A method of image correlation is presented to study sequential microscopic observations of human Haversian cortical bone. Imaging biological tissues is sometimes challenging owing to their complex microstructures in particular when microcracks appear. Bone microfractures can be studied in micro compression tests where the progressive growth of small cracks is imaged by light microscopy. The two-dimensional displacement field on the sample surface is then tracked by various digital image correlation methods based on cross-correlation formulation. Because of the potential high number of sequential observations, the method calculates the displacements at given growth steps obtained either by direct comparison of the studied step and the undeformed initial state, called ‘direct correlation’, or by iterative comparisons of successive pairs of observations, called ‘gradual correlation’. In the gradual procedure, two cases are studied, referred to as ‘invariant gradual correlation’ and ‘varying gradual correlation’, when the correlation domain is transferred till the last observation or reinitialised for each image pairs. As bone is highly heterogeneous, two types of correlation procedures are considered with or without domain partition (WDP or WODP) delimiting material and strong discontinuities. The precision of the methods is specifically evaluated for experimental observations.Copyright © 2012 John Wiley & Sons, Ltd.

A method of image correlation is presented to study sequential microscopic observations of human Haversian cortical bone. Imaging biological tissues is sometimes challenging owing to their complex microstructures in particular when microcracks appear. Bone microfractures can be studied in micro compression tests where the progressive growth of small cracks is imaged by light microscopy. The two-dimensional displacement field on the sample surface is then tracked by various digital image correlation methods based on cross-correlation formulation.

Retinopathy is a surgical process in which maladies of the human eye are treated by laser irradiation. A two-dimensional numerical model of the human eye geometry has been developed to investigate transient thermal effects due to laser radiation. In particular, the influence of choroidal pigmentation and that of choroidal blood convection—parameterized as a function of choroidal blood perfusion—are investigated in detail. The Pennes bio-heat transfer equation is invoked as the governing equation, and finite volume formulation is employed in the numerical method. For a 500- μm diameter spot size, laser power of 0.2 W, and 100% absorption of laser radiation in the retinal pigmented epithelium (RPE) region, the peak RPE temperature is observed to be 103 °C at 100 ms of the transient simulation of the laser surgical period. Because of the participation of pigmented layer of choroid in laser absorption, peak temperature is reduced to 94 °C after 100 ms of the laser surgery period. The effect of choroidal blood perfusion on retinal cooling is found to be negligible during transient simulation of retinopathy. A truncated three-dimensional model incorporating multiple laser irradiation of spots is also developed to observe the spatial effect of choroidal blood perfusion and choroidal pigmentation. For a circular array of seven uniformly distributed spots of identical diameter and laser power of 0.2 W, transient temperature evolution using simultaneous and sequential mode of laser surgical process is presented with analysis.Copyright © 2012 John Wiley & Sons, Ltd.

Retinal laser surgery is simulated in three dimensions with the use of the bio-heat transfer model. Sequential and simultaneous modes of irradiation for single-spot and multiple-spot array are considered. The effects of retinal and choroidal pigmentation as well as choroidal blood perfusion on the retinal temperature distribution are analyzed. Irrespective of blood perfusion, choroidal pigmentation is found to have significant effect on retinal temperature distribution.

Nasal obstruction frequently has been associated with obstructive sleep apnea (OSA). Although correction of an obstructed nasal airway is considered an important component in OSA treatment, the effect of nasal surgery on OSA remains controversial. Variation in airway anatomy between before and after nasal surgery may cause significant differences in airflow patterns within the upper airway. In this paper, anatomically accurate models of the interaction between upper airway and soft palate were developed from prenasal and post-nasal surgery multidetector computed tomography data of a patient with OSA and nasal obstruction. Computational modeling for inspiration and expiration was performed by using fluid–structure interaction method. The airflow characteristics such as velocity, turbulence intensity and pressure drop, and displacement distribution of soft palate are selected for comparison. Airway resistances significantly decrease after the nasal surgery, especially in the velopharynx region because of an enlarged pharyngeal cavity and a reduced upstream resistance. Meanwhile, the decreased aerodynamic force would result in a smaller displacement of soft palates, which would lead to slight impact of the soft palate motion on the airflow characteristics. The present results suggest that airflow distribution in the whole upper airway and soft palate motions have improved following nasal surgery. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, fluid-structure interaction models of the upper airway and soft palate were developed from prenasal and post-nasal surgery multidetector computerized tomography data of a patient with obstructive sleep apnea and nasal obstruction. The airflow characteristics such as velocity, turbulence intensity and pressure drop, and displacement distribution of soft palate are selected for comparison. The present results suggest that airflow distribution in the whole upper airway and soft palate motions have improved following nasal surgery.

