Mesoscale simulation of blood flow in small vessels

Computational modeling of blood flow in microvessels with internal diameter 20-500 microm is a major challenge. It is because blood in such vessels behaves as a multiphase suspension of deformable particles. A continuum model of blood is not adequate if the motion of individual red blood cells in the suspension is of interest. At the same time, multiple cells, often a few thousands in number, must also be considered to account for cell-cell hydrodynamic interaction. Moreover, the red blood cells (RBCs) are highly deformable. Deformation of the cells must also be considered in the model, as it is a major determinant of many physiologically significant phenomena, such as formation of a cell-free layer, and the Fahraeus-Lindqvist effect. In this article, we present two-dimensional computational simulation of blood flow in vessels of size 20-300 microm at discharge hematocrit of 10-60%, taking into consideration the particulate nature of blood and cell deformation. The numerical model is based on the immersed boundary method, and the red blood cells are modeled as liquid capsules. A large RBC population comprising of as many as 2500 cells are simulated. Migration of the cells normal to the wall of the vessel and the formation of the cell-free layer are studied. Results on the trajectory and velocity traces of the RBCs, and their fluctuations are presented. Also presented are the results on the plug-flow velocity profile of blood, the apparent viscosity, and the Fahraeus-Lindqvist effect. The numerical results also allow us to investigate the variation of apparent blood viscosity along the cross-section of a vessel. The computational results are compared with the experimental results. To the best of our knowledge, this article presents the first simulation to simultaneously consider a large ensemble of red blood cells and the cell deformation.     

Predicting drug pharmacokinetics and effect in vascularized tumors using computer simulation

In this paper, we investigate the pharmacokinetics and effect of doxorubicin and cisplatin in vascularized tumors through two-dimensional simulations. We take into account especially vascular and morphological heterogeneity as well as cellular and lesion-level pharmacokinetic determinants like P-glycoprotein (Pgp) efflux and cell density. To do this we construct a multi-compartment PKPD model calibrated from published experimental data and simulate 2-h bolus administrations followed by 18-h drug washout. Our results show that lesion-scale drug and nutrient distribution may significantly impact therapeutic efficacy and should be considered as carefully as genetic determinants modulating, for example, the production of multidrug-resistance protein or topoisomerase II. We visualize and rigorously quantify distributions of nutrient, drug, and resulting cell inhibition. A main result is the existence of significant heterogeneity in all three, yielding poor inhibition in a large fraction of the lesion, and commensurately increased serum drug concentration necessary for an average 50% inhibition throughout the lesion (the IC(50) concentration). For doxorubicin the effect of hypoxia and hypoglycemia ("nutrient effect") is isolated and shown to further increase cell inhibition heterogeneity and double the IC(50), both undesirable. We also show how the therapeutic effectiveness of doxorubicin penetration therapy depends upon other determinants affecting drug distribution, such as cellular efflux and density, offering some insight into the conditions under which otherwise promising therapies may fail and, more importantly, when they will succeed. Cisplatin is used as a contrast to doxorubicin since both published experimental data and our simulations indicate its lesion distribution is more uniform than that of doxorubicin. Because of this some of the complexity in predicting its therapeutic efficacy is mitigated. Using this advantage, we show results suggesting that in vitro monolayer assays using this drug may more accurately predict in vivo performance than for drugs like doxorubicin. The nonlinear interaction among various determinants representing cell and lesion phenotype as well as therapeutic strategies is a unifying theme of our results. Throughout it can be appreciated that macroscopic environmental conditions, notably drug and nutrient distributions, give rise to considerable variation in lesion response, hence clinical resistance. Moreover, the synergy or antagonism of combined therapeutic strategies depends heavily upon this environment.     

Gastric flow and mixing studied using computer simulation

The fed human stomach displays regular peristaltic contraction waves that originate in the proximal antrum and propagate to the pylorus. High-resolution concurrent manometry and magnetic resonance imaging (MRI) studies of the stomach suggest a primary function of antral contraction wave (ACW) activity unrelated to gastric emptying. Detailed evaluation is difficult, however, in vivo. Here we analyse the role of ACW activity on intragastric fluid motions, pressure, and mixing with computer simulation. A two-dimensional computer model of the stomach was developed with the 'lattice-Boltzmann' numerical method from the laws of physics, and stomach geometry modelled from MRI. Time changes in gastric volume were specified to match global physiological rates of nutrient liquid emptying. The simulations predicted two basic fluid motions: retrograde 'jets' through ACWs, and circulatory flow between ACWs, both of which contribute to mixing. A well-defined 'zone of mixing', confined to the antrum, was created by the ACWs, with mixing motions enhanced by multiple and narrower ACWs. The simulations also predicted contraction-induced peristaltic pressure waves in the distal antrum consistent with manometric measurements, but with a much lower pressure amplitude than manometric data, indicating that manometric pressure amplitudes reflect direct contact of the catheter with the gastric wall. We conclude that the ACWs are central to gastric mixing, and may also play an indirect role in gastric emptying through local alterations in common cavity pressure.     

