Effects of Blood Flow Pulse Frequency on Mass Transfer Efficiency of a Commercial Hollow Fibre Oxygenator

The clinical advantages achievable through pulsatile blood perfusion during cardio-pulmonary bypass have recently suggested the design of new pulsatile systems for extracorporeal circulation. Still it is not clear whether current commercial membrane oxygenators could be adopted with such systems, since their behaviour with pulsatile perfusion has not been satisfactorily documented yet. In a previous paper, we assessed that pulsatile perfusion of a widely used hollow fibre oxygenator (Sorin® Monolyth) at 60 bpm provides more time-consistent oxygen transfer than steady perfusion. The present work is aimed to evaluate how the pulse frequency influences the gas transfer performance of the same device. The oxygenator was subjected to in vitro trials using a roller pump with pulsatile module (Stöckert Instrumente®) to generate pulsed flow. Four different pulse frequencies (45, 60, 75 and 90 bpm) were investigated at a fixed blood flow rate (4.0 l/min). The experiments lasting six hours were carried out using bovine blood with inlet conditions according to AAMI standards requirements. Blood samples were withdrawn every hour and O2 and CO2 transfer rates were evaluated. The experimental findings confirm that with pulsatile blood flow no time decay take place during prolonged perfusion. Moreover, when pulse frequency increases, transition levels occur for both O2 and CO2. Over these thresholds gas transfer rates display significant increases (p < 0.05), though of little magnitude (up to 2.5% for oxygen over 60 bpm; up to 3.7% for carbon dioxide over 75 bpm).

Influence of Membrane Oxygenators on the Pulsatile flow in Extracorporeal Circuits: An Experimental Analysis

An experimental analysis was carried out to evaluate the effects induced by two typical extracorporeal circuits on the pressure and flow generated by a roller pump with a pulsatile module. The hydraulic behaviour of the patient was simulated by means of a mechanical mock-up system consisting of a few lumped parameters reproducing the physiologic vascular impedance. Pressure and flow tracings were acquired at different locations along the circuit using an automatic data acquisition system. Nine test conditions with different pulse frequency and systolic time values were examined using a mean volumetric flow rate of approximately 4 l/min. A complete analysis of the results obtained in terms of pressure drops and inflow-outflow differences across the components of the arterial line, as well as the calculation of the hydraulic pulsatile power along the circuit, allowed us to assess the influence of the various components upon the pulsatility. The results indicated that the membrane oxygenators tested slightly affect the pulsatility of the flow and the pressure; on the contrary the arterial pipe line is responsible for large damping and head losses. To optimize the use of pulsatile flow for cardiopulmonary bypass it is necessary to reduce the length of the arterial pipe lines thus integrating the circuit as much as possible.

Tuning of a deformable image registration procedure for skin component mechanical properties assessment

Several studies report the mechanical properties of skin tissues but their values largely depend on the measurement method. Therefore, we investigated the feasibility of recognizing the cellular constituents mechanical properties of pigmented skin by Confocal Laser Scanner Microscopy (CLSM). With this purpose, an healthy volunteer was examined in three areas nearby a pigmented skin lesion in two configurations: deforming and non deforming the nevus. The tissue displacement of the nevus was then assessed by means of deformable registration of the images in these two configurations. There are several registration strategy able to overcome this task, among them, we proposed two methods with different deformation models: a Free Form Deformation (FFD) model based on b-spline and a second one based on Demons Registration Algorithm (DRA). These two strategies need the definition of several parameters in order to obtain optimal registration performances. Thus, we tuned these parameters by means of simulated data and evaluated their registration abilities on the real in vivo CLSM acquisitions in the two configurations. The results showed that the registration using DRA had a better performance in comparison to the FFD one, in particular in two out of the three areas the DRA performance was significantly better than the FFD one. The registration procedure highlighted deformation differences among the chosen areas.

Virtual surgeries in patients with congenital heart disease: a multi-scale modelling test case

The objective of this work is to perform a virtual planning of surgical repairs in patients with congenital heart diseases--to test the predictive capability of a closed-loop multi-scale model. As a first step, we reproduced the pre-operative state of a specific patient with a univentricular circulation and a bidirectional cavopulmonary anastomosis (BCPA), starting from the patient's clinical data. Namely, by adopting a closed-loop multi-scale approach, the boundary conditions at the inlet and outlet sections of the three-dimensional model were automatically calculated by a lumped parameter network. Successively, we simulated three alternative surgical designs of the total cavopulmonary connection (TCPC). In particular, a T-junction of the venae cavae to the pulmonary arteries (T-TCPC), a design with an offset between the venae cavae (O-TCPC) and a Y-graft design (Y-TCPC) were compared. A multi-scale closed-loop model consisting of a lumped parameter network representing the whole circulation and a patient-specific three-dimensional finite volume model of the BCPA with detailed pulmonary anatomy was built. The three TCPC alternatives were investigated in terms of energetics and haemodynamics. Effects of exercise were also investigated. Results showed that the pre-operative caval flows should not be used as boundary conditions in post-operative simulations owing to changes in the flow waveforms post-operatively. The multi-scale approach is a possible solution to overcome this incongruence. Power losses of the Y-TCPC were lower than all other TCPC models both at rest and under exercise conditions and it distributed the inferior vena cava flow evenly to both lungs. Further work is needed to correlate results from these simulations with clinical outcomes.

Failure of silicone gel breast implants: is the mechanical weakening due to shell swelling a significant cause of prostheses rupture?

Silicone gel-filled breast implants nowadays are commonly used in breast surgery. Despite the improvements carried out during the years in the device design and manufacturing technologies, the long-term reliability of such prostheses is still doubted and the phenomena involved in the prostheses failure not yet clearly defined. This study investigates rupture causes by analysing the mechanical properties of failed and intact implants in the recent generation of silicon gel breast implants. The main scope is to assess whether mechanical weakness of the shells should be considered as a major cause of breast implant rupture or, on the contrary, the prosthesis shell damage is likely due to other random factors. Some tests were performed on the shells of a wide number of explanted prostheses, to evaluate the mechanical properties as a function of prostheses status at explantation (intact/ruptured) and variable degree of swelling. A weakening of the shell mechanical properties, so as a significant difference in the ultimate strength and stiffness of intact versus ruptured prostheses, was found. This attenuation of the properties may be justified as a consequence of the shell swelling phenomenon during implantation and has to be considered as a significant mechanism for silicone gel breast implant failure.