The anatomies of pelvic structures are critical for the diagnosis of pelvic floor dysfunctions. However, because of the complex background, the imaging appearances of pelvic organs and muscles are frequently distorted by noise and partial volume effect. Magnetic resonance imaging with its clear imaging quality of the female pelvic cavity is preferred for many studies. As such, correct segmentations of the pelvic structures on MR images are required for accurate diagnoses. Effective algorithms for axial T2-weighted MR images have been proposed, which are based on the imaging features of different structures and various image clues. In this paper, we review these algorithms and evaluate their performance, and discuss implementation issues and aspects towards constructing the three-dimensional models.Copyright © 2012 John Wiley & Sons, Ltd.

Segmentation results on an axial T2-weighted MR image of female pelvic cavity, from top to down: bladder, vagina, rectum, and levator ani muscle (on the left), and the 3D model built from the segmentation results (on the right).

The numerical solution of D-bar integral equations is the key in inverse scattering solution of many complex problems in science and engineering including conductivity imaging. Recently, a couple of methodologies were considered for the numerical solution of D-bar integral equation, namely product integrals and multigrid. The first one involves high computational complexity and other one has low convergence rate disadvantages. In this paper, a new and efficient sinc-convolution algorithm is introduced to solve the two-dimensional D-bar integral equation to overcome both of these disadvantages and to resolve the singularity problem not tackled before effectively. The method of sinc-convolution is based on using collocation to replace multidimensional convolution-form integrals- including the two-dimensional D-bar integral equations - by a system of algebraic equations. Separation of variables in the proposed method allows elimination of the formulation of the huge full matrices and therefore reduces the computational complexity drastically. In addition, the sinc-convolution method converges exponentially with a convergence rate of . Simulation results on solving a test electrical impedance tomography problem confirm the efficiency of the proposed sinc-convolution-based algorithm. Copyright © 2012 John Wiley & Sons, Ltd.

The sinc-convolution method is employed to solve a two-dimensional D-bar equation of inverse scattering. Application of the proposed algorithm for solving planar D-bar equations that arise in the inverse conductivity problem on a numerically simulated chest phantom is considered. Results show that the sinc-convolution method solves D-bar equations and reconstructs the conductivity images with much higher accuracy and lower computational burden as compared with multigrid method, arguably the best of the existing numerical solution methods to D-bar equation.

This paper describes a novel approach for the simulation of surgery by a combined technique of model order reduction and extended finite element method (X-FEM) methods. Whereas model order reduction techniques employ globally supported (Ritz) shape functions, a combination with X-FEM methods on a locally superimposed patch is developed for cutting simulation without remeshing. This enables to obtain models with very few degrees of freedom that run under real-time constrains even for highly non-linear tissue constitutive equations. To show the performance of the technique, we studied an application to refractive surgery in the cornea. Copyright © 2012 John Wiley & Sons, Ltd.

This paper describes a novel approach for the simulation of surgery by a combined technique of model order reduction and extended finite element method (X-FEM) methods. Whereas model order reduction techniques employ globally supported (Ritz) shape functions, a combination with X-FEM methods on a locally superimposed patch is developed for cutting simulation without remeshing. This enables to obtain models with very few degrees of freedom that run under real-time constrains even for highly non-linear tissue constitutive equations.

Human aortas are subjected to large mechanical stresses because of blood flow pressurization and through contact with the surrounding tissue. It is essential that the aorta does not lose stability by buckling with deformation of the cross-section (shell-like buckling) (i) for its proper functioning to ensure blood flow and (ii) to avoid high stresses in the aortic wall. A numerical bifurcation analysis employs a refined reduced-order model to investigate the stability of a straight aorta segment conveying blood flow. The structural model assumes a nonlinear cylindrical orthotropic laminated composite shell composed of three layers representing the tunica intima, media and adventitia. Residual stresses because of pressurization are evaluated and included in the model. The fluid is formulated using a hybrid model that contains the unsteady effects obtained from linear potential flow theory and the steady viscous effects obtained from the time-averaged Navier–Stokes equations. The aortic segment loses stability by divergence with deformation of the cross-section at a critical flow velocity for a given static pressure, exhibiting a strong subcritical behaviour with partial or total collapse of the inner wall. Preliminary results suggest directions for further study in relation to the appearance and growth of dissection in the aorta. Copyright © 2012 John Wiley & Sons, Ltd.

A numerical bifurcation analysis employs a refined reduced-order model to investigate the stability of a straight aorta segment conveying blood flow. The aortic segment loses stability by divergence with deformation of the cross-section at a critical flow velocity for a given static pressure, exhibiting a strong subcritical behaviour with partial or total collapse of the inner wall. Preliminary results suggest directions for further study in relation to the appearance and growth of dissection in the aorta.

