A blood vessel model based on velocity profiles

Advanced Constitutive Modeling of the Thixotropic Elasto-Visco-Plastic Behavior of Blood: Steady-State Blood Flow in Microtubes

The present work focuses on the in-silico investigation of the steady-state blood flow in straight microtubes, incorporating advanced constitutive modeling for human blood and blood plasma. The blood constitutive model accounts for the interplay between thixotropy and elasto-visco-plasticity via a scalar variable that describes the level of the local blood structure at any instance. The constitutive model is enhanced by the non-Newtonian modeling of the plasma phase, which features bulk viscoelasticity. Incorporating microcirculation phenomena such as the cell-free layer (CFL) formation or the Fåhraeus and the Fåhraeus-Lindqvist effects is an indispensable part of the blood flow investigation. The coupling between them and the momentum balance is achieved through correlations based on experimental observations. Notably, we propose a new simplified form for the dependence of the apparent viscosity on the hematocrit that predicts the CFL thickness correctly. Our investigation focuses on the impact of the microtube diameter and the pressure-gradient on velocity profiles, normal and shear viscoelastic stresses, and thixotropic properties. We demonstrate the microstructural configuration of blood in steady-state conditions, revealing that blood is highly aggregated in narrow tubes, promoting a flat velocity profile. Additionally, the proper accounting of the CFL thickness shows that for narrow microtubes, the reduction of discharged hematocrit is significant, which in some cases is up to 70%. At high pressure-gradients, the plasmatic proteins in both regions are extended in the flow direction, developing large axial normal stresses, which are more significant in the core region. We also provide normal stress predictions at both the blood/plasma interface (INS) and the tube wall (WNS), which are difficult to measure experimentally. Both decrease with the tube radius; however, they exhibit significant differences in magnitude and type of variation. INS varies linearly from 4.5 to 2 Pa, while WNS exhibits an exponential decrease taking values from 50 mPa to zero.

Cardiovascular simulation toolbox

A toolbox for Matlab Simulink (trademark of Mathworks corp. etc.) was developed to simulate various models of flow in the cardiovascular system and study effects of different pathological conditions. The toolbox was based on well-known analog lumped models of blood flow in vessels, the varying elastance heart model, blood flow through vessels, shunts, and valves as well as models of oxygen exchange at lungs and tissue. The toolbox is modular providing the basic building blocks of the cardiovascular system. Parameters for the individual components may be set by the user to adapt the component to the simulated system. Several examples are shown. This modeling system is described and is also available for downloading as an open source for free use. The authors see this as the basis for wide collaboration and standardization in modeling. A web site will be available for accepting contributions from other researchers and to create a free exchange.

Model-based estimation of male urethral resistance and elasticity using pressure-flow data

To assess urethral resistance and changes in the urethral elasticity during voiding, a lumped parameter model of the urethra was developed. The model uses pressure and flow measurements to estimate time-dependent resistance and elasticity factor. The model includes a resistance that has a function of the cross-section and urethral elasticity. Two resistivity types are compared in the constricted flow-controlling zone of the urethra: Poiseouille resistance and the Bernoulli effect. Using real pressure-flow data sets, the model was used to estimate urethral resistance and changes in urethral elasticity during voiding. Estimation of the elasticity show that in a normal patient relaxation of the urethra is a process that continues until the end of voiding. This has important implications with regard to the present methods that are used in the clinic to assess urethral obstruction or constriction. The resistance as calculated by this model, may be a useful indicator of urethral constriction and obstruction, since it is especially independent of the bladder function. Changes in the urethral elasticity during voiding which are estimated by the model add a new diagnostic parameter to pressure-flow studies.

Hemodynamic mechanisms of penile erection

A model of penile hemodynamics was developed to explain the process of erection that is not yet fully understood. Contradicting observations regarding blood flow and vessels occlusion during erection were examined. The model that was based on the physical structure and physiological function of the system was validated by comparing its predictions to clinical and experimental observations. Simulation of the process for both normal and pathological conditions indicates that pressure buildup in the corpus cavernosum during erection depends mainly on the interaction between the arterial inflow system and the venous draining system and that the venous draining vessels do not fully collapse and flow through the penis continues throughout the erection period. In pathological conditions, the model predicts that tumescence can be obtained without functional rigidity and demonstrates that small increases in vessel stiffness can result in such behavior.

Intraoperative monitoring of IMA flow: what does it mean?

BACKGROUND

This study examines whether the measurement of internal thoracic artery (ITA) graft flow can determine the adequacy of the ITA-left anterior descending coronary artery (LAD) anastomosis.

METHODS

To study a wide range of clinical problems, we used a computer simulation of the cardiovascular system. The model included a time-varying elastance model of the heart, a systemic circulation represented by a multielement nonlinear model of the aorta and its major branches, a nonlinear model of the LAD circulation, and a model of the ITA bypass graft.

RESULTS

With a mild LAD stenosis, ITA graft flow was low and flow reversal occurred. As the percent stenosis increased, ITA flow and the percentage of ITA-to-total LAD flow increased. The ITA graft helped to maintain resting LAD blood flow. A partial obstruction (40%) at the ITA-LAD anastomosis reduced ITA graft flow at similar levels of LAD stenosis. However, overlap in flow values comparing a normal with a partially obstructed anastomosis occurred.

CONCLUSIONS

Flow patterns in the ITA are highly dependent on the degree of stenosis of the LAD as well as the integrity of the anastomosis. The predictive power of ITA flow measurement increases with severe stenosis or total occlusion of the proximal LAD and with high coronary blood flow demands.