Uterine artery blood flow volume in pregnant women with an abnormal pulsatility index of the uterine arteries delivering normal or intrauterine growth restricted newborns

The aim of this study was to assess and compare uterine artery (UtA) blood flow volume in pregnant patients with an abnormal uterine Doppler pulsatility index (PI) who delivered fetuses with an appropriate weight for gestational age (AGA) or with intrauterine growth restricted (IUGR). We prospectively recruited singleton pregnancies with abnormal uterine arteries P.I. between 18 and 38 weeks of gestation regardless of estimated fetal weight (EFW). Vessel diameter and blood flow velocity were measured along the UtA upstream to the vessel bifurcation in both the right and left UtAs. Uterine blood flow volumes measured in these pregnancies were compared to historical Control-pregnancies. Forty-three patients delivered at term a normal weight newborn (AGA-pregnancies). Thirty patients delivered growth restricted newborns at 32 weeks (i.r. 29-36w) with a median weight of 1160 gr (i.r. 1000-2065 gr) (IUGR-pregnancies). At mid-gestation (18 + 0 - 25 + 6 weeks + days of gestation) a significantly lower uterine blood flow volume per unit weight was observed between the two study groups and compared to controls: 142 ml/min/kg in IUGR-pregnancies, 217 ml/min/kg in AGA-pregnancies and 538 ml/min/kg in Control-pregnancies. These striking differences in blood flow volume were already present at mid-gestation, at a time when EFW was still normal. In late gestation (27 + 0 - 37 + 6 weeks + days of gestation), pregnancies with an abnormal uterine P.I. showed persistently low UtA flow (<50% of controls) even when corrected for fetal weight: 81 ml/min/kg in IUGR-pregnancies, 105 ml/min/kg in AGA-pregnancies, and 193 ml/min/kg in Control-pregnancies; p < 0.0001. Our findings are consistent with other recent studies regarding the association between reduced uterine blood flow volume and fetal growth restriction. However, the study brings new insight into the finding of abnormal uterine P.I. in normally grown fetuses typically dismissed as "falsely abnormal" or "false positive" findings. Our study suggests that blood flow volume measurement may serve as a new tool to assess this group of patients and possibly those with ischemic placental diseases that may provide some basis for therapeutic interventions.

Design of a ‘driven cylinder’ viscometer for bone cement rheological characterization

The long-term success of surgical applications requiring bone cement is strongly influenced by the cement’s rheological properties. Previous studies showed a clear non-Newtonian, pseudoplastic, time-dependent rheological behaviour of acrylic bone cement during the working time. However, the particular nature of this material raises issues about its rheological characterization: the aim of this paper is to develop a new device, called ‘driven cylinder’ viscometer, able to accomplish the rheological characterization of acrylic bone cement. Three different fluids were tested by using the ‘driven cylinder’ viscometer: (a) liquid soap, (b) low-viscosity bone cement, and (c) vertebroplasty bone cement. For the sake of comparison, the rheological behaviour of the fluids (a) and (b) was also evaluated using traditional viscometers. The developed device allowed evaluation of the constitutive rheological parameters for non-Newtonian, power-law fluids. Independent evaluation of the viscosity of liquid soap and low-viscosity bone cement carried out by means of parallel-plate rotational rheometers showed a good agreement with the trends obtained by the ‘driven cylinder’ viscometer. The device versatility suggests its application for a complete description of pseudoplastic and time-dependent rheological properties of acrylic bone cements, which is a mandatory step for virtual tools of cement-based surgical procedures.

Blood flow volume of uterine arteries in human pregnancies determined using 3D and bi-dimensional imaging, angio-Doppler, and fluid-dynamic modeling

The primary aim of this pilot study was to study uterine artery (UtA) blood flow volume in uneventful human pregnancies delivered at term, at mid and late gestation by means of 3D and bi-dimensional ultrasound imaging with angio-Doppler combined with fluid-dynamic modeling. Secondary aims were to correlate flow volume to placental site and to UtA Pulsatility Index (PI). Women with singleton, low-risk pregnancies were examined at mid and late gestation. The structure and course of the uterine artery (UtA) was studied in each patient by means of 3D-angio-Doppler and included vessel diameter D, blood flow velocity and PI (measured along the UtA). Fetal weight estimation and placental insertion site were assessed by ultrasound. A robust fluid-dynamic modeling was applied to calculate absolute flow and flow per unit fetal weight. Mean UtA diameter and blood flow velocity increased significantly (p < 0.0001) from mid-gestation to late gestation from 2.6 mm and 67.5 cm/s, to 3.0 mm and 85.3 cm/s, respectively, yielding an increasing absolute flow troughout gestation. h coefficient, derived by fluid-dynamic modeling to calculate mean velocity, increased significantly from 0.52 at mid-gestation to 0.57 at late gestation. UtA blood flow volume ml/min/kg-fetal weight was significantly higher at mid-gestation than at late gestation (535 ml/min/kg vs 193 ml/min/kg; p < 0.0001). In cases with strictly lateral placentas the ipsilateral UtA accommodates at mid and late gestation 63% and 67% of the total UtA flow. In central placentas UtA flow was evenly distributed between the two vessels. An inverse correlation was observed between PI and blood flow volume ml/min/kg (Pearson's coefficient r = -0.54). Our work confirms the technological and methodological limitations in the measurement of uterine artery blood flow. However, Doppler measurements supported by three-dimensional angio imaging of the uterine vessel, high resolution imaging and diameter measurement, and a robust mathematical model of local circulation adds a genuine new area of investigation into human uterine circulation during pregnancy.

Computational models to predict stenosis growth in carotid arteries: which is the role of boundary conditions?

