, bridging the gap between theory and experiment. Multiscale models offer a promising approach to capturing the complexities of blood rheology at various length scales. Finally, we explore the clinical implications of blood rheology, including its significance in conditions like polycythemia, neonatal respiratory distress, and circulatory inadequacy. By understanding blood rheology comprehensively, we can advance our knowledge of complex blood flow dynamics and its potential applications in healthcare
The Underlying Physiology of Arterial Pulse Wave Morphology in Spatial Domain
Cardio-vascular events are among the worldās leading causes of morbidity and mortality. Most postulates suppose that culinary delights can be implicated in incidences of cardio-vascular diseases. This school of thought holds well in many respects. Much as the truistic value of the said school is acknowledged, we conceived of physiological disposition as an endogenous dominant factor in the events being considered, whereas culinary measures constitute an exogenous contributory factor. In this work we aimed at studying the effects of distance (stature) on pulse waveforms. Certain elements of our study showed that pulse wavelength was dominant in prescribing cardio-vascular physiology
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