A new method to evaluate patient characteristic response to ultrafiltration during hemodialysis.

BACKGROUND: Several factors are involved in the pathogenesis of dialysis discomfort interfering with optimal fluid removal and reducing the efficacy of the treatment; the most important one is a decrease in blood volume caused by an imbalance between ultrafiltration (UF) and plasmarefilling (PR) rates. OBJECTIVES: This study is aimed at devising a method to tailor the dialysis therapy to each individual patient, by analyzing the relationship between PR and UF during the sessions in stable patients and widening the knowledge of fluid exchanges during the treatment. METHODS: Thirty stable patients undergoing maintenance hemodialysis were enrolled. Three dialysis sessions were monitored for each patient; systemic pressure, blood composition, blood volume % variation, weight loss and conductivity were recorded repeatedly. A Plasma Refilling Index (PRI), defined and calculated by means of parameters measured throughout the dialysis, was introduced as a novel instrument to study plasma refilling phenomena. Results. The PRI provides understanding of patient response (in terms of plasma refilling) to the set UF. In the monitored sessions, the PRI trend is found to be characteristic of each patient; a PRI course that is at variance with the characteristic trend is a signal of inadequate or unusual dialysis scheduling. Moreover, statistical analysis highlights two different PRI trends during the first hour and during the rest of the treatment, suggesting the presence of different treatment phases. CONCLUSION: The main advantage of the PRI index is that it is non-invasive peculiar to each patient and easy to compute in a dialysis routine based on online data recorded by the monitor. A deviation from the characteristic trend may be a warning for the clinician. The analysis of the PRI trend also suggests how to modulate UF as a function of interstitial to intravascular fluid removal balance during dialysis.

The cardiac torsion as a sensitive index of heart pathology: A model study.

The torsional behaviour of the heart (i.e. the mutual rotation of the cardiac base and apex) was proved to be sensitive to alterations of some cardiovascular parameters, i.e. preload, afterload and contractility. Moreover, pathologies which affect the fibers architecture and cardiac geometry were proved to alter the cardiac torsion pattern. For these reasons, cardiac torsion represents a sensitive index of ventricular performance. The aim of this work is to provide further insight into physiological and pathological alterations of the cardiac torsion by means of computational analyses, combining a structural model of the two ventricles with simple lumped parameter models of both the systemic and the pulmonary circulations. Starting from diagnostic images, a 3D anatomy based geometry of the two ventricles was reconstructed. The myocytes orientation in the ventricles was assigned according to literature data and the myocardium was modelled as an anisotropic hyperelastic material. Both the active and the passive phases of the cardiac cycle were modelled, and different clinical conditions were simulated. The results in terms of alterations of the cardiac torsion in the presence of pathologies are in agreement with experimental literature data. The use of a computational approach allowed the investigation of the stresses and strains in the ventricular wall as well as of the global hemodynamic parameters in the presence of the considered pathologies. Furthermore, the model outcomes highlight how for specific pathological conditions, an altered torsional pattern of the ventricles can be present, encouraging the use of the ventricular torsion in the clinical practice.

Fluid dynamic models as a guide to determine prosthetic heart valve diameter.

The diameter of prosthetic heart valves is usually chosen according to the anatomic annulus size as determined during open-heart surgery. Therefore, this approach does not take into account the dimensional changes induced by heart pathology and surgical procedures. In addition, current practice fails to consider the variations of heart dimensions due to hemodynamic improvement following valve replacement. Here we suggest a method to determine the appropriate prosthesis diameter according to the hemodynamic features of the patient, to its kind of activity, and to the type of prosthesis. Assuming that the pressure drop across a valve can be calculated as delta p = apv 2/2, and considering the variation of blood flow with time and its change induced by frequency, it is possible to obtain the relationship between pressure drop and prosthetic valve diameter. The results obtained with this analytical method have been plotted on diagrams which allow the graphical determination of the proper valve diameter.

A numerical fluid mechanical study of repaired congenital heart defects. Application to the total cavopulmonary connection.