This work addresses the problem of prescribing proper boundary conditions at the artificial boundaries that separate the vascular district from the remaining part of the circulatory system. A multiscale (MS) approach is used where the Navier-Stokes equations for the district of interest are coupled to a non-linear system of ordinary differential equations which describe the circulatory system. This technique is applied to three 3D models of a carotid bifurcation with increasing stenosis resembling three phases of a plaque growth. The results of the MS simulations are compared to those obtained by two stand-alone models. The MS shows a great flexibility in numerically predicting the haemodynamic changes due to the presence of a stenosis. Nonetheless, the results are not significantly different from a stand-alone approach where flows derived by the MS without stenosis are imposed. This is a consequence of the dominant role played by the outside districts with respect to the stenosis resistance.

Modeling and mechanobiology of cerebral aneurysms

The purpose of this work is to review the computational models of the adaptive behavior of the cerebral vascular wall aimed at simulating aneurysm formation and enlargement. Cerebral aneurysms are localized abnormal enlargements of the intracranial arterial vessels. The origin of this pathology is still unclear: however, aneurysm formation is thought to be the result of interplay between biomechanical properties of the vessel wall and their possible changes, such as adaptive response to mechanical stimuli. Recently, different computational approaches were suggested in the literature aiming to describe the mechanobiology of the cerebral vascular wall. Most of the computational adaptive models showed a common approach for the geometrically non-linear kinematic description of the phenomenon, whilst the constitutive laws defining the rates of growth variables may differ considerably according to the specific phenomenon considered. These studies allowed the reproduction of some peculiar aspects of aneurysm mechanobiology; however, continued interdisciplinary research is mandatory for a better understanding of the mechanisms involved in the evolution of cerebral aneurysms.

An axisymmetric computational model of skin expansion and growth

Skin expansion is the principal technique used in plastic surgery to repair large cutaneous defects, typically after tumour removal, burn care, craniofacial surgery and post-mastectomy breast reconstruction. It allows a gain of new tissue by means of gradual expansion of a prosthesis, surgically implanted beneath the patient's skin. Nevertheless, wide clinical use is not supported by a deep quantitative knowledge of the phenomena occurring during the expansion. A finite element model of the skin expansion was developed to evaluate the stresses and the strains of the skin due to the expander inflation and validated by proper in vitro experiments; furthermore, a growth model based on the mechanical stimulus was implemented to estimate the skin area gain. The developed computational approach, composed of the skin expansion model interaction and the growth law, proved its validity to investigate skin expansion phenomena: its use suggests a new predictive tool to optimize clinical procedures and the expander devices' design.

Spatial velocity profile changes along the cord in normal human fetuses: can these affect Doppler measurements of venous umbilical blood flow?

OBJECTIVE

Several studies have assumed a parabolic velocity profile through the umbilical vein (UV) to derive the mean spatial velocity that is indispensable for flow rate calculations. However, the structure and arrangement of the umbilical cord suggest that velocity profiles may vary. The aim of this study was to evaluate UV spatial flow velocity profiles at different sites along the umbilical cord.

METHODS

Ten singleton pregnancies with a gestational age between 26 and 34 weeks were included in the study. Ultrasound equipment with an inbuilt function for analysis of the spatial velocity profile along a line located in a fixed plane was used to obtain UV velocity profiles. Velocity profiles were obtained at the placental insertion and in a free intra-amniotic loop of the cord. Two-dimensional (2D) velocity distribution coefficients were evaluated as ratios between mean and maximum velocities along the investigated lines.

RESULTS

2D velocity distribution coefficients at the placental insertion (0.85 +/- 0.03) were significantly higher (P < 0.00001) than those obtained from a free loop of cord (0.76 +/- 0.03). Values indicated that velocity profiles are approximately flat at the placental insertion and become more parabolic moving downstream. Moreover, profiles become skewed in association with cord curvature and show peculiar biphasic shapes immediately downstream from the placenta.

CONCLUSIONS

Flow velocity profiles in the UV are not perfectly parabolic and modify along the cord. These characteristics may affect the evaluation of UV blood flow rate.

Umbilical flow distribution to the liver and the ductus venosus in human fetuses during gestation: an anatomy-based mathematical modeling

The partitioning of umbilical vein blood flow between fetal liver and ductus venosus may be an indicator of the fetal well-being, because the goal of the ductus venosus is to supply oxygen and nutrients to heart and brain. Both distribution and blood flow rate of the umbilical vein are functions of the local vascular impedances that, in turn, depend on the anatomical features of the related vessels. In order to investigate the venous blood flows in human fetuses during a normal gestation, a simple lumped parameter mathematical model was developed on the basis of some information achievable by ultrasonographic techniques. Particularly, the diameter and length of umbilical vein and ductus venosus and the volume of the liver were used to derive the vascular impedances. Three different impedance models were adopted for the umbilical vein, the ductus venosus and the hepatic circulation. A linear model described viscous hydraulic dissipations through the umbilical vein, while a quadratic pressure-flow relationship was used for the ductus venosus due to the irregular local hemodynamics at its inlet. Finally, the equivalent impedance of the whole hepatic network was related to the hepatic volume assuming a tree-like, symmetric and self-similar fractal geometry. The hepatic vascular resistances predicted according to the fractal analysis were quite consistent with some experimental measurements in fetal lambs. In agreement with clinical observations, the model predicted blood flows through the ductus venosus and umbilical vein increasing (from about 25 to 75 ml/min and from about 45 to 370 ml/min, respectively) throughout the gestation (20-40 weeks), while the flow fraction shunted via the ductus venosus diminishes (from about 50 to 20%).

Multiscale modelling as a tool to prescribe realistic boundary conditions for the study of surgical procedures

This work was motivated by the problems of analysing detailed 3D models of vascular districts with complex anatomy. It suggests an approach to prescribing realistic boundary conditions to use in order to obtain information on local as well as global haemodynamics. A method was developed which simultaneously solves Navier-Stokes equations for local information and a non-linear system of ordinary differential equations for global information. This is based on the principle that an anatomically detailed 3D model of a cardiovascular district can be achieved by using the finite element method. In turn the finite element method requires a specific boundary condition set. The approach outlined in this work is to include the system of ordinary differential equations in the boundary condition set. Such a multiscale approach was first applied to two controls: (i) a 3D model of a straight tube in a simple hydraulic network and (ii) a 3D model of a straight coronary vessel in a lumped-parameter model of the cardiovascular system. The results obtained are very close to the solutions available for the pipe geometry. This paper also presents preliminary results from the application of the methodology to a particular haemodynamic problem: namely the fluid dynamics of a systemic-to-pulmonary shunt in paediatric cardiac surgery.