Children born with single ventricle heart defects typically undergo a staged surgical procedure culminating in a total cavopulmonary connection (TCPC) or Fontan surgery. The goal of this work was to perform physiologic, patient-specific hemodynamic simulations of two post-operative TCPC patients by using fluid–structure interaction (FSI) simulations. Data from two patients are presented, and post-op anatomy is reconstructed from MRI data. Respiration rate, heart rate, and venous pressures are obtained from catheterization data, and inflow rates are obtained from phase contrast MRI data and are used together with a respiratory model. Lumped parameter (Windkessel) boundary conditions are used at the outlets. We perform FSI simulations by using an arbitrary Lagrangian–Eulerian finite element framework to account for motion of the blood vessel walls in the TCPC. This study is the first to introduce variable elastic properties for the different areas of the TCPC, including a Gore-Tex conduit. Quantities such as wall shear stresses and pressures at critical locations are extracted from the simulation and are compared with pressure tracings from clinical data as well as with rigid wall simulations. Hepatic flow distribution and energy efficiency are also calculated and compared for all cases. There is little effect of FSI on pressure tracings, hepatic flow distribution, and time-averaged energy efficiency. However, the effect of FSI on wall shear stress, instantaneous energy efficiency, and wall motion is significant and should be considered in future work, particularly for accurate prediction of thrombus formation. Copyright © 2012 John Wiley & Sons, Ltd.

In this work, we present physiologic, patient-specific hemodynamic simulations of the postoperative Fontan procedure in two patients. The effects of fluid-structure interaction with variable wall properties on presumed clinically relevant parameters such as hepatic flow distribution, energy efficiency, and wall shear stress are explored and results are discussed.

In this study, a finite element model of a tissue-mimicking, viscoelastic phantom with a stiffer cylindrical inclusion subjected to an acoustic radiation force (ARF) is presented, and the resulting shear waves through the heterogeneous media are simulated, analyzed, and compared with experimental data. Six different models for the ARF were considered and compared. Each study used the same finite element model, but applied the following: (1) full radiation push; (2) focal region push; (3) single element focal point source; or (4) various thresholds of the full radiation push. For each case, displacements at discrete locations were determined and compared. The finite element simulation results for the full radiation push matched well with the experimental data with respect to replicating the shear wave speed and attenuation in the peak displacements through the background medium and inclusion, but did not illustrate comparable recovery after the peak displacements. As a result of this study, it has been shown that a focal region or point source push is not adequate to accurately model the effects of the full radiation push, but thresholding the full push can produce comparable results and reduce computation time. Copyright © 2012 John Wiley & Sons, Ltd.

A finite element model of a tissue-mimicking, viscoelastic phantom with a stiffer cylindrical inclusion subjected to an acoustic radiation force is presented, and the resulting shear waves through the heterogeneous media are simulated, analyzed, and compared with experimental data. This study shows that a focal region or point source push is not adequate to accurately model the effects of the full radiation push, but thresholding the full push can produce comparable results and reduce computation time.

Magnetic resonance imaging provides very good contrast between different soft tissues; however, in some cases, this technique is not so suitable to image calcified structures like bones. The quality of images is often degraded by blur edges or noises, which makes it difficult to accurately identify bone structures. In this paper, we proposed a new curvelet preprocessing method for local image enhancement to especially improve the quality of spinal MRI. Our objective is to both sharpen boundaries and smoothen the intensity variation of the vertebra. In the first phase, we extract features through curvelet coefficients and the gradient of the original image, then we utilize fuzzy cluster method to classify the whole image scope into the ‘edge’ region and the ‘nonedge’ region. In the second phase, we locally sharpen or smoothen the image by adaptive adjustment of curvelet coefficients and Gaussian smoothing method in different subregions. To evaluate the effect of the preprocessing method, we examine the gradient of the image and its segmentation results as the assessments. The experiment results show that the feature extraction method is effective for classification and the vertebra performs higher contrast on boundaries and less noises after the enhancement, which indeed helps increase the accuracy of further segmentation.Copyright © 2012 John Wiley & Sons, Ltd.

A new method based on curvelet transform and fuzzy cluster is proposed for feature extraction and local image enhancement of an MRI. We implement different enhancement techniques on different regions of the MRI to fulfill the local enhancement and denoising. Experiments of vertebra segmentation show good performance of the proposed method.

Mechanobiological interactions are essential for the adaption of the cardiovascular system to altered environmental and internal conditions, but are poorly understood with regard to abdominal aortic aneurysm (AAA) pathogenesis, growth and rupture. In the present study, we therefore calculated mechanical AAA quantities using nonlinear finite element methods and correlated these to [18F]-fluorodeoxyglucose (FDG)-metabolic activity in the AAA wall detected by positron emission tomography/computed tomography (PET/CT). The interplay between mechanics and FDG-metabolic activity was analyzed in terms of maximum values and the three-dimensional spatial relationship, respectively.

