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.

Mechanical behaviour of nickel-titanium rotary endodontic instruments in simulated clinical conditions: a computational study.

AIM: To develop an accurate finite element (FE) model for studying rotary endodontic instruments and to demonstrate the usefulness of the FE method in improving the knowledge of the mechanical behaviour of these instruments during root canal preparation. METHODOLOGY: An accurate geometrical model of a Ni-Ti ProTaper F1 instrument was created. The interaction between the rotating instrument and differently shaped root canals during the insertion and removal procedure was studied using FE analyses. The complex thermo-mechanical behaviour of the Ni-Ti alloy was reproduced using an ad hoc computational subroutine. With the aim of demonstrating the enhanced performance of the shape memory alloy employment, the same analysis was performed on a 'virtual' ProTaper F1 made of stainless steel. RESULTS: The Ni-Ti instrument operated in its pseudo-elastic range and was able to recover its original shape and to follow the canal curvature without deviation. The radius and the position of the canal curvature are the most critical parameters that determined the stress in the instrument with higher stress levels being produced by decreasing the radius and moving from the apical to the mid root position. CONCLUSIONS: The most demanding working conditions were observed in canals with sharp curves, especially in areas where the instruments had larger diameters. To prevent possible damage to instruments and fracture, it is advised that the instruments should be discarded following their use in such canals.

Modelling drug elution from stents: effects of reversible binding in the vascular wall and degradable polymeric matrix.

Today the most popular approach for the prevention of the restenosis consists in the use of the drug eluting stents. The stent acts as a source of drug, from a coating or from a reservoir, which is transported into and through the artery wall. In this study, the behaviour of a model of a hydrophilic drug (heparin) released from a coronary stent into the arterial wall is investigated. The presence of the specific binding site action is modelled using a reversible chemical reaction that explains the prolonged presence of drug in the vascular tissue. An axi-symmetric model of a single stent strut is considered. First an advection-diffusion problem is solved using the finite element method. Then a simplified model with diffusion only in the arterial wall is compared with: (i) a model including the presence of reversible binding sites in the vascular wall and (ii) a model featuring a drug reservoir made of a degradable polymeric matrix. The results show that the inclusion of a reversible binding for the drug leads to delayed release curves and that the polymer erosion affects the drug release showing a quicker elution of the drug from the stent.

Expansion and drug elution model of a coronary stent.

The present study illustrates a possible methodology to investigate drug elution from an expanded coronary stent. Models based on finite element method have been built including the presence of the atherosclerotic plaque, the artery and the coronary stent. These models take into account the mechanical effects of the stent expansion as well as the effect of drug transport from the expanded stent into the arterial wall. Results allow to quantify the stress field in the vascular wall, the tissue prolapse within the stent struts, as well as the drug concentration at any location and time inside the arterial wall, together with several related quantities as the drug dose and the drug residence times.

Use of rapid prototyping models in the planning of percutaneous pulmonary valved stent implantation.

Percutaneous replacement of the pulmonary valve is a recently developed interventional technique which involves the implantation of a valved stent in the pulmonary trunk. It relies upon careful consideration of patient anatomy for both stent design and detailed procedure planning. Medical imaging data in the form of two-dimensional scans and three-dimensional interactive graphics offer only limited support for these tasks. The paper reports the results of an experimental investigation on the use of arterial models built by rapid prototyping techniques. An analysis of clinical needs has helped to specify proper requirements for such model properties as cost, strength, accuracy, elastic compliance, and optical transparency. Two different process chains, based on the fused deposition modelling technique and on the vacuum casting of thermoset resins in rubber moulds, have been tested for prototype fabrication. The use of anatomical models has allowed the cardiologist's confidence in patient selection, prosthesis fabrication, and final implantation to be significantly improved.

MRI-based multiscale models for the hemodynamic and structural evaluation of surgically reconstructed aortic arches.