Biomechanical properties of the human umbilical cord

The umbilical cord is a complex and fascinating structure that connects the fetus to the placenta and encases the umbilical vessels. The response of its tissues to mechanical loading due to fetal movements and uterine contractions is not well understood. The aim of this study is the evaluation of the mechanical properties of the main components of the human umbilical cord. Fresh umbilical cord specimens were collected from neonates born at term of the gestation and submitted to compliance tests. Furthermore, uniaxial tensile and stress-relaxation tests were performed on samples of umbilical vein and Wharton's jelly. Both materials exhibited nonlinear stress-strain response with increasing strain, increasing the elastic modulus (E(high) about 10-20 times E(low)) and significant viscoelastic behavior. In addition, anisotropy of the vein was observed. Although the circumferential properties of the vein (mean E(high) about 2.4 MPa) were similar to those after birth, the longitudinal stiffness of both materials was higher (mean E(high) over 10 MPa) and comparable to that of the ligaments. These findings suggest a mechanism of protection acting against excessive elongations of the cord, which could cause undue restriction of the umbilical vessel area and interference with the fetal blood circulation.

Doppler investigation in intrauterine growth restriction--from qualitative indices to flow measurements: a review of the experience of a collaborative group

In 1997 we started a collaboration among three groups, combining our experience with Doppler examination of the human fetus, blood flow studies on fetal lamb, and mathematical modeling of human circulation. In preliminary investigations on fetal lambs, the same Doppler method designed for the human fetus was used to measure venous blood flow in the umbilical veins of seven fetal lambs. Doppler measurements and diffusion technique groups for umbilical venous flow were 210.8+/-18.8 and 205.7+/-38.5 ml/min/kg, respectively (p = 0.881). In human pregnancy the interobserver variabilities for the vein diameter, mean velocity, and absolute umbilical venous blood were 2.9%, 7.9%, and 12.7%, respectively. A cross-sectional study allowed us to establish normal reference values. Venous blood flow/kg of estimated fetal weight showed a nonsignificant linear reduction with gestational age, from 128.7 ml/min/kg at 20 weeks to 104.2 ml/min/kg at 38 weeks. In a series of 37 growth-restricted fetuses, the UV flow per kilogram was significantly lower in the more severe growth-restricted fetuses (abdominal circumference below the second percentile and abnormal umbilical arterial p.i.) than in normal comparable fetuses (p < 0.001). In a series of 140 normal fetuses, we calculated that the absolute blood flow rate in the ductus venosus (DV) increases significantly with advancing gestational age from 20 to 38 weeks of gestation (from 23.2+/-9.6 ml/min to 43.5+/-21.5 ml/min). This means that the percentage of umbilical blood flow shunted through the DV decreases significantly during gestation (from 50% at midgestation to 20% at 38 weeks). In a series of 45 growthrestricted fetuses, delivered because of nonreactive fetal heart rate (group 2) and for other reasons but still with a normal heart rate pattern (group 1), we measured the ductal inlet diameter. In these fetuses, the diameters at the ductal isthmus, normalized for the dimension of the abdominal circumference (inlet diameter/abdominal circumference), were significantly larger (group 1 = 6.8+/-2.3; group 29.4+/-2.8 ) than in the control group (6.1+/-0.3). This means that in this subset of fetuses the amount of blood shunted can be increased as a compensatory mechanism.

Modeling of the Norwood circulation: effects of shunt size, vascular resistances, and heart rate

Hypoplastic left heart syndrome is the most common lethal cardiac malformation of the newborn. Its treatment, apart from heart transplantation, is the Norwood operation. The initial procedure for this staged repair consists of reconstructing a circulation where a single outlet from the heart provides systemic perfusion and an interpositioning shunt contributes blood flow to the lungs. To better understand this unique physiology, a computational model of the Norwood circulation was constructed on the basis of compartmental analysis. Influences of shunt diameter, systemic and pulmonary vascular resistance, and heart rate on the cardiovascular dynamics and oxygenation were studied. Simulations showed that 1) larger shunts diverted an increased proportion of cardiac output to the lungs, away from systemic perfusion, resulting in poorer O2 delivery, 2) systemic vascular resistance exerted more effect on hemodynamics than pulmonary vascular resistance, 3) systemic arterial oxygenation was minimally influenced by heart rate changes, 4) there was a better correlation between venous O2 saturation and O2 delivery than between arterial O2 saturation and O2 delivery, and 5) a pulmonary-to-systemic blood flow ratio of 1 resulted in optimal O2 delivery in all physiological states and shunt sizes.

In vitro steady-flow analysis of systemic-to-pulmonary shunt haemodynamics

A modified Blalock-Taussig shunt is a connection created between the systemic and pulmonary arterial circulations to improve pulmonary perfusion in children with congenital heart diseases. Survival of these patients is critically dependent on blood flow distribution between the pulmonary and systemic circulations which in turn depends upon the flow resistance of the shunt. Previously, we investigated the pressure-flow relationship in rigid shunts with a computational approach. to estimate the pulmonary blood flow rate on the basis of the in vivo measured pressure drop. The present study aims at evaluating, in vitro how the anastomotic distensibility and restrictions due to suture presence affect the shunt pressure-flow relationship. Two actual Gore-Tex shunts (3 and 4 mm diameters) were sutured to compliant conduits by a surgeon and tested at different steady flow rates (0.25-11 min(-1)) and pulmonary pressures (3-34 mmHg). Corresponding computational models were also created to investigate the role of the anastomotic restrictions due to sutures. In vitro experiments showed that pulmonary artery pressure affects the pressure-flow relationship of the anastomoses. particularly at the distal site. However, this occurrence scarcely influences the total shunt pressure drop. Comparisons between in vitro and computational models without anastomotic restrictions show that the latter underestimates the in vitro pressure drops at any flow rate. The addition of the anastomotic restrictions (31 and 47% of the original area of 3 and 4 mm shunts, respectively) to the computational models reduces the gap, especially at high shunt flow rate and high pulmonary pressure.

