Culture of 3D bioprinted bone constructs requires an increased fluid dynamic stimulation.

In vitro flow-induced mechanical stimulation of developing bone tissue constructs has been shown to favor mineral deposition in scaffolds seeded with cells directly exposed to the fluid flow. However, the effect of fluid dynamic parameters, such as shear stress (SS), within 3D bioprinted constructs is still unclear. Thus, this study aimed at correlating the SS levels and the mineral deposition in 3D bioprinted constructs, evaluating the possible dampening effect of the hydrogel. Human mesenchymal stem cells (hMSCs) were embedded in 3D bioprinted porous structures made of alginate and gelatin. 3D bioprinted constructs were cultured in an osteogenic medium assessing the influence of different flow rates (0, 0.7 and 7 ml/min) on calcium and collagen deposition through histology, and bone volume (BV) through micro-computed tomography. Uniform distribution of calcium and collagen was observed in all groups. Nevertheless, BV significantly increased in perfused groups as compared to static control, ranging from 0.35±0.28 mm3, 11.90±8.74 mm3 and 25.81±5.02 mm3 at week 3 to 2.28±0.78 mm3, 22.55±2.45 mm3 and 46.05±5.95 mm3 at week 6 in static, 0.7 and 7 ml/min groups, respectively. SS values on construct fibers in the range 10-100 mPa in 7 ml/min samples were twice as high as those in 0.7 ml/min samples showing the same trend of BV. The obtained results suggest that it is necessary to enhance the flow-induced mechanical stimulation of cell-embedding hydrogels to increase the amount of mineral deposited by hMSCs, compared to what is generally reported for the development of in vitro bone constructs. STATEMENT OF SIGNIFICANCE: In this study, we evaluated for the first time how the hydrogel structure dampens the effect of flow-induced mechanical stimulation during the culture of 3D bioprinted bone tissue constructs. By combining computational and experimental techniques we demonstrated that those shear stress thresholds generally considered for culturing cells seeded on scaffold surface, are no longer applicable when cells are embedded in 3D bioprinted constructs. Significantly, more bone volume was formed in constructs exposed to shear stress values generally considered as detrimental than in constructs exposed shear stress values generally considered as beneficial after 3 weeks and 6 weeks of dynamic culture using a perfusion bioreactor.

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.

Haematocrit heterogeneity in blood flows past microfluidic models of oxygenating fibre bundles.

Blood oxygenators act as an extracorporeal artificial lung during certain types of cardiac surgery and intensive care therapies. Inside these devices, blood is forced to flow across an oxygenating bundle, encountering interstitial gaps comparable to those typical of the microvasculature. Despite the well-known effects of such length scales on haemorheology and red blood cell (RBC) behavior, these are generally overlooked in oxygenator modeling and design; it is persistently assumed that RBCs are homogeneously distributed throughout the oxygenating bundle, independently of their microstructure arrangement or main flow directions. The goal of this study is to provide preliminary experimental evidence of heterogeneous RBC distributions inside oxygenating fibre bundles. To this end, a number of microchannels were manufactured inspired by actual oxygenating devices, considering simplified versions of their microstructure. These comprise staggered arrays of micro pillars, which were perfused with RBC suspensions, with feed haematocrit (Ht) and velocities relevant for clinical use. The microchannels were imaged using a microscope and high-speed camera to accurately capture cell distribution. The imaged blood flows revealed the non-uniform nature of RBC distributions in the arrays, characterized by local Ht gradients particularly around the O2 sources inside the bundle. These heterogeneous distributions should be accounted for during oxygenator design, as RBC concentration plays a key role in O2 transport and, ultimately, overall device performance.

Computational evaluation of oxygen and shear stress distributions in 3D perfusion culture systems: macro-scale and micro-structured models.