The surgical reconstruction of the aortic arch is necessary in pediatric patients suffering from different types of congenital heart malformations, in particular, coarctation of the aorta. Among the reconstruction techniques used in surgical practice end-to-end anastomosis (E/E), Gore-tex graft interposition (GGI) and Gore-tex patch graft aortoplasty (GPGA) are compared in this study with a control model, employing a computational fluid-structure-interaction scheme. This study analyzes the impact of introducing synthetic materials on aortic hemodynamics and wall mechanics. Three-dimensional (3D) geometries of a porcine aortic arch were derived from magnetic resonance imaging (MRI) images. Inlet conditions were derived from MRI velocimetry. A multiscale approach was used for the imposition of outlet conditions, wherein a lumped parameter net provided an active afterload. Evidence was found that ring-like repairs increased blood velocity, whereas GPGA limited it. Vortex presence was greater and longer lasting in GGI. The highest power losses corresponded to GPGA. GGI had an intermediate effect, while E/E dissipated only slightly more than the control case. Wall stresses peak in a longitudinal strip on the subject's left side of the vessel, particularly in the frontal area. There was a concentration of stress at the suture lines. All surgical techniques performed equally well in restoring physiological pressures.

A method for coronary bifurcation centerline reconstruction from angiographic images based on focalization optimization.

A method for the reconstruction of a vessel centerline from angiographic images is outlined in this work. A typical coronary artery segment with bifurcations was emulated with a 3D printed static phantom and several angiograms were acquired at various angular positions on the C-Arm. The effectiveness of the reconstruction turned out to be largely influenced by the intrinsic parameters of the angiographic system, particularly the homogeneous coordinates system scaling factor λ. Therefore, recourse was made to a heuristic optimization method to estimate the optimal value of λ for each view. We measured the reliability of the reconstruction method by varying the fitness function of the optimization step and measuring the distances of 8 test points in comparison to the corresponding points identified in the µCT centerline. Preliminary results showed that, with an adequate number of views, the adoption of the optimal fitness function allowed the median distance error to be decreased below the acceptance threshold of 10%. As expected, the reliability of the method is improved by increasing the number of processed views.

Effects of respiration and gravity on infradiaphragmatic venous flow in normal and Fontan patients.

BACKGROUND: In the Fontan circulation, pulmonary and systemic vascular resistances are in series. The implications of this unique arrangement on infradiaphragmatic venous physiology are poorly understood. METHODS AND RESULTS: We studied the effects of respiration and gravity on infradiaphragmatic venous flows in 20 normal healthy volunteers (control) and 48 Fontan patients (atriopulmonary connection [APC] n=15, total cavopulmonary connection [TCPC] n=30). Hepatic venous (HV), subhepatic inferior vena caval (IVC), and portal venous (PV) flow rates were measured with Doppler ultrasonography during inspiration and expiration in both the supine and upright positions. The inspiratory-to-expiratory flow rate ratio was calculated to reflect the effect of respiration, and the supine-to-upright flow rate ratio was calculated to assess the effect of gravity. HV flow depended heavily on inspiration in TCPC compared with both control and APC subjects (inspiratory-to-expiratory flow rate ratio 3.4, 1.7, and 1.6, respectively; P:<0.0001). Normal PV flow was higher in expiration, but this effect was lost in TCPC and APC patients (inspiratory-to-expiratory flow rate ratio 0.8, 1.0, and 1.1, respectively; P:=0.01). The respiratory influence on IVC flow was the same in all groups. Gravity decreased HV flow more in APC than in TCPC patients (supine-to-upright flow rate ratio 3.2 versus 2.1, respectively; P:<0.04) but reduced PV flow equally in all groups. CONCLUSIONS: Gravity and respiration have important influences on infradiaphragmatic venous return in Fontan patients. Although gravity exerts a significant detrimental effect on lower body venous return, which is more marked in APC than in TCPC patients, the beneficial effects of respiration in TCPC patients are mediated primarily by an increase in HV flow. These effects may have important short- and long-term implications for the hemodynamics of the Fontan circulation.

Aortic tissue properties in porcine models: A comparison of ex vivo mechanical test results after simulated aortic arch reconstructions.