Role of ductus venosus in distribution of umbilical blood flow in human fetuses during second half of pregnancy

Color Doppler sonography was used to study umbilical and ductus venosus (DV) flow in 137 normal fetuses between 20 and 38 wk of gestation. Hepatic flows were also evaluated. In all parts of the venous circulation examined, blood flow increased significantly with advancing gestational age. The weight-specific amniotic umbilical flow did not change significantly during gestation (120 +/- 44 ml. min(-1). kg(-1)), whereas DV flow decreased significantly (from 60 to 17 ml. min(-1). kg(-1)). The percentage of umbilical blood flow shunted through the DV decreased significantly (from 40% to 15%); consequently, the percentage of flow to the liver increased. The right lobe flow changed from 20 to 45%, whereas the left lobe flow was approximately constant (40%). These changes are related to different patterns of growth of the umbilical veins and DV diameters. The present data support the hypothesis that the DV plays a less important role in shunting well-oxygenated blood to the brain and myocardium in late normal pregnancy than in early gestation, which leads to increased fetal liver perfusion.

Computational model of the fluid dynamics in systemic-to-pulmonary shunts

A systemic-to-pulmonary shunt is a connection created between the systemic and pulmonary arterial circulations in order to improve pulmonary perfusion in children with congenital heart diseases. Knowledge of the relationship between pressure and flow in this new, surgically created, cardiovascular district may be helpful in the clinical management of these patients, whose survival is critically dependent on the blood flow distribution between the pulmonary and systemic circulations. In this study a group of three-dimensional computational models of the shunt have been investigated under steady-state and pulsatile conditions by means of a finite element analysis. The model is used to quantify the effects of shunt diameter (D), curvature, angle, and pulsatility on the pressure-flow (DeltaP-Q) relationship of the shunt. Size of the shunt is the main regulator of pressure-flow relationship. Innominate arterial diameter and angles of insertion have less influence. Curvature of the shunt results in lower pressure drops. Inertial effects can be neglected. The following simplified formulae are derived: DeltaP=(0. 097Q+0.521Q(2))/D(4) and DeltaP=(0.096Q+0.393Q(2))/D(4) for the different shunt geometries investigated (straight and curved shunts, respectively).

Scaling approach to study the changes through the gestation of human fetal cardiac and circulatory behaviors

During human gestation, fetal body size increases considerably and important transformations occur to hemodynamics of the cardiovascular system of the fetus. Vascular compliances and resistances as well as the cardiac function show important changes. In order to investigate these modifications, a mathematical approach based on scaling techniques was developed. Vascular and cardiac parameters of the human fetus were related by allometric equations to the anatomical dimensions of vessels that, in turn, depend on the fetal body weight and the gestational age. A scaling factor (b) was identified for each parameter under study: vascular resistances and flow inertances decrease with gestational age (b= -0.33 for flow inertances) whereas vascular compliances remarkably increase (b= 1.33). Scaling factors were also adopted for the fetal cardiac parameters, according to experimental data on the development of fetal myocardium. Parameter values calculated for each week of the last trimester of the fetal gestation, were tested using a mathematical lumped parameter model, previously developed for a human fetus near the term of the gestation. The validation of the scaling method adopted for the parameters was performed by comparing the results of the simulations with a group of data obtained by Doppler velocimetry at different stages of fetal normal gestation. The adopted allometric equations were appropriate in describing the development of the human fetal circulatory system. The ductus venosus, the ductus arteriosus, and the foramen ovale, that conclude their function at the birth moment, as well as the lungs and the brain, do not follow the general growth rate and require different scaling factors.

Use of mathematical model to predict hemodynamics in cavopulmonary anastomosis with persistent forward flow

BACKGROUND

The bidirectional cavopulmonary anastomosis with additional pulmonary blood flow is used as a staged procedure or a definitive palliation of univentricular hearts. In this paper the flow competition occurring between the caval and the pulmonary flows is investigated. The hemodynamics in the superior vena cava and the blood flow distribution into the lungs, as well as the systemic arterial oxygen availability, are correlated with the severity of the right ventricle outflow tract obstruction and the pulmonary arteriolar resistance.

MATERIALS AND METHODS

Computer models of the pre- and postoperative hemodynamics of univentricular hearts were developed. The effects of increasing severity of the right ventricle outflow tract obstruction, with a pulmonary arteriolar resistance ranging from 0.8 to 7.9 nonindexed Woods units, were simulated.

RESULTS

The study indicates that the presence of an additional pulmonary blood flow from the native pulmonary artery may be beneficial. Since an excessive additional blood flow may cause central venous hypertension, its optimal value should be chosen according to the value of pulmonary arteriolar resistance. The model was utilized to simulate four clinical cases.

CONCLUSIONS

The simulations show that the model can predict the postoperative hemodynamics and could therefore be usefully applied to predict quantitatively the effect of the native pulmonary blood flow following bidirectional cavopulmonary anastomosis.

Calculating blood flow from Doppler measurements in the systemic-to-pulmonary artery shunt after the Norwood operation: a method based on computational fluid dynamics

Hypoplastic left heart syndrome is currently the most lethal cardiac malformation of the newborn infant. Survival following a Norwood operation depends on the balance between systemic and pulmonary blood flow, which is highly dependent on the fluid dynamics through the interposition shunt between the two circulations. We used computational fluid dynamic (CFD) models to determine the velocity profile in a systemic-to-pulmonary artery shunt and suggested a simplified method of calculating the blood flow in the shunt based on Doppler measurements. CFD models of systemic-to-pulmonary shunts based on the finite element method were studied. The size of the shunt has been varied from 3 to 5 mm. Velocity profiles at proximal and distal positions were evaluated and correlations between maximum and mean spatial velocity were found. Twenty-one Doppler measurements in the proximal and distal part of the shunt were obtained from six patients with hypoplastic left heart syndrome. Combining Doppler velocities and CFD velocity profiles, blood flow rate in the shunt was calculated. Flow rate evaluated from aortic Doppler and oxygen saturation measurements were performed for comparison. Results showed that proximal shunt Doppler velocities were always greater than the correspondent distal ones (ratio equal to 1.15 +/- 0.11). CFD models showed a similar behaviour (ratio equal to 1.21 +/- 0.03). CFD models gave a V(mean)/V(max) ratio of 0. 480 at the proximal junction and of 0.579 at the distal one. The agreement between the flow evaluated in the proximal and distal areas of the shunt was good (0.576 +/- 0.150 vs. 0.610 +/- 0.166 l/min). Comparison of these data with saturation data and aortic Doppler measurements correlate less well (0.593 +/- 0.156 vs. 1.023 +/- 0.493 l/min). A formula easily to quantify shunt flow rate is proposed. This could be used to evaluate the effects of different therapeutic and pharmacological manoeuvres in this unique circulation.