We present a combined macro-scale/micro-scale computational approach to quantify oxygen transport and flow-mediated shear stress to human chondrocytes cultured in three-dimensional scaffolds in a perfusion bioreactor system. A macro-scale model was developed to assess the influence of the bioreactor design and to identify the proper boundary conditions for the micro-scale model. The micro-scale model based on a micro-computed tomography (microCT) reconstruction of a poly(ethylene glycol terephthalate)/poly(butylene terephthalate) (PEGT/PBT) foam scaffold, was developed to assess the influence of the scaffold micro-architecture on local shear stress and oxygen levels within the scaffold pores. Experiments were performed to derive specific oxygen consumption rates for constructs perfused under flow rates of 0.3 and 0.03 ml min(-1). While macro-scale and micro-scale models predicted similar average oxygen levels at different depths within the scaffold, microCT models revealed small local oxygen variations within the scaffold micro-architecture. The combined macro-scale/micro-scale approach indicated that 0.3 ml min(-1), which subjected 95% of the cells to less than 6.3 mPa shear, would maintain the oxygen supply throughout the scaffold above anoxic levels (>1%), with 99.5% of the scaffold supplied with 8-2% O(2). Alternatively, at 0.03 ml min(-1), the macro-scale model predicted 6% of the cells would be supplied with 0.5-1% O(2), although this region of cells was confined to the periphery of the scaffold. Together with local variations predicted by the micro-scale model, the simulations underline that in the current model system, reducing the flow below 0.03 ml min(-1) would likely have dire consequences on cell viability to pronounced regions within the engineered construct. The presented approach provides a sensitive tool to aid efficient bioreactor optimization and scaffold design.

Chondrocyte response to high regimens of cyclic hydrostatic pressure in 3-dimensional engineered constructs.

PURPOSE: Despite widespread use of 3-dimensional (3D) micro-porous scaffolds to promote their potential application in cartilage tissue engineering, only a few studies have examined the response to hydrostatic pressure of engineered constructs. A high cyclic pressurization, currently believed to be the predominant mechanical signal perceived by cells in articular cartilage, was used here to stimulate bovine articular chondrocytes cultured in a synthetic 3D porous scaffold (DegraPol). METHODS: Construct cultivation lasted 3 days with applied pressurization cycles of amplitude 10 MPa, frequency 0.33 Hz, and stimulation sessions of 4 hours/day. RESULTS: At 3 days of culture, with respect to pre-culture conditions, the viability of the pressurized constructs did not vary, whereas it underwent a 16% drop in the unpressurized controls. Synthesis of alfa-actin was 34% lower in all cultured constructs. Synthesis of collagen II/collagen I did not vary in pressurized constructs, was 76% lower in unpressurized controls, and was around 230% higher in pressurized constructs with respect to unpressurized controls. Chondrocytes showed a phenotypic spherical morphology at time zero and at 3 days of pressurized culture. CONCLUSIONS: Although the passage from 2D expansion to 3D geometry was effective to guide cell differentiation, only mechanical conditioning enabled the maintenance and further cell differentiation toward a mature chondrocytic phenotype.

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.

A new bioreactor for the controlled application of complex mechanical stimuli for cartilage tissue engineering.

Mechanical stimuli have been shown to enhance chondrogenesis on both animal and human chondrocytes cultured in vitro. Different mechanical stimuli act simultaneously in vivo in cartilage tissue and their effects have been extensively studied in vitro, although often in a separated manner. A new bioreactor is described where different mechanical stimuli, i.e. shear stress and hydrostatic pressure, can be combined in different ways to study the mechanobiology of tissue engineered cartilage. Shear stress is imposed on cells by forcing the culture medium through the scaffolds, whereas a high hydrostatic pressure up to 15 MPa is generated by pressurizing the culture medium. Fluid-dynamic experimental tests have been performed and successful validation of the bioreactor has been carried out by dynamic culture of tissue-engineered cartilage constructs. The bioreactor system allows the investigation of the combined effects of different mechanical stimuli on the development of engineered cartilage, as well as other possible three-dimensional tissue-engineered constructs.