Surgical interventions on the arterial wall can produce modifications to its tissue characteristics, and the addition of synthetic materials of different types can have implications on hemodynamics and blood vessel wall behavior. This work studies the midterm effects of end-to-end anastomosis (E/E), Gore-tex graft interposition (GGI) and Gore-tex patch graft aortoplasty (GPGA) in aortic arch reconstruction. The study comprised of two groups of healthy Danish sows. The sows in the first group (short term (ST)) weighed about 40 kg, underwent a surgical operation and were sacrificed on the same day. The sows in the second group (midterm (MT)) weighed 5-10 kg, underwent a surgical operation and were then allowed to grow to a weight of about 30-40 kg, before being sacrificed. One sow in each group was scheduled for E/E and one sow for GGI. One sow in ST and two sows in MT received GPGA. The overall average wall thickness was 1.93 mm. Relaxation constant values were significantly higher for ST (5.221 +/- 1.832 sec) than for MT (2.184 +/- 1.216 sec). GPGA showed a greater impact on relaxation than other procedures, enhancing the viscous character. The working-point Young's modulus (Epw ) was not significantly different in ST and MT. Circumferential samples had different Epw (0.419 +/- 0.77 MPa) from longitudinal samples (0.902 +/- 0.378 MPa). There also appeared to be a significant difference between samples cut longitudinally on the left and the right sides of the wall. The overall average Epw value was 0.6609 +/- 0.3641 MPa.

Use of computational fluid dynamics in the design of surgical procedures: application to the study of competitive flows in cavo-pulmonary connections.

Computational fluid dynamic methods based on a finite-element technique were applied to the study of (1) competition of flows in the inferior and superior venae cavae in total cavopulmonary connection, and (2) competition between flow in the superior vena cava and forward flow from a stenosed pulmonary artery in bidirectional cavopulmonary anastomosis. Models corresponding to various degrees of offsetting and shape of the inferior vena caval anastomosis were simulated to evaluate energy dissipation and flow distribution between the two lungs. A minimal energy loss with optimal flow distribution between the two lungs was obtained by enlarging the inferior vena caval anastomosis toward the right pulmonary artery. This modified technique of total cavopulmonary connection is described. A computational model of the operation was developed in an attempt to understand the mechanisms of postoperative failure. In tight pulmonary artery stenosis (75%), the pulsatile forward flow is primarily directed to the left pulmonary artery, with little influence on superior vena caval pressure and the right pulmonary artery. Pulsatile forward flows corresponding to 15%, 30%, 45%, and 60% of the systemic artery output increased the mean pulmonary artery and superior vena caval pressures by 1, 1.7, 2.4, and 3.6 mm Hg, respectively. Although the modeling studies were not able to determine the cause of postoperative failure, they emphasize the impact of local geometry on flow dynamics. More simulations are required for further investigation of the problem.

Subdiaphragmatic venous hemodynamics in the Fontan circulation.

OBJECTIVE: We investigated the subdiaphragmatic venous physiology in patients subjected to the Fontan operation to understand some of the early and late problems of this circulation. METHODS: Flows were evaluated by Doppler ultrasonography in the subhepatic inferior vena cava, hepatic vein, and portal vein during respiratory monitoring and with a tilt table. Twenty control subjects (group A) and 56 patients who had the Fontan operation, 27 in functional class I (group B) and 29 in class III or IV (group C), were studied. Inspiratory/expiratory flow ratio was calculated to reflect respiratory effects, and upright/supine flow ratio was calculated to assess gravity effects. Inferior vena caval, hepatic venous, and wedged hepatic venous pressures were measured during catheterization in 21 control subjects and 25 Fontan patients. The difference between wedged and hepatic venous pressures represents the transhepatic venous pressure gradient. RESULTS: Fontan hepatic venous flow depended more on inspiration than control, but without difference between groups B and C (inspiratory/expiratory flow ratios: 1.7, 2.9, and 2.9, respectively; P <.02). Normal portal venous flow was higher in expiration; this effect was lost in group B and reversed in group C (inspiratory/expiratory flow ratios: 0.8, 1.0, and 1.3; P <.0005). Gravity reduced portal venous flow in groups A and B, but progression to functional class III or IV (group C) exacerbated this effect (upright/supine flow ratios: 0.8, 0.7, and 0.5; P <.01). Inferior vena caval, hepatic venous, and wedged hepatic venous pressures (in millimeters of mercury) in the Fontan groups were all elevated compared with the control group (inferior vena cava, 14.4 +/- 4.4 vs 5.9 +/- 2.3; hepatic vein, 14.7 +/- 4.5 vs 5.9 +/- 1.9; wedged hepatic vein, 14.7 +/- 4.0 vs 8.3 +/- 2.6; P <.0001). However, transhepatic venous pressure gradient in the Fontan group was lower than in the control group (0.5 +/- 0.5 vs 2.4 +/- 2.0; P <.001). Univariate analysis of inferior vena caval pressure and transhepatic venous pressure gradient showed significant inverse correlation (r = 0.6, P <.002). CONCLUSIONS: In patients who are in functionally poorer condition after the Fontan operation, portal venous flow loses normal expiratory augmentation and adverse gravity influence is enhanced. These suboptimal flow dynamics, coupled with higher splanchnic venous pressures and lower transhepatic venous pressure gradients, suggest that hepatic sinusoids are congested, acting as "open tubes." Transhepatic gradient loss is incrementally worse with higher caval pressures. These observations may be responsible for late gastrointestinal problems in patients who have had the Fontan operation.