Computational fluid dynamic and magnetic resonance analyses of flow distribution between the lungs after total cavopulmonary connection

Total cavopulmonary connection is a surgical procedure adopted to treat complex congenital malformations of the right heart. It consists basically in a connection of both venae cavae directly to the right pulmonary artery. In this paper a three-dimensional model of this connection is presented, which is based on in vivo measurements performed by means of magnetic resonance. The model was developed by means of computational fluid dynamics techniques, namely the finite element method. The aim of this study was to verify the capability of such a model to predict the distribution of the blood flow into the pulmonary arteries, by comparison with in vivo velocity measurements. Different simulations were performed on a single clinical case to test the sensitivity of the model to different boundary conditions, in terms of inlet velocity profiles as well as outlet pressure levels. Results showed that the flow distribution between the lungs is slightly affected by the shape of inlet velocity profiles, whereas it is influenced by different pressure levels to a greater extent.

The hemodynamic effects of double-orifice valve repair for mitral regurgitation: a 3D computational model

OBJECTIVES

A 3D computational model has been implemented for the evaluation of the hemodynamics of the double orifice repair. Critical issues for surgical decision making and echo-Doppler evaluation of the results of the procedure are investigated.

METHODS

A parametric 3D computational model of the double-orifice mitral valve based on the finite elements model has been constructed from clinical data. Nine different geometries were investigated, corresponding to three total inflow areas (1.5, 2.25 and 3 cm2) and to three orifice configurations (two equal orifices, two orifices of different areas, i.e. one twice as much the other one, and a single orifice). The simulations were performed in transit; the fluid was initially quiescent and was accelerated to the maximum flow rate with a cubic function. For each case, some characteristic values of velocity and pressure were determined: velocities were calculated downstream of each orifice, at the centre of it (Vcen1, Vcen2). The maximum velocity was also determined for each orifice (Vmax1, Vmax2). Maximum pressure drops (deltap(max)) across the valve were compared with the estimations (deltap(Bernoulli)) based on the Bernoulli formula (4 V2).

RESULTS

In each simulation, no notable difference was observed between Vcen1 and Vcen2, and between Vmax1 and Vmax2, regardless of the valve configuration. Maximum velocity and deltap(max) were related to the total orifice area and were not influenced by the orifice configuration. Deltap(Bernoulli) calculated with Vmax was well correlated with the deltap(max) obtained throughout the simulations (y = 0.9126x + 0.3464, r = 0.996); on the contrary the pressure drops estimated using Vcen underestimated (y = 0.6757x + 0.3073, r = 0.999) the actual pressure drops.

CONCLUSIONS

The hemodynamic behaviour of a double orifice mitral valve does not differ from that of a physiological valve of same total area: pressure drops and flow velocity across the valve are not influenced by the configuration of the valve. Echo Doppler estimation of the maximum velocities is a reliable method for the calculation of pressure gradients across the repaired valve.

Factors affecting the respiratory ratio during cardiopulmonary by-pass

Despite the wide use of hypothermic cardiopulmonary bypass (CPB) during open heart surgery there is little information about the patient metabolism. In particular no complete studies addressed the assessment of the respiratory ratio (RR) during CPB at different core temperatures. Therefore a clinical study was performed in order to evaluate the oxygen consumption (VO2) and carbon dioxide production (VCO2) in adult patients with valvular or coronary heart disease undergoing CPB. Twenty-five patients (16 male, 9 female) aged between 26 and 76 (54.2+/-12.4 mean +/- SD) were the subjects of this study. Measurements (102) were taken at various perfusion flow rates (from 1.6 to 2.9 L/min(-1) x m(-2)) and temperatures (from 24 to 37 degrees C). Arterial and mixed venous gas analyses were performed and O2 and CO2 concentrations were calculated, including the carbamate contribute. We calculated VO2, VCO2 and then RR from artero-venous differences in O2 and CO2 contents. Both VO2 and VCO2 showed a positive linear correlation with temperature (r = 0.82 and r = 0.59 respectively) and with blood flow rate (r = 0.61 and r = 0.29 respectively). The mean RR was 0.78+/-0.28 and more than 84% of RR values fell in the range 0.5-1.2. No significant correlation between RR and temperature and blood flow rate was observed. VCO2 and RR showed a positive linear correlation with the gas to blood flow rate ratio (r = 0.37 and r = 0.49 respectively).

Dilatation of the ductus venosus in human fetuses: ultrasonographic evidence and mathematical modeling

Autonomic regulation of blood flow through the fetal ductus venosus has been suggested, but the existence of a sphincter at the ductal entrance in human fetuses has yet to be established. In this paper two cases of apparent ductus venosus dilatation in two growth-restricted human fetuses are reported. Prolonged ultrasonographic analysis (45 min) showed rapid and substantial changes (>80%) of ductal diameters. Pulsed Doppler analysis was used to investigate flow velocity in the ductus venosus and umbilical vein for both normal and dilated conditions. Dilated conditions caused manifest modifications of velocity tracings. Systolic peak velocity in the ductus did not change visibly, whereas velocity at the atrial contraction showed evident reduction; consequently, pulsatility indexes increased. Furthermore, the umbilical vein presented flow velocity pulsations. The mean blood flow rate through the ductus seemed to increase substantially (>70%) for high dilatation. To investigate these findings further, we performed simulations of ductal dilatation by means of a lumped-parameter mathematical model of the human fetal circulation. Model results agreed with clinical evidence and confirmed the relationship between ductal dilatation and the observed velocity alterations. Simulated systolic peak velocity slightly increased for small dilatation (<30%), whereas atrial velocity was reduced when the ductus dilated. Furthermore, the model indicated that umbilical venous pressure decreases for increasing dilatation, whereas no change occurs in the central venous pressure. The present results seem to indicate the presence of active dilatation of the ductus venosus in human fetuses.