Fluorodeoxyglucose-positron emission tomography/computed tomography (FDG-PET/CT) data sets of n = 18 AAA patients were studied. Maximum FDG-uptake (SUV_max) in the AAA wall varied from 1.32 to 4.60 (average SUV_max 3.31 ±0.87). Maximum wall stresses and strains ranged from 10.0 to 64.0 N∕cm² (38.2 ±13.8  N∕cm²) and from 0.190 to 0.260 (0.222 ±0.023), respectively. SUV_max was significantly correlated to maximum wall stress and strain (SUV_max to stress: r = 0.71,p = 0.0005; SUV_max to strain: r = 0.66,p = 0.0013). To evaluate the three-dimensional spatial interaction between FDG-uptake and acting wall stress, element-wise correlations were performed. In all but 2 AAAs, positive element-wise correlation of FDG-uptake to wall stress was obtained, with the Pearson's correlation coefficient ranging from −0.168 to 0.738 ( 0.372 ±0.263).

The results indicate that mechanical stresses are correlated quantitatively and spatially to FDG-uptake in the AAA wall. It is hypothesized that unphysiologically increased loading in the AAA wall triggers biological tissue reaction, such as inflammation or regenerative processes, causing elevated FDG-metabolic activity. These findings strongly support experimental hypotheses of mechanotransduction mechanisms in vivo. Copyright © 2011 John Wiley & Sons, Ltd.

The study investigates mechanobiological interactions in the wall of abdominal aortic aneurysms. FDG-PET/CT imaging is used to measure the metabolic activity in the tissue, whereas mechanical quantities are assessed by means of finite element analyses. Results indicate that mechanical stresses are correlated to FDG-uptake in the AAA wall and it is hypothesized that unphysiologically increased loading in the AAA wall is one potential trigger for biological tissue reaction.

Because of its ability to deal with any geometry, image-based computational fluid dynamics (CFD) has been progressively used to investigate the role of hemodynamics in the underlying mechanisms governing the natural history of cerebral aneurysms. Despite great progress in methodological developments and many studies using patient-specific data, there are still significant controversies about the precise governing processes and divergent conclusions from apparently contradictory results. Sorting out these issues requires a global vision of the state of the art and a unified approach to solving this important scientific problem. Towards this end, this paper reviews the contributions made using patient-specific CFD models to further the understanding of these mechanisms, and highlights the great potential of patient-specific computational models for clinical use in the assessment of aneurysm rupture risk and patient management.Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, head–neck boundary conditions and modeling of the head are studied circumspectly. The neck is modeled using discrete elements and the head model is three-dimensional. In the study presented here, a viscoelastic foundation (i.e., foundation defined by both springs and dampers) concept is introduced to simulate the head–neck boundary conditions during the impact load to the head. Time histories of the brain response in finite element head models with a viscoelastic neck are compared with the corresponding solutions of finite element head models with an elastic neck, and without a neck. It is observed that the magnitude of peaks in the brain's response time histories, at a later stage (i.e., 6 to 15 ms) of the simulation, decreases when dampers are induced to the elastic neck. A parametric study is also conducted to examine the brain response while varying different damping coefficient values for the neck. The magnitude of peaks in the brain's response time histories for models with different neck damping coefficients is observed to maintain some form of proportionality. In other words, the magnitude of peaks in the brain's response time histories decreases with an increased damping coefficient of the neck at the later stage of the simulation (i.e., 6 to 15 ms). From the outcomes of this study, it can be determined that the head–neck boundary conditions during head impact loading are important for studying the brain's response at the later stages of the head impact. Copyright © 2011 John Wiley & Sons, Ltd.

We present a robust and computationally efficient parameter estimation strategy for fluid–structure interaction problems. The method is based on a filtering algorithm restricted to the parameter space, known as the reduced-order unscented Kalman filter. It does not require any adjoint or tangent problems. In addition, it can easily be run in parallel, which is of great interest in fluid–structure problems where the computational cost of the forward simulation is already a challenge in itself. We illustrate our methodology with the estimation of the artery wall stiffness from the wall displacement measurements – as they could be extracted from medical imaging – in a three-dimensional idealized abdominal aortic aneurysm. We also show preliminary results about the estimation of the proximal Windkessel resistance, which is an important parameter for setting appropriate fluid boundary conditions. Copyright © 2011 John Wiley & Sons, Ltd.

Reduced-order unscented Kalman filtering for fluid-structure systems. It does not require any adjoint or tangent problems and can be easily run in parallel. Three-dimensional examples for the estimation of artery wall stiffness and Windkessel proximal resistance from the wall displacement measurements are illustrated.