Determination of cerebrospinal fluid shunt function with water-soluble contrast medium.

Determination of cerebrospinal fluid shunt patency with water-soluble contrast medium is a simple, rapid, reliable, and safe technique. Since September, 1974, the authors performed 113 examinations. With the Spitz-Holter valve, only the atrial catheter can be studied, but, with the Pudenz valve and with the shunting devices that have a double-dome reservoir, both the proximal and the distal catheter can be visualized. Through the ventricular catheter a full ventriculographic study can be made, demonstrating ventricular size, malposition of the catheter, and the lesion that caused the hydrocephalus, or its evolution. The problem of collapsed ventricules, in which clinical and "manual" evaluation of the flushing device can give misleading findings, is emphasized. The injection of the atrial or peritoneal catheter in the pathological cases demonstrated its blockage, level of disconnection, malposition, sleeve, or cyst formation. Computerized tomography has only slightly decreased the number of these studies: when the ventricles are large, the examination with water-soluble contrast medium is still needed to demonstrate the exact level of malfunction. This demonstration has decreased the number of the total revisions complete changes of shunting systems, eliminating some unnecessary changes of normally functioning catheters.

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.

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).

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 surgical approach to intraorbital tumors in children.

A series of 20 children operated for intraorbital tumors is presented. Ten of the patients were operated by the lateral approach, requiring orbitotomy in only 4 cases. Ten patients were operated by the medial transcranial transfrontal exposure. The surgical approach is mainly related to the location of the tumor, regardless of its malignancy. The relevance of the different neuroradiological procedures and the advantages of the different surgical approach are discussed.

Computational transient simulations with varying degree and shape of pulmonic stenosis in models of the bidirectional cavopulmonary anastomosis.

The bidirectional cavopulmonary anastomosis is a surgical technique utilized to treat severe congenital malformations of the right part of the heart. It is obtained by anastomosing the superior vena cava to the superior aspect of the undivided right pulmonary artery. Transient simulations with a three-dimensional model of the bidirectional cavopulmonary anastomosis were carried out to evaluate the haemodynamics of different types of pulmonic stenosis (shape and severity of the obstruction). Models with a tunnel-like (supravalvar) or discrete (valvar) pulmonic stenosis with different values of reduction of cross-sectional area (60 and 75%) were investigated and compared to a model without stenosis. Calculations were based on a finite element method analysis. The results showed that a tighter stenosis can lead to a blood volume flow to the left lung reaching 70% of the total pulmonary flow. Moreover, the flow fields are highly influenced by the presence and shape of the pulmonic stenosis; the most intense jets in the left pulmonary artery occur for a discrete pulmonic stenosis of 75%. The flow in the right pulmonary artery is nearly steady because it is damped down by the steady caval flow.

Effects of pulmonary afterload on the hemodynamics after the hemi-Fontan procedure.

A computational fluid dynamics study based on the application of the finite volume method has been performed to investigate the effects of the pulmonary afterload on the hemodynamics after the hemi-Fontan procedure. This operation is generally used as part of a series of staged procedures to treat complex congenital malformations of the heart. It consists of re-directing the superior vena caval flow from the right atrium into the pulmonary arteries, by-passing the right ventricle while excluding the inferior caval flow from the lungs. To reproduce correctly the pulmonary afterload conditions, a simplified lumped-parameter mechanical model of the pulmonary circulation has been developed and linked to the finite volume solver. In addition, the effect of a stenosis in the left pulmonary artery was also examined. In this paper the adopted methodology is presented, together with some of the preliminary results. The model has been used to simulate the local fluid dynamics for different values of the pulmonary arteriolar resistance and lung resistances, allowing a quantitative evaluation of the dissipated energy and the flow distribution into the lungs. The results show that both flow distribution into the lungs and energy dissipation after the hemi-Fontan procedure are only minimally affected by the pulmonary arteriolar resistance.

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).