Effects of blood flow pulse frequency on mass transfer efficiency of a commercial hollow fibre oxygenator

The clinical advantages achievable through pulsatile blood perfusion during cardio-pulmonary bypass have recently suggested the design of new pulsatile systems for extracorporeal circulation. Still it is not clear whether current commercial membrane oxygenators could be adopted with such systems, since their behaviour with pulsatile perfusion has not been satisfactorily documented yet. In a previous paper, we assessed that pulsatile perfusion of a widely used hollow fibre oxygenator (Sorin Monolyth) at 60 bpm provides more time-consistent oxygen transfer than steady perfusion. The present work is aimed to evaluate how the pulse frequency influences the gas transfer performance of the same device. The oxygenator was subjected to in vitro trials using a roller pump with pulsatile module (Stockert Instrumente) to generate pulsed flow. Four different pulse frequencies (45, 60, 75 and 90 bpm) were investigated at a fixed blood flow rate (4.0 l/min). The experiments lasting six hours were carried out using bovine blood with inlet conditions according to AAMI standards requirements. Blood samples were withdrawn every hour and O2 and CO2 transfer rates were evaluated. The experimental findings confirm that with pulsatile blood flow no time decay take place during prolonged perfusion. Moreover, when pulse frequency increases, transition levels occur for both O2 and CO2. Over these thresholds gas transfer rates display significant increases (p < 0.05), though of little magnitude (up to 2.5% for oxygen over 60 bpm; up to 3.7% for carbon dioxide over 75 bpm).

Blood flow through the ductus venosus in human fetus: calculation using Doppler velocimetry and computational findings

The present study was performed to assess a new method to calculate the blood flow rate through the ductus venosus (DV) in normal human fetuses using available echo-Doppler data. Color Doppler sonographic unit was used to study DV flow in 26 normal fetuses between 20 and 36 wk of gestation. Maximal velocity flow tracings and vessel diameters were obtained at the isthmic and the outlet portion of the DV. Time-averaged velocities in the DV were measured from the recorded tracings. The velocity distribution in the two investigated cross-sectional areas of the DV was evaluated by means of computational model simulations and the velocity shape coefficients h(in) and h(out), (i.e., the ratios between the maximal and mean spatial velocities) were calculated as a function of vessel geometry. These values allowed us to convert maximal Doppler velocities into mean spatial velocities for each fetus. Blood flow rate was evaluated both at the isthmus and at the outlet of the vessel by means of two formulae based on the ultrasonographic measures and the results of the computational model. The value of the DV blood flow rate was calculated as the average between the results provided by the two formulae. The velocity distributions both at the isthmus (h(in) = 0.677 +/- 0.040) and the outlet (h(out) = 0.374 +/- 0.072) of the ductus are skewed toward the inner wall. Ductus geometry, i.e., the isthmic/outlet diameter ratio, affects the shape of the velocity profiles in the vessel, particularly that at the outlet. The coefficients of variation for repeated measurements of the ductal diameters were 9.5 +/- 7.7% and 6.7 +/- 4.9% at the isthmus and the outlet, respectively. The two formulae gave values statistically identical for the time-average blood flow rate (36.3 +/- 22.1 vs. 39.4 +/- 24.0 mL/min; R = 0.946, p = NS). The mean percent difference between the results of the two formulae was 7.1%. Thus, in human fetuses, the use of the two formulae based on both Doppler data and computational model simulations makes it possible to calculate the ductal flow rate. When the difference between the calculations of the two formulae exceeds the 30% of their average value, it is convenient to adopt the flow rate value calculated at the isthmus instead of the average of the two measures. The measurements at the outlet of the ductus were more difficult to obtain, and the spatial velocity profile at the outlet depends more on the DV anatomy.

Mass transfer efficiency of a commercial hollow fibre oxygenator during six-hour in vitro perfusion with steady and with pulsatile blood flow

Detailed data about the behaviour of commercial membrane oxygenators with pulsatile blood flow are rarely available. This work deals with an experimental evaluation of the effects induced on gas transfer efficiency by pulsatile perfusion of a hollow fibre oxygenator (Monolyth Sorin Biomedica). The oxygenator was subjected to two in vitro trials both carried out with identical experimental protocols except for the flow type, steady and pulsatile. A roller pump with pulsatile module (Stöckert Instrument) was used to generate both flow types. Three different mean blood flow rates (3.2, 4.0 and 4.8 L/min) were tested. The experiments lasting six hours were carried out using bovine blood with inlet conditions according to AAMI standard requirements. Blood samples were withdrawn every hour and the calculated gas transfer obtained in the two sessions were compared. The device proved to be well-designed for steady flow and to be liable to similar gas transfer performance when used in pulsatile conditions. Furthermore, the use of pulsatile flow rather than steady flow provided more consistent conditions and resulted in a higher eventual oxygen transfer efficiency (final mean difference = 6.2%, p < 0.05), proving to be able to avoid any performance decays.

Influence of membrane oxygenators on the pulsatile flow in extracorporeal circuits: an experimental analysis

An experimental analysis was carried out to evaluate the effects induced by two typical extracorporeal circuits on the pressure and flow generated by a roller pump with a pulsatile module. The hydraulic behaviour of the patient was simulated by means of a mechanical mock-up system consisting of a few lumped parameters reproducing the physiologic vascular impedance. Pressure and flow tracings were acquired at different locations along the circuit using an automatic data acquisition system. Nine lest conditions with different pulse frequency and systolic time values were examined using a mean volumetric flow rate of approximately 4 l/min. A complete analysis of the results obtained in terms of pressure drops and inflow-outflow differences across the components of the arterial line, as well as the calculation of the hydraulic pulsatile power along the circuit, allowed us to assess the influence of the various components upon the pulsatility. The results indicated that the membrane oxygenators tested slightly affect the pulsatility of the flow and the pressure; on the contrary the arterial pipe line is responsible for large damping and head losses. To optimize the use of pulsatile flow for cardiopulmonary bypass it is necessary to reduce the length of the arterial pipe lines thus integrating the circuit as much as possible.