The effects of large blood vessels on temperature distributions during simulated hyperthermia.

Several three-dimensional vascular models have been developed to study the effects of adding equations for large blood vessels to the traditional bioheat transfer equation of Pennes when simulating tissue temperature distributions. These vascular models include "transiting" vessels, "supplying" arteries, and "draining" veins, for all of which the mean temperature of the blood in the vessels is calculated along their lengths. For the supplying arteries this spatially variable temperature is then used as the arterial temperature in the bioheat transfer equation. The different vascular models produce significantly different locations for both the maximum tumor and the maximum normal tissue temperatures for a given power deposition pattern. However, all of the vascular models predict essentially the same cold regions in the same locations in tumors: one set at the tumors' corners and another around the inlets of the large blood vessels to the tumor. Several different power deposition patterns have been simulated in an attempt to eliminate these cold regions; uniform power in the tumor, annular power in the tumor, preheating of the blood in the vessels while they are traversing the normal tissue, and an "optimal" power pattern which combines the best features of the above approaches. Although the calculations indicate that optimal power deposition patterns (which improve the temperature distributions) exist for all of the vascular models, none of the heating patterns studied eliminated all of the cold regions. Vasodilation in the normal tissue is also simulated to see its effects on the temperature fields.(ABSTRACT TRUNCATED AT 250 WORDS)     

Pulsatile blood flow effects on temperature distribution and heat transfer in rigid vessels

The effect of blood velocity pulsations on bioheat transfer is studied. A simple model of a straight rigid blood vessel with unsteady periodic flow is considered. A numerical solution that considers the fully coupled Navier-Stokes and energy equations is used for the simulations. The influence of the pulsation rate on the temperature distribution and energy transport is studied for four typical vessel sizes: aorta, large arteries, terminal arterial branches, and arterioles. The results show that: the pulsating axial velocity produces a pulsating temperature distribution; reversal of flow occurs in the aorta and in large vessels, which produces significant time variation in the temperature profile. Change of the pulsation rate yields a change of the energy transport between the vessel wall and fluid for the large vessels. For the thermally important terminal arteries (0.04-1 mm), velocity pulsations have a small influence on temperature distribution and on the energy transport out of the vessels (8 percent for the Womersley number corresponding to a normal heart rate). Given that there is a small difference between the time-averaged unsteady heat flux due to a pulsating blood velocity and an assumed nonpulsating blood velocity, it is reasonable to assume a nonpulsating blood velocity for the purposes of estimating bioheat transfer.     

A circle of Willis simulation using distensible vessels and pulsatile flow

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.     

Effect of hyperthermia on tumor blood flow

Differences in blood perfusion rates between tumors and normal tissue can be utilized to selectively heat many solid tumors. Blood flow in normal tissues is considerably increased at temperatures commonly applied during localized hyperthermia. In contrast, tumor blood flow may respond to localized heat typically in two different blood flow patterns: Flow may either decrease continuously with increasing exposure time and/or temperature or flow may exhibit a transient increase followed by a decline. A decrease in blood flow at high thermal doses can be observed in most of the tumors, whereas an increase in flow at low thermal doses seems to occur less frequently. The inhibition of blood flow at high thermal doses may lead to physiological changes in the microenvironment of the cancer cells that increase the cell killing effect of hyperthermia. Flow increases at low thermal doses can enhance the efficiency of other treatment modalities, such as irradiation or the administration of antiproliferate drugs.     