Finite element (FE) models accurately compute the mechanical response of bone and bone-like materials when the models include their detailed microstructure. In order to simulate non-linear behavior, which currently is only feasible at the expense of extremely high computational costs, coarser models can be used if the local morphology has been linked to the apparent mechanical behavior. The aim of this paper is to implement and validate such a constitutive law. This law is able to capture the non-linear structural behavior of bone-like materials through the use of fabric tensors. It also allows for irreversible strains using an elastoplastic material model incorporating hardening. These features are expressed in a constitutive law based on the anisotropic continuum damage theory coupled with isotropic elastoplasticity in a finite strain framework. This material model was implemented into METAFOR (LTAS-MNNL, University of Liège, Belgium), a non-linear FE software. The implementation was validated against experimental data of cylindrical samples subjected to compression. Three materials with bone-like microstructure were tested: aluminum foams of variable density (ERG, Oakland, CA, USA), polylactic acid foam (CERM, University of Liège, Liège, Belgium), and cancellous bone tissue of a deer antler (Faculty of Veterinary Medicine, University of Liège, Liège, Belgium). Copyright © 2011 John Wiley & Sons, Ltd.

The aim of this paper is to implement and validate a non-linear constitutive law for bone and bone-like materials including the microstructure through the use of fabric tensors and allowing for irreversible strains using an elastoplastic material model incorporating hardening in a finite strain framework. The model here is validated against experimental data of cylindrical samples subjected to compression for three materials with bone-like microstructure (aluminum foams, polymeric foam, and deer antler), leading to error of less than 5% on the strain range tested.

The aim of the present work is to describe the integration of a mathematical model for the baroreceptor reflex mechanism to provide regulatory action into a dimensionally heterogeneous (3D–1D–0D) closed-loop model of the cardiovascular system. Such heterogeneous model comprises a 1D description of the arterial tree, a 0D network for the venous, cardiac and pulmonary circulations and 3D patient-specific geometries for vascular districts of interest. Thus, the detailed topological description of the arterial network allows us to perform vasomotor control actions in a differentiated way, while gaining insight about the effects of the baroreflex regulation over hemodynamic quantities of interest throughout the entire network. Two examples of application are presented. Firstly, we simulate the hemorrhage in the abdominal aorta artery and analyze the action of the baroreflex over the system. Secondly, the self-regulated closed-loop model is applied to study the influence of the control action in the hemodynamic environment that determines the blood flow pattern in a cerebral aneurism in the presence of a regurgitating aortic valve. Copyright © 2011 John Wiley & Sons, Ltd.

The aim of the present work is to describe the integration of a mathematical model for the baroreceptor reflex mechanism to provide regulatory action into a dimensionally heterogeneous closed-loop model of the cardiovascular system. In this paper, we simulate the hemorrhage in the abdominal aorta artery and analyze the action of the baroreflex over the system, and study the influence of the control action in the hemodynamic environment that determines the blood flow pattern in a cerebral aneurism in the presence of a regurgitating aortic valve.

To study the transformation of fluctuations in filtration rate into tubular fluid chloride concentration oscillations alongside the macula densa, we have developed a mathematical model for tubuloglomerular feedback (TGF) signal transduction along the pars recta, the descending limb, and the thick ascending limb (TAL) of a short-looped nephron. The model tubules are assumed to have compliant walls and, thus, a tubular radius that depends on the transmural pressure difference. Previously, it has been predicted that TGF transduction by the TAL is a generator of nonlinearities: if a sinusoidal oscillation is added to a constant TAL flow rate, then the time required for a fluid element to traverse the TAL is oscillatory in time but nonsinusoidal. The results from the new model simulations presented here predict that TGF transduction by the loop of Henle is also, in the same sense, a generator of nonlinearities. Thus, this model predicts that oscillations in tubular fluid alongside the macula densa will be nonsinusoidal and will exhibit harmonics of sinusoidal perturbations of pars recta flow. Model results also indicate that the loop acts as a low-pass filter in the transduction of the TGF signal. Copyright © 2011 John Wiley & Sons, Ltd.

A mathematical model for signal transduction along a short loop of Henle of the rat kidney is used to study the transformation of fluctuations in filtration rate into tubular fluid chloride concentration oscillations along the macula densa. Model predicts that oscillations in tubular fluid alongside the macula densa will be nonsinusoidal and will exhibit harmonics of sinusoidal perturbations of pars recta flow, and that the loop acts as a low-pass filter in the transduction of the tubuloglomerular feedback signal.