A computational fluid dynamics study based on the application of the finite element method has been performed to investigate the local hemodynamics of the total cavopulmonary connection. This operation is used to treat congenital malformations of the right heart and consists of a by-pass of the right ventricle. In this paper the adopted methodology is presented, together with some of the preliminary results. A three-dimensional parametric model of the connection and a lumped-parameter mechanical model of the pulmonary circulation have been developed. The three-dimensional model has been used to simulate the local fluid dynamics for different designs of the connection, allowing a quantitative evaluation of the dissipated energy in each of the examined configurations. The pulmonary afterload of the three-dimensional model has been reproduced by coupling it with the pulmonary mechanical model. The results show that, from a comparative point of view, the energetic losses can be greatly reduced if a proper hydraulic design of the connection is adopted, which also allows control of the blood flow distribution into the lungs.

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.

Hydraulic functional characterisation of aortic mechanical heart valve prostheses through lumped-parameter modelling.

Lumped-parameter modelling techniques are proposed as a method for studying the hydraulic characteristics of mechanical prosthetic heart valves (PHVs). The global hydraulic behaviour of PHVs in the open position was modelled by taking into account the (nonlinear) resistive and (linear) inertial factors governing the time-dependent relationship between transvalvular pressure drop and fluid flow rate, and neglecting the leaflets' opening and closure transient phenomena. Statistically defined indices associated to the parameters' values attest how properly the model describes PHV hydraulic behaviour. Local fluid dynamics is not modelled with this approach. The proposed method was implemented in a software program and applied to the characterisation of the aortic StJude Medical, StJude Medical Hemodynamic Plus and CarboMedics PHVs, basing on steady- and pulsatile-flow hydraulic-bench experimental data. The results showed that reliable parameters expressing hydraulic resistance can be derived from steady-flow data (R(2)>0.995). Inertance parameters derived from pulsatile-flow experiments are liable to a degree of uncertainty (confidence intervals up to 17%), however, comparing the reconstructed vs. measured pressure drop during systolic time demonstrates that this deficiency is mostly due to the missing description of initial, transient oscillations presumably related to the leaflets' opening (not modelled).

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).

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.

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.

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.

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.

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.

Assessment of the influence of the compliant aortic root on aortic valve mechanics by means of a geometrical model.

In recent years several researchers have suggested that the changes in the geometry and angular dimensions of the aortic root which occur during the cardiac cycle are functional to the optimisation of aortic valve function, both in terms of diminishing leaflet stresses and of fluid-dynamic behaviour. The paper presents an analytical parametric model of the aortic valve which includes the aortic root movement. The indexes used to evaluate the valve behaviour are the circumferential membrane stress and the stress at the free edge of the leaflet, the index of bending strain, the bending of the leaflet at the line attachment in the radial and circumferential directions and the shape of the conduit formed by the leaflets during systole. In order to evaluate the role of geometric changes in valve performance, two control cases were considered, with different reference geometric configuration, where the movement of the aortic root was ignored. The results obtained appear consistent with physiological data, especially with regard to the late diastolic phase and the early ejection phase, and put in evidence the role of the aortic root movement in the improvement of valve behaviour.

Computational fluid dynamic simulations of cavopulmonary connections with an extracardiac lateral conduit.

Complex congenital heart defects due to the absence of a ventricular chamber can often be treated by the Fontan surgical procedure. The objective of this work was to quantify the haemodynamics in the Fontan operation (cavopulmonary connection) with extracardiac lateral conduit. Four different models based on the finite element method were constructed with different lengths of inferior anastomosis (range 18-25 mm) and inclinations of the conduit (33 and 47.5 degrees). Mass conservation and Navier-Stokes equations were solved by means of the FIDAP code, based on the finite element method. The left-to-right pulmonary flow ratio and percentage inferior caval blood to the left lung were the highest with the smallest anastomosis and highest inclination: 1.35 and 83.26%, respectively. Dissipated power percentage was higher with the largest anastomosis than with the smallest (19.4 vs 15.8%). It was concluded that, when performing a total cavopulmonary connection, an extracardiac lateral conduit: (i) diverts more flow to the left lung, and (ii) shows higher energy losses when compared with a connection with intra-atrial tunnel. This study could be useful to evaluate the incidence of pulmonary arteriovenous malformations.

Computational fluid dynamics of artificial heart valves.