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.

2D µ-Particle Image Velocimetry and Computational Fluid Dynamics Study Within a 3D Porous Scaffold.

Transport properties of 3D scaffolds under fluid flow are critical for tissue development. Computational fluid dynamics (CFD) models can resolve 3D flows and nutrient concentrations in bioreactors at the scaffold-pore scale with high resolution. However, CFD models can be formulated based on assumptions and simplifications. µ-Particle image velocimetry (PIV) measurements should be performed to improve the reliability and predictive power of such models. Nevertheless, measuring fluid flow velocities within 3D scaffolds is challenging. The aim of this study was to develop a µPIV approach to allow the extraction of velocity fields from a 3D additive manufacturing scaffold using a conventional 2D µPIV system. The µ-computed tomography scaffold geometry was included in a CFD model where perfusion conditions were simulated. Good agreement was found between velocity profiles from measurements and computational results. Maximum velocities were found at the centre of the pore using both techniques with a difference of 12% which was expected according to the accuracy of the µPIV system. However, significant differences in terms of velocity magnitude were found near scaffold substrate due to scaffold brightness which affected the µPIV measurements. As a result, the limitations of the µPIV system only permits a partial validation of the CFD model. Nevertheless, the combination of both techniques allowed a detailed description of velocity maps within a 3D scaffold which is crucial to determine the optimal cell and nutrient transport properties.

µ-Particle tracking velocimetry and computational fluid dynamics study of cell seeding within a 3D porous scaffold.

Cell seeding of 3D scaffolds is a critical step in tissue engineering since the final tissue properties are related to the initial cell distribution and density within the scaffold unit. Perfusion systems can transport cells to the scaffold however; the fact that cells flow inside the scaffold pores does not guarantee cell deposition onto the scaffold substrate and cell attachment. The aim of this study was to investigate how fluid flow conditions modulate cell motion and deposition during perfusion. For such a purpose, a multiphase-based computational fluid dynamics (CFD) model was developed in conjunction with particle tracking velocimetry experiments (PTV) which for the first time were applied to observe cell seeding inside a 3D scaffold. CFD and PTV results showed the strong effect of gravity for lower flow rates leading to cell sedimentation and poor transport of cells to the scaffold. Higher flow rates help overcome the effect of gravity so more cells travelling inside the scaffold were found. Nonetheless, fluid flow drags cells along the fluid streamlines without intercepting the scaffold substrate. As a consequence, if cells do not deposit into the scaffold substrate, cell adhesion cannot occur. Therefore, cell-scaffold interception should be promoted and the present computational model which predicts the effect of gravity and fluid drag on cells trajectories could serve to optimise bioreactors and enhance cell seeding efficiency.

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.

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.

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.

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.

Fluid-structure interaction problems in bio-fluid mechanics: a numerical study of the motion of an isolated particle freely suspended in channel flow.

In this paper a problem belonging to the moving boundary class is tackled with a 2-D application of computational fluid dynamics techniques. The motion of an isolated rigid particle freely suspended in an incompressible Newtonian fluid in a narrow channel is studied numerically at a low Reynolds number, yet different from zero. The actual problem consists of two coupled problems: the motion of the viscous fluid and that of the rigid particle suspended and convected with the fluid. The full Navier-Stokes equations (i.e. both transient and convective terms are included) are solved in the fluid domain by means of the finite element method, while the motion of the particle is determined on the basis of a rigid act of motion. Results from simulations corresponding to differential initial positions of the particle are shown in this paper: they allow one to study the rotational motions of the particle as well as its displacements. The goal of the paper is to analyse the lateral displacement behaviour of the particle, already observed in experimental studies in microcirculation. In particular, lateral migrations are supposed to be due to inertial forces acting in the fluid around the moving particle combined with the proximity of the resting wall (wall effect). Preliminary results are in fairly good agreement with those available in the literature.

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.