Finite element analysis of cancellous bone failure in the vertebral body of healthy and osteoporotic subjects.

The aim of this work is to assess the fracture risk prediction of the cancellous bone in the body of a lumbar vertebra when the mechanical parameters of the bone, i.e. stiffness, porosity, and strength anisotropy, of elderly and osteoporotic subjects are considered. For this purpose, a non-linear three-dimensional continuum-based finite element model of the lumbar functional spinal unit L4-L5 was created and strength analyses of the spongy tissue of the vertebral body were carried out. A fabric-dependent strength criterion, which accounts for the micro-architecture of the cancellous bone, based on histomorphometric analyses was used. The strength analyses have shown that the cancellous bone of none of the subject types undergoes failure under loading applied during normal daily life like axial compression; however, bone failure occurs for the osteoporotic segment, subjected to a combination of the compression preloading and moments in the sagittal or in the frontal plane, which are conditions that may not be considered to occur 'daily'. In particular, critical stress conditions are met because of the high porosity values in the horizontal direction within the cancellous bone. The computational approach presented in the paper can potentially predict the material fracture risk of the cancellous bone in the vertebral body and it may be usefully employed to draw failure maps representing, for a given micro-architecture of the spongy tissue, the critical loading conditions (forces and moments) that may lead to such a risk. This approach could be further developed in order to assess the effectiveness of biomedical devices within an engineering approach to the clinical problem of the spinal diseases.

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion.

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice-Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.

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.

The in-vivo wear performance of prosthetic femoral heads with titanium nitride coating.

This paper reports the study performed on four titanium nitride (TiN) coated prosthetic femoral heads collected at revision surgery together with patient data. Surface topology has been examined using Scanning Electron Microscopy (SEM) and elemental analysis of both coating and substrate have been evaluated using energy-dispersive X-ray spectrometry. Quantitative assessment of the surface topography is achieved using contacting profilometry. The average Ra roughness value is calculated at five different locations for each femoral head. The UHMWPE counterface worn volume has been measured directly on the acetabular components. TiN fretting and coating breakthrough occurred in two of the four components examined. In the damaged coating areas the surface profile is macroscopically saw-toothed with average tooth height 1.5 microm. The average Ra value is 0.02 microm on the undamaged surfaces and 0.37 microm on the damaged ones. Failure of the coating adhesion resulted in the release of TiN fragments and of metallic particulate from the substrate fretting corrosion and in the increase of the head surface roughness affecting counterface debris production. Our results suggest that TiN-coated titanium alloy femoral heads are inadequate in the task of resisting third body wear mechanisms in vivo.

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 model of multicomponent cardiac fibre.

In order to simulate the contraction of a cardiac myofibre, a multicomponent fibre model has been developed. This model is composed of a series of segments which are activated in succession. Each segment is represented by the Hill's three component model of the sarcomere. The contractile element behaviour is described by the Huxley's theory and the time dependence agrees with the activation factor proposed by Julian for skeletal muscle, and modified by Wong for cardiac muscle. The two elastic elements have non-linear exponential characteristics. The isometric contraction of the multicomponent fibre has been simulated by means of a computer program. The results show the tension generated by the fibre, the propagation of the contraction along the fibre and the different contribution of each segment depending on its position inside the fibre.

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.

Experimental and computational approach for the evaluation of the biomechanical effects of dental bridge misfit.

Dental bridges supported by osseointegrated implants are commonly used to treat the partially or completely edentulous jaw. The bridges are manufactured in metal alloy using a sequence of technological steps which well match the requirement to get custom overstructures but does not guarantee geometrical and dimensional tolerances. Dentists often experience that a perfect fit of the bridge with the abutments is almost impossible to achieve. When a misfitting bridge is forced on the abutments, deformations may occur inducing a permanent preload at the fixture-bone interface and the greater the misfit the greater is the preload and the risk of implant failure. This work gives an evaluation of the biomechanical effects induced by a misfitting bridge when forced on two supporting dental implants. The strains induced in the bridge have been measured using two purposely designed and fabricated experimental devices allowing different types of misfit. FEM 3D models of the bridge and of the bridge anchored to the bone by implants have been developed. The former has been validated by simulating the same loading conditions as in the experimental tests and comparing the bridge strains. Both models have been used for the evaluation of the stress induced in the bridge and at the fixture-bone interface by bridge length errors. The results show that the method may help to estimate the stress distribution in the bridge and bone as a consequence of different dental bridge misfits.

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).

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.

Mechanobiology of engineered cartilage cultured under a quantified fluid-dynamic environment.