Mathematical modelling of the human foetal cardiovascular system based on Doppler ultrasound data

A lumped parameter model of the human foetal circulation primarily based on blood velocity data derived from the Doppler analysis was developed in this study. It consists of two major parts, the heart and the foetal vascular circulation. The heart model accounts for both ventricular and atrial contractility. The circulation was divided into 19 compliant vascular compartments in order to describe all of the clinically monitored sites. The model parameters refer to the final gestation period and were derived either from literature on foetal sheep circulation or from anatomical dimension monitoring of the human foetus. No control mechanism is incorporated into the model. The model was validated by comparing several index values of simulated velocity curves to those of the experimental Doppler waveforms. The mean and maximum percentual errors in the estimation of the experimental results by the model are 7.7% and 20.1%, respectively. Velocity and pressure tracings of the foetal circulation were investigated, as well as regional blood flow rate distribution.

Hemodynamic changes across the human ductus venosus: a comparison between clinical findings and mathematical calculations

We investigated the hemodynamics of the ductus venosus in the human fetus by means of a combined approach based on Doppler and computational techniques. The aim of our study was to assess the blood velocity changes across the ductus venosus. Color Doppler equipment was used to investigate 29 normal fetuses between 20 and 39 weeks of gestation. Velocities at the systolic peak (S), diastolic peak (D) and atrial contraction (A) were measured at the isthmus and at the outlet of the ductus venosus, and the corresponding angle-independent indices (S/A, (S-A)/S, (S-A)/D) were calculated. A parametric computational model was developed in order to investigate the influence of anatomical features of the ductus venosus on the hemodynamics of the vessel. In all the fetuses the S, D and A velocities at the outlet portion were significantly lower than those at the isthmic part of the ductus venosus (p < 0.0001). The mean percentages of velocity reduction were 23.1%, 26.5% and 33.6%, respectively. Computational simulations also showed a relevant decrease of the velocity along the ductus venosus during the whole cardiac cycle. Velocity reduction along the ductus was mainly due to its conicity and this reduction generally caused velocity values at the outlet to be below the normal range. Conversely, angle-independent indices measured both at the isthmus and at the outlet lay within the same range of the reported reference values and therefore were not influenced by sampling site.

A mathematical model of circulation in the presence of the bidirectional cavopulmonary anastomosis in children with a univentricular heart

The bidirectional cavopulmonary anastomosis is used as a staged procedure or a definitive palliation of univentricular hearts. It is often performed in the presence of an additional blood flow arising from the native pulmonary outflow tract. In this paper, the effects of the severity of the pulmonary outflow obstruction and the pulmonary arteriolar resistance are analysed with regard to the haemodynamics in the superior vena cava and the blood distribution into the lungs. A computer model has been developed, which can represent both the preoperative and the postoperative (systemic and pulmonary) circulations in a patient with a double-outlet univentricular heart. It is particularly detailed in the region of the large vessels and includes components that account for local three-dimensional effects due to the actual shape of the anastomosis. Results have indicated that the mean pressure in the superior vena cava increases from 8.2 to 19.2 mmHg with pulmonary arteriolar resistance ranging from 0.8 to 7.9 Woods units and pulmonary outflow obstruction ranging from 50 to 100%. The percentage flow distribution to the right lung has turned out to be heavily affected by the flow competition and has ranged from 43 to 50% of the total flow to the lungs in the systolic phase, and from 51 to 62% in the diastolic phase. The model allows routinely used clinical indices to be computed, as well as the evaluation of new indices, which is potentially helpful in the clinical assessment of postoperative haemodynamics (e.g. the right-to-left lung flow ratio and the superior vena cava-to-pulmonary flow ratio).

Numerical analysis of steady flow in aorto-coronary bypass 3-D model

Intimal hyperplasia and atherosclerosis have a predominant role in the failure of coronary artery bypass procedures. Theoretical studies and in vivo observations have shown that these pathologies are much more likely to occur in the proximity of end-to-side anastomosis, thus indicating that fluid dynamic conditions may be included in the pathogenic causes of the initiation, progression and complication of intimal hyperplasia. In order to study the fluid dynamics at the anastomosis of an aortocoronary bypass, a three-dimensional mathematical model based on a FEM approach was developed. Steady-state simulations were studied in two different geometrical models of anastomosis which differ in their insertion angles (45 and 60 degree). Flow fields with three-dimensional helical patterns, secondary flows, and shear stresses were also investigated. The results show the presence of low shear stresses on the top wall just beyond the toe of the anastomosis and in the region of the coronary artery before the junction. A high wall shear stress region is present on the lateral wall of the coronary artery immediately downstream from the anastomosis. The influence of flow rate distribution on the secondary flows is also illustrated. These results confirm the sensitivity of flow behavior to the model's geometrical parameters and enhance the importance of reproducing the anastomosis junction as closely as possible in order to evaluate the effective shear stress distribution.

Computational analysis of the ductus venosus fluid dynamics based on Doppler measurements

The simplified Bernoulli equation is currently used to evaluate pressure gradients on the basis of Doppler velocity measurements when direct pressure data require highly invasive procedures. Recently, this method was applied to the ductus venosus (DV) in order to estimate the fetal central venous pressure. The complex geometry- and consequently hemodynamics-of this fetal region suggests caution in automatically converting Doppler velocity measurements to pressure data. To investigate the reliability of the Bernoulli equation for this practice, we simulated the hemodynamics of the branching between the umbilical vein (UV) and the DV on the basis of ultrasonographic data from a normal fetus, using a simplified parametric 3D numerical model of a bent tube with varying cross section (UV) and a smaller trumpet-shaped branch (DV). A finite element formulation has been adopted to solve the governing Navier-Stokes equations. The results show that the simplified Bernoulli equation, despite of its simplicity, provides a good estimation of the pressure drop between the UV and the DV outlet section (with an error of about 0.25 mmHg, equal to 15%, compared with the model results). Nevertheless, attention must be paid to the velocity measurement sites, as discussed in this paper. In turn, the error becomes notable (2.8 mmHg, i.e., 34%) for high velocity values, thus suggesting that the error in evaluating the pressure drop with the simplified Bernoulli equation during fetal inspiratory movements may be substantial.