Thanks to advances in medical imaging technologies and numerical methods, patient-specific modelling is more and more used to improve diagnosis and to estimate the outcome of surgical interventions. It requires the extraction of the domain of interest from the medical scans of the patient, as well as the discretisation of this geometry. However, extracting smooth multi-material meshes that conform to the tissue boundaries described in the segmented image is still an active field of research. We propose to solve this issue by combining an implicit surface reconstruction method with a multi-region mesh extraction scheme. The surface reconstruction algorithm is based on multi-level partition of unity implicit surfaces, which we extended to the multi-material case. The mesh generation algorithm consists in a novel multi-domain version of the marching tetrahedra. It generates multi-region meshes as a set of triangular surface patches consistently joining each other at material junctions. This paper presents this original meshing strategy, starting from boundary points extraction from the segmented data to heterogeneous implicit surface definition, multi-region surface triangulation and mesh adaptation. Results indicate that the proposed approach produces smooth and high-quality triangular meshes with a reasonable geometric accuracy. Hence, the proposed method is well suited for subsequent volume mesh generation and finite element simulations. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we propose a new model reduction technique aimed at real-time blood flow simulations on a given family of geometrical shapes of arterial vessels. Our approach is based on the combination of a low-dimensional shape parametrization of the computational domain and the reduced basis method to solve the associated parametrized flow equations. We propose a preliminary analysis carried on a set of arterial vessel geometries, described by means of a radial basis functions parametrization. In order to account for patient-specific arterial configurations, we reconstruct the latter by solving a suitable parameter identification problem. Real-time simulation of blood flows are thus performed on each reconstructed parametrized geometry, by means of the reduced basis method. We focus on a family of parametrized carotid artery bifurcations, by modelling blood flows using Navier–Stokes equations and measuring distributed outputs such as viscous energy dissipation or vorticity. The latter are indexes that might be correlated with the assessment of pathological risks. The approach advocated here can be applied to a broad variety of (different) flow problems related with geometry/shape variation, for instance related with shape sensitivity analysis, parametric exploration and shape design.Copyright © 2011 John Wiley & Sons, Ltd.

Hollow fiber membrane bioreactors (HFMB) are extensively used for the development of tissue substitutes for bones and cartilages. In an HFMB, the nutrient transport is dependent on the material properties of the porous scaffold and fiber membrane and also on the fluid flow through the hollow fiber. The difficulty in obtaining real-time data along with the presence of large number of variables in experimental studies have lead to increased application of computational models for the performance analysis of bioreactors. A major difficulty in the computational analysis of HFMB is the modeling of the interactions at the fluid and porous scaffold interfaces, which has often been neglected or incorporated using specific boundary conditions. In this study, a new FEM is developed to analyze the fluid flow in the fluid-porous region with the interface coupled directly into the FEM. Distribution of nutrients in the bioreactor is studied by coupling mass transport equations to the fluid-porous finite element framework. The new model is implemented to study the influence of permeability, cell density, and flow rate on the nutrient concentration distribution in the HFMB. The developed computational framework is an ideal tool to study fluid flow through porous-open channels and can also be used for the design of bioreactors for optimal tissue growth. Copyright © 2011 John Wiley & Sons, Ltd.

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time–frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high-order PDEs. As a consequence, the time integration of high-order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two-dimensional and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and a standard approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, that is, surface area, surface-enclosed volume, solvation free energy, and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson–Boltzmann equation model. To further demonstrate the utility of the present PDE transform-based surface method, we solve the Poisson–Nernst–Planck equations with a PDE transform surface of a protein. Second-order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform-based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable, and efficient approach for biomolecular surface generation in Cartesian meshes. Copyright © 2011 John Wiley & Sons, Ltd.

Lumped parameter and one-dimensional models of the cardiovascular system generally employ ideal cardiac and/or venous valves that open and close instantaneously. However, under normal or pathological conditions, valves can exhibit complex motions that are mainly determined by the instantaneous difference between upstream and downstream pressures. We present a simple valve model that predicts valve motion on the basis of this pressure difference, and can be used to investigate not only valve pathology, but a wide range of cardiac and vascular factors that are likely to influence valve motion. Copyright © 2011 John Wiley & Sons, Ltd.

Given a sinusoidal pressure difference (Δp) with increasing amplitude, this figure shows the resultant time-varying state of the proposed valve model (ζ, 0 = Dclosed, 1 = Dopen). Valve opening/closure is more rapid for greater pressure differences.

Blood flow in arterial systems is described by the three-dimensional Navier–Stokes equations within a time-dependent spatial domain that accounts for the viscoelasticity of the arterial walls. These equations are simplified by assuming cylindrical geometry, axially symmetric flow, and hydrostatic equilibrium in the radial direction. In this paper, an efficient semi-implicit method is formulated in such a fashion that numerical stability is obtained at a minimal computational cost. The resulting computer model is relatively simple, robust, accurate, and extremely efficient. These features are illustrated on nontrivial test cases where the exact analytical solution is known and by an example of a realistic flow through a complex arterial system. Copyright © 2011 John Wiley & Sons, Ltd.

In this work, five computational methodologies to register plantar pressure images are compared: (1) the first methodology is based on matching the external contours of the feet; (2) the second uses the phase correlation technique; (3) the third addresses the direct maximization of cross-correlation using the Fourier transform; (4) the fourth minimizes the sum of squared differences using the Fourier transform; and (5) the fifth methodology iteratively optimizes an intensity (dis)similarity measure based on Powell's method. The accuracy and robustness of the five methodologies were assessed by using images from three common plantar pressure acquisition devices: a Footscan system, an EMED system, and a light reflection system. Using the residual error as a measure of accuracy, all methodologies revealed to be very accurate even in the presence of noise. The most accurate was the methodology based on the iterative optimization, when the mean squared error was minimized. It achieved a residual error inferior to 0.01 mm and 0.6 mm for non-noisy and noisy images, respectively. On the other hand, the methodology based on image contour matching was the fastest, but its accuracy was the lowest. Copyright © 2011 John Wiley & Sons, Ltd.