Natural cartilage remodels both in vivo and in vitro in response to mechanical forces and hence mechanical stimulation is believed to have a potential as a tool to modulate extra-cellular matrix synthesis in tissue-engineered cartilage. Fluid-induced shear is known to enhance chondrogenesis on animal cells. A well-defined hydrodynamic environment is required to study the biochemical response to shear of three-dimensional engineered cell systems. We have developed a perfused-column bioreactor in which the culture medium flows through chondrocyte-seeded porous scaffolds, together with a computational fluid-dynamic model of the flow through the constructs' microstructure. A preliminary experiment of human chondrocyte growth under static versus dynamic conditions is described. The median shear stress imposed on the cells in the bioreactor culture, as predicted by the CFD model, is 3 x 10(-3) Pa (0.03 dyn/cm(2)) at a flow rate of 0.5 ml/min corresponding to an inlet fluid velocity of 44.2 mum/s. Providing a fluid-dynamic environment to the cells yielded significant differences in cell morphology and in construct structure.

Modelling evaluation of the testing condition influence on the maximum stress induced in a hip prosthesis during ISO 7206 fatigue testing.

In vivo fatigue failure of hip prosthesis stems has been extensively reported in literature. The ISO 7206 international standard has been developed to assess the fatigue reliability of hip prostheses. It describes the fatigue testing apparatus and procedure and it is currently adopted by several testing laboratories throughout the world. In this work we evaluate the maximum stress in a titanium alloy commercial stem in different testing conditions, ranging within the standard specification, using the finite element method applied to a 3D model of the stem. The calculated maximum von Mises stress ranges from +4.5 to -1.5% (for different cement constraint levels) and from +6.7 to -6.8% (for different stem angular orientations) with respect to that calculated at the nominal testing conditions. The results suggest that the ISO 7206 testing specification will give experimental data of reasonable accuracy, with probably no more scatter than that found in typical specimen test results. This is particularly important in the case of components manufactured from materials showing a fatigue resistance highly sensitive to stress variations, such as the Ti6A14V alloy, for which a small increase of the maximum applied stress corresponds to a significant decrease of the statistical fatigue life.

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.

A lumped parameter model to evaluate the fluid dynamics of different coronary bypasses.

Coronary bypass grafting is a surgical procedure frequently performed to obtain myocardial reperfusion downstream from severe coronary stenoses. Different surgical techniques may be adopted which include the use of graft made of internal mammary artery or saphenous vein, and the adoption of multiple or sequential bypasses for more than one stenosis. The haemodynamics of the surgically reconstructed coronary bed is strongly dependent on the bypass configuration and may induce atherogenic processes affecting the long-term potency of the bypass. We have improved a closed-loop mathematical model of the cardiovascular system including a more detailed description of the coronary tree which allows the calculation of the flow rate and pressure curves in all the vessels considered. Pathological situations, such as stenoses, have been simulated and investigated. Models of the internal mammary artery and of the saphenous vein have also been developed in order to simulate coronary artery bypasses. The four simulated bypass configurations have been the single saphenous vein, the sequential saphenous vein, the single internal mammary artery and the sequential internal mammary artery. Results of the simulations of the different bypass grafting configurations indicate that between single saphenous vein and single internal mammary artery the latter shows better haemodynamics both for the flow rate pattern and for the calculated wall shear stress. The sequential bypasses show better haemodynamics in comparison with the single bypass in the proximal segments and worse performance in the distal ones. The models may be applied as an investigative tool to evaluate actual cases of surgically treatable coronary stenoses. They can predict the modification in blood flow waveforms, mean velocities, shear stress and distribution of blood flow in the coronary branches as a function of the adopted bypass configuration.

Wear of polyethylene cups in total hip arthroplasty: a parametric mathematical model.

This paper presents a parametric mathematical model of the head-cup wear coupling in total hip arthroplasty (THA). The model evaluates the dependence of acetabular volumetric wear upon the characteristic parameters of patient and hip prosthesis. Archard's law is assumed to calculate the wear coupling behaviour. The wear factor is taken from pin-on-disc wear tests as a function of materials and finishing of the articular joint. The forces acting on the hip joint are taken from experimental data found in the literature whilst the load distribution is calculated under the hypotheses of perfectly rigid ideal wear coupling. The sliding distance is obtained by combining the three elementary displacements -- due to rotations around the three axes -- at the generic bearing surface location. The simulations show that the polymeric wear volume per step cycle decreases ranging from fast walking speeds to low running speeds, it increases linearly with patient body weight and with femoral head diameter, it decreases slightly for positive variations of the socket inclination angle and it increases exponentially with femoral head roughness. The volumetric wear rate per year calculated for a standard reference patient is 5.8 mm3. The relevant iso-wear maps show a marginal pattern with the maximum located near the cup superior borderline. At the instant of peak load, the iso-stress maps show a paracentral pattern with the maximum superior to the cup polar point, and the iso-sliding distance maps show a marginal pattern with two maxima located near the cup's superior and inferior borderlines.

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.

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).

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.

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.

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.