The effects of changing bone and muscle size on limb inertial properties and limb dynamics: a computer simulation

The magnitude and distribution of bone and muscle mass within limbs affect limb inertial properties, maximum movement speed and the energy required to maintain submaximal movements. Musculoskeletal modeling and movement simulations were used to determine how changes in bone and muscle cross-sectional area (and thus mass) affect human thigh and shank inertial properties, the maximum speed of unloaded single-leg cycling and the energy required to sustain submaximal single-leg cycling. Depending on initial conditions, shank moments of inertia increased 61-72 kg cm2 per kg added bone and 72-100 kg cm2 per kg added muscle. Thigh moments of inertia increased 46-63 kg cm2 per kg bone and 180-225 kg cm2 per kg muscle. Maximum unloaded cycling velocity increased with increased muscle mass (approximately 2.2-2.9 rpm/kg muscle), but decreased with increased cortical bone mass (approximately 2.0-2.8 rpm/kg bone). The internal work associated with unloaded submaximal cycling increased with increased muscle mass (approximately 0.42-0.48 J/kg muscle) and bone mass (approximately 0.18-0.22 J/kg bone).     

A literature review: the effects of magnetic field exposure on blood flow and blood vessels in the microvasculature

The effect of magnetic field (MF) exposure on microcirculation and microvasculature is not clear or widely explored. In the limited body of data that exists, there are contradictions as to the effects of MFs on blood perfusion and pressure. Approximately half of the cited studies indicate a vasodilatory effect of MFs; the remaining half indicate that MFs could trigger either vasodilation or vasoconstriction depending on initial vessel tone. Few studies indicate that MFs cause a decrease in perfusion or no effect. There is a further lack of investigation into the cellular effects of MFs on microcirculation and microvasculature. The role of nitric oxide (NO) in mediating microcirculatory MF effects has been minimally explored and results are mixed, with four studies supporting an increase in NO activity, one supporting a biphasic effect, and five indicating no effect. MF effects on angiogenesis are also reported: seven studies supporting an increase and two a decrease. Possible reasons for these contradictions are explored. This review also considers the effects of magnetic resonance imaging (MRI) and anesthetics on microcirculation. Recommendations for future work include studies aimed at the cellular/mechanistic level, studies involving perfusion measurements both during and post-exposure, studies testing the effect of MFs on anesthetics, and investigation into the microcirculatory effects of MRI.     

Formation of the branching pattern of blood vessels in the wall of the avian yolk sac studied by a computer simulation

The present study was performed to provide data to support the notion previously believed but not proved experimentally or theoretically, that blood vessels are formed by the selection of capillaries in the network. In an attempt to understand the mechanism of formation of blood vessel branching structures, the transformation of a capillary network to a branching system in the wall of quail yolk sac was successively recorded by a series of photographs, and a computer simulation was carried out for the process of in vivo vascularization based on the photographs. The simulation demonstrated that a positive feedback system participated in the formation of a branching structure. That is, vessels which had been much used were enlarged, whereas less used vessels were reduced in their size and finally extinguished. The enlarged vessels became major components of the branching system. As the body of an embryo grew, it was observed that polygonal capillary networks enlarged, which led each polygon of the network to divide into a few finer polygons. Then, some of the capillary vessels were again selected and formed a branching system. This process repeated during the body growth, indicating that the vascular system developed adaptively to the body growth. A region where the growth was fast, received much blood flow and produced finer networks of capillaries. Thus, it was experimentally demonstrated for the first time that capillaries in the network are successively selected by a positive feedback mechanism and form blood vessels.     

Uterine blood flow in sows: effects of pregnancy stage and litter size

Female pigs were assigned to three groups at 94 days of age: a control group (CTR), a group undergoing the ligation and severing of the left oviduct (LIG), and a group undergoing right hysteroovariectomy (HHO). They were inseminated at 307 days of age. At 35 days of pregnancy, an ultrasonic transit time flow probe was implanted around the middle artery of one uterine horn in 33 sows and uterine blood flow was measured during thirteen 24-h periods between 44 and 111 days. Despite large differences in ovulation rate per uterine horn (4.8, 8.3 and 16.9 in the LIG, CTR and HHO groups, respectively), variation of litter size was considerably reduced with advancement of pregnancy (3.0, 6.6 and 10.8 foetuses per uterine horn at 35 days, and 3.0, 5.8 and 4.9 at 112 days (slaughter), respectively). Uterine blood flow increased linearly during pregnancy. It was lower in the LIG sows (0.82 to 1.74 L x min(-1) x horn(-1) from 44 to 111 days) than in the CTR and HHO sows (1.22 to 2.84 and 1.09 to 2.63 L x min(-1) x horn(1), respectively). It was more closely related to litter weight than to litter size and amounted to 0.42 L x min(-1) x kg foetus(-1) at 111 days. Uterine blood flow per foetus decreased when litter size increased. It increased from 0.31 to 0.72, 0.26 to 0.60 and 0.20 to 0.43 L x min(-1) x foetus(-1) from 44 to 111 days when there were 2 to 3, 4 to 5, and 6 to 8 foetuses in the uterine horn, respectively. This explains why piglets from large litters are lighter at birth.     