Because of their deformability and tendency to form aggregates, red blood cells (RBCs) immensely affect the hydrodynamic properties of blood flow in microcirculation. In this paper, RBCs' two-dimensional deformation and motion in Poiseuille flow and in a stenosed arteriole is numerically investigated by the immersed boundary–lattice Boltzmann method. The RBCs are modeled as suspended capsules of fluid in plasma flow. A neo-Hookean elastic model with bending resistance is utilized for the RBC membrane. Also, the suspending plasma is modeled as an incompressible Newtonian fluid. To take the effects of aggregation and dissociation of RBCs into account, intercellular interaction is modeled by the Morse potential. The effects of essential parameters namely, mechanical resistance of the RBC membrane, plasma viscous forces, and cell membrane adhesion strength on RBC behavior are presented. Motions and deformations of RBCs in a stenosis and the effects of the stenosed zone on the behavior of cell aggregates were also simulated and analyzed in this study. Copyright © 2011 John Wiley & Sons, Ltd.

Hemodynamics is thought to be a fundamental factor in the formation, progression, and rupture of cerebral aneurysms. Understanding these mechanisms is important to improve their rupture risk assessment and treatment. In this study, we analyze the blood flow field in a growing cerebral aneurysm using experimental particle image velocimetry (PIV) and computational fluid dynamics (CFD) techniques. Patient-specific models were constructed from longitudinal 3D computed tomography angiography images acquired at 1-y intervals. Physical silicone models were constructed from the computed tomography angiography images using rapid prototyping techniques, and pulsatile flow fields were measured with PIV. Corresponding CFD models were created and run under matching flow conditions. Both flow fields were aligned, interpolated, and compared qualitatively by inspection and quantitatively by defining similarity measures between the PIV and CFD vector fields. Results showed that both flow fields were in good agreement. Specifically, both techniques provided consistent representations of the main intra-aneurysmal flow structures and their change during the geometric evolution of the aneurysm. Despite differences observed mainly in the near wall region, and the inherent limitations of each technique, the information derived is consistent and can be used to study the role of hemodynamics in the natural history of intracranial aneurysms. Copyright © 2011 John Wiley & Sons, Ltd.

Hyperthermia treatment of tumors uses localized heating to damage cancer cells and can also be utilized to increase the efficacy of other treatment methods such as chemotherapy. Magnetic nanoparticle hyperthermia is one of the least invasive techniques of delivering heat. It is based on injecting magnetic nanoparticles into the tumor and subjecting them to an alternating magnetic field. The technique is aimed at damaging the tumor without affecting the surrounding healthy tissue. In this preliminary study, we consider a simplified model (two concentric spheres that represent the tumor and its surrounding tissues) that employs a numerical solution of the Pennes bioheat equation. The model assumes a Gaussian distribution for the spatial variation of the applied thermal energy and an exponential decay function for the time variation. The objective of the study is to optimize the parameters that control the spatial and the time variation of the thermal energy. The optimization process is performed by formulating a fitness function that rewards damage in the region representing the tumor but penalizes damage in the surrounding tissues. Because of the flatness of this fitness function near the optimum, a genetic algorithm is used as the optimization method for its robust non-gradient-based approach. The overall aim of this work is to propose a methodology that can be used for hyperthermia treatment in a clinical scenario.Copyright © 2011 John Wiley & Sons, Ltd.

This paper assumes that a neo-Hookean matrix with neo-Hookean fibres is representative of soft tissue. Under this assumption, a unit cell model is proposed to investigate the fibre–matrix interfacial stress field for biological soft tissue under biaxial loadings. In this unit cell model, the soft tissue is treated as a composite where the matrix is unidirectionally reinforced with a single family of aligned fibres. The results are compared with the model of Guo et al., which accounts for the fibre–matrix interfacial stress field, and Qiu and Pence's model, which does not proceed from the assumption that the fibres are themselves neo-Hookean. It is found that the stress representative of the fibre–matrix interface plays an important role in the deformation of the composite, and the model of Guo et al. underestimates this stress under large biaxial deformation. Copyright © 2011 John Wiley & Sons, Ltd.