A large number of in vitro studies during the last thirty years have assessed the fluid dynamic behavior of different artificial heart valves. The present study illustrates the utility of the Finite Element Method for fluid dynamic evaluation of prosthetic heart valves. The valves investigated were the Bjork-Shiley Convex-Concave (curved disc), the Medtronic-Hall (flat disc) and the Carbomedics (bileaflet). These three types were chosen in order to clarify the role of different occluder geometries on global and local fluid dynamics. The Finite Element Method was used to calculate pressure and velocity fields in the fluid domain around each valve. There were significant differences, mainly in local fluid dynamics, between the three valves. The Reynolds number also plays an important role.

Principle of operation, design criteria and fluid dynamics of a new bileaflet heart valve prosthesis.

Bileaflet heart valves show the best fluid dynamic behaviour among mechanical valves and, as a consequence, give the best clinical results. A new bileaflet heart valve has been designed whose main characteristics are the kind of leaflet movement, low profile, fluid dynamics and material. Two flat leaflets move freely inside a very low profile housing ring. The movement is described by the rolling without sliding of the leaflet surface around a cylindrical surface on the inner wall of the housing. The opening angle is 85 degrees. Both the leaflets and the housing are machined from a solid piece of titanium and then covered with carbon by ion beam techniques. The design phase and the first fluid dynamic evaluation were done by numerical methods.

Virtual extracorporeal circulation process.

Virtual instruments for an extracorporeal circulation (ECC) process were developed to simulate the reactions of a patient to different artificial perfusion conditions. The computer simulation of the patient takes into account the hydraulic, volume, thermal and biochemical phenomena and their interaction with the devices involved in ECC (cannulae dimensions, oxygenator and filter types, pulsatile or continuous pump and thermal exchangers). On the basis of the patient's initialisation data (height, weight, Ht) and perfusion variables (pump flow rate, water temperature, gas flow rate and composition) imposed by the operator, the virtual ECC monitors simulated arterial and venous pressure tracings in real time, along with arterial and venous flow rate tracings, urine production tracing and temperature levels. Oxyhemoglobin arterial and venous blood saturation together with other related variables (pO2, pCO2, pH, HCO3 are also monitored. A drug model which allows the simulation of the effect of vasodilator and diuretic drugs is also implemented. Alarms are provided in order to check which variables (pressure, saturation, pH, urine flow) are out of the expected ranges during the ECC simulation. Consequently the possibility of modifying the control parameters of the virtual devices of the ECC in run-time mode offers an interaction mode between the operator and the virtual environment.

Haemodynamic alteration in patients undergoing chronic haemodialysis.

Fifteen elderly patients, 13 of them undergoing chronic haemodialysis, 1 acute and 1 coming from Continuous Ambulatory Peritoneal Dialysis (CAPD) either with no significant cardiovascular alteration or presenting various cardiovascular pathologies were studied to investigate the possibility of onset of hypotensive episodes during dialytic treatment depending on cardiac or vascular alteration in the patients. Monitoring of the arterial pressure on the contralateral arm and on the lower limbs by using the Takeda System, made it possible to compute the Windsor Index (WI). The figures obtained were correlated to the Ejection Fraction Index (EFI) to investigate the relation between WI alteration and haemodynamic variations in the patient. The results show that cardiothoracic recirculation is much more present in those patients with pathologies that affect EFI which worsens during dialysis due to the loss of fluid. Moreover the results obtained from the two patients with temporary access and no evident cardiovascular pathology show the constancy of the haemodynamic parameters throughout the dialytic treatment.

A new pulsatile blood pump for adult cardiopulmonary bypass: design criteria and preliminary fluid dynamic evaluation.

A new pulsatile pumping device for adult cardiopulmonary bypass has been designed. Its main characteristic consists in having a fully disposable pumping head, since polymeric materials have been adopted for the housing as well as for the built-in inlet and outlet valves. Furthermore, the valves show an innovative design, as they are ring-shaped and accomplish their task by virtue of their elastic deformability. The design phase of the pumping head and the first fluid dynamic evaluations have been performed by numerical methods. Particularly, a three-dimensional CAD model of the pumping head (in the current configuration) is presented in this paper. On the basis of this model, computational fluid dynamic analysis of the hydraulic behaviour has been performed for some components. The obtained results show complex velocity patterns in the pumping chamber during the filling phase as well as limited pressure gradients across the inlet valve.