3D models of blood flow in the cerebral vasculature

The circle of Willis (CoW) is a ring-like arterial structure located in the base of the brain and is responsible for the distribution of oxygenated blood throughout the cerebral mass. To investigate the effects of the complex 3D geometry and anatomical variability of the CoW on the cerebral hemodynamics, a technique for generating physiologically accurate models of the CoW has been created using a combination of magnetic resonance data and computer-aided design software. A mathematical model of the body's cerebral autoregulation mechanism has been developed and numerous computational fluid dynamics simulations performed to model the hemodynamics in response to changes in afferent blood pressure. Three pathological conditions were explored, namely a complete CoW, a fetal P1 and a missing A1. The methodology of the cerebral hemodynamic modelling is proposed with the potential for future clinical application in mind, as a diagnostic tool.     

Evaluation of the mass transfer rate using computer simulation in a three-dimensional interwoven hollow fiber-type bioartificial liver

Objectives

To determine the most efficient design of a hollow fiber-based bioreactor device for a bioartificial liver support system through comparative bioengineering evaluations.

Results

We compared two types of hollow fiber-based bioreactors, the interwoven-type bioreactor (IWBAL) and the dialyzer-type bioreactor (DBAL), by evaluating the overall mass transfer coefficient (K) and the convective coefficient (X). The creatinine and albumin mass transfer coefficients and convective coefficients were calculated using our mathematical model based on the homoporous theory and the modified Powell method. Additionally, using our model, we simulated the mass transport efficiency in clinical-scale BALs. The results of this experiment demonstrate that the mass transfer coefficients for creatinine and albumin increased proportionally with velocity with the IWBAL, and were consistently greater than that found with the DBAL. These differences were further enhanced in the simulation of the large-scale model.

Conclusions

Our findings indicate that the IWBAL with its unique 30° cross hollow fiber design can provide greater solute removal and more efficient metabolism when compared to the conventional DBAL design.

     

Distribution of blood flow and neutrophil kinetics in bronchial vasculature of sheep

Baile, Elisabeth M., Peter D. Paré, David Ernest, andPeter M. Dodek. Distribution of blood flow and neutrophil kinetics in bronchial vasculature of sheep. J. Appl.Physiol. 82(5): 1466-1471, 1997.The bronchialcirculation, as opposed to the pulmonary circulation, is the likelysource of the edema and inflammatory cells that contribute to airflowobstruction and airway narrowing associated with asthma and pulmonaryedema. The purpose of this study was to understand the mechanism ofedema formation and inflammation in airway walls. Therefore, we soughtfirst to determine the normal bronchial venous drainage pathways. Inanesthetized, ventilated, open-chest sheep we measured the relativedistribution of ⁵¹Cr-labeled redblood cells to the right and left ventricles after injection into thebronchial artery (n = 7).Using this information, we then studied the kinetics of leukocytes inthe bronchial vascular bed. We measured the extraction of¹¹¹In-labeled neutrophils duringtheir first pass through the microvasculature after injection into thebronchial artery or right ventricle (n = 6). In the first set of experiments, we found >85% of the systemic blood flow to the lung returns to the left ventricle. In the second setof experiments, we found that extraction of neutrophils in thebronchial vasculature (50-60%) was less(P < 0.05) than that in thepulmonary vasculature (80%). This finding may be explained bydifferences in the anatomy and/or hydrodynamic dispersal forces between the pulmonary and bronchial vascular beds or may reflect sequestration of neutrophils within the pulmonary microvasculature while traversing bronchial-to-pulmonary anastomotic pathways.

     

Hydromechanic effects of rotations on human blood vessels on a short-radius centrifuge

An "imitation" task of evaluating the adequacy of model gravitation (SRC) and natural one with consideration of the distribution of liquid environment in human lower extremities (interval evaluation) has been formulated and solved. A reversed "imitation" task of calculating the SRC rotation frequency with consideration of a patient's individual height on the basis of zero difference on the criterion suggested. The methods developed were realized in a doctor's interface that provides a mode of a calculation experiment. Probation on real information showed great possibilities of using the interface as a technical means for a doctor to solve tasks of cosmic medicine, traumathology and orthopedics.