Spatial–temporal calcium dynamics due to calcium release, buffering and re-uptaking plays a central role in studying excitation–contraction (E–C) coupling in both normal and diseased cardiac myocytes. In this paper, we employ a meshless method, namely, the local radial basis function collocation method (LRBFCM), to model such calcium behaviors by solving a nonlinear system of reaction–diffusion partial differential equations. In particular, a simplified structural unit containing a single transverse tubule (T-tubule) and its surrounding half sarcomeres is investigated using the meshless method. Numerical results are compared with those generated by finite element methods, showing the capability and efficiency of the LRBFCM in modeling calcium dynamics in ventricular myocytes. The single T-tubule model is also extended to the whole-cell scale with T-tubules excluded to demonstrate the scalability of the proposed meshless method in handling very large domains. The experiments have shown that the LRBFCM is suitable to multiscale modeling of calcium dynamics in ventricular myocytes with high accuracy and efficiency. Copyright © 2011 John Wiley & Sons, Ltd.

The immersed boundary (IB) method is a mathematical and numerical framework for problems of fluid–structure interaction, treating the particular case in which an elastic structure is immersed in a viscous incompressible fluid. The IB approach to such problems is to describe the elasticity of the immersed structure in Lagrangian form, and to describe the momentum, viscosity, and incompressibility of the coupled fluid–structure system in Eulerian form. Interaction between Lagrangian and Eulerian variables is mediated by integral equations with Dirac delta function kernels. The IB method provides a unified formulation for fluid–structure interaction models involving both thin elastic boundaries and also thick viscoelastic bodies. In this work, we describe the application of an adaptive, staggered-grid version of the IB method to the three-dimensional simulation of the fluid dynamics of the aortic heart valve. Our model describes the thin leaflets of the aortic valve as immersed elastic boundaries, and describes the wall of the aortic root as a thick, semi-rigid elastic structure. A physiological left-ventricular pressure waveform is used to drive flow through the model valve, and dynamic pressure loading conditions are provided by a reduced (zero-dimensional) circulation model that has been fit to clinical data. We use this model and method to simulate aortic valve dynamics over multiple cardiac cycles. The model is shown to approach rapidly a periodic steady state in which physiological cardiac output is obtained at physiological pressures. These realistic flow rates are not specified in the model, however. Instead, they emerge from the fluid–structure interaction simulation. Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce. A time-stepping algorithm is then presented for this system, which is shown to be first order accurate and energy gradient stable. The results of an array of numerical experiments are presented, which demonstrate a wide range of solutions produced by various choices of model parameters.Copyright © 2011 John Wiley & Sons, Ltd.

In this paper, we develop a thermodynamically consistent four-species model of tumor growth on the basis of the continuum theory of mixtures. Unique to this model is the incorporation of nutrient within the mixture as opposed to being modeled with an auxiliary reaction-diffusion equation. The formulation involves systems of highly nonlinear partial differential equations of surface effects through diffuse-interface models. A mixed finite element spatial discretization is developed and implemented to provide numerical results demonstrating the range of solutions this model can produce.

Proton transport plays an important role in biological energy transduction and sensory systems. Therefore, it has attracted much attention in biological science and biomedical engineering in the past few decades. The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom. The density of all other ions in the solvent is assumed to obey the Boltzmann distribution in a dynamic manner. The impact of protein molecular structure and its charge polarization on the proton transport is considered explicitly at the atomic scale. A variational solute–solvent interface is designed to separate the explicit molecule and implicit solvent regions. We formulate a total free-energy functional to put proton kinetic and potential energies, the free energy of all other ions, and the polar and nonpolar energies of the whole system on an equal footing. The variational principle is employed to derive coupled governing equations for the proton transport system. Generalized Laplace–Beltrami equation, generalized Poisson–Boltzmann equation, and generalized Kohn–Sham equation are obtained from the present variational framework. The variational solvent–solute interface is generated and visualized to facilitate the multiscale discrete/continuum/quantum descriptions. Theoretical formulations for the proton density and conductance are constructed based on fundamental laws of physics. A number of mathematical algorithms, including the Dirichlet-to-Neumann mapping, matched interface and boundary method, Gummel iteration, and Krylov space techniques are utilized to implement the proposed model in a computationally efficient manner. The gramicidin A channel is used to validate the performance of the proposed proton transport model and demonstrate the efficiency of the proposed mathematical algorithms. The proton channel conductances are studied over a number of applied voltages and reference concentrations. A comparison with experimental data verifies the present model predictions and confirms the proposed model. Copyright © 2011 John Wiley & Sons, Ltd.

The present work proposes a multiscale/multiphysics model for the understanding of the molecular mechanism of proton transport in transmembrane proteins involving continuum, atomic, and quantum descriptions, assisted with the evolution, formation, and visualization of membrane channel surfaces. We describe proton dynamics quantum mechanically via a new density functional theory based on the Boltzmann statistics, while implicitly model numerous solvent molecules as a dielectric continuum to reduce the number of degrees of freedom.

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the active strain assumption, in which it is assumed that there is a multiplicative decomposition of the deformation tensor into a passive and active part holds, the latter carrying the information of the electrical potential propagation and anisotropy of the cardiac tissue into the equations of either incompressible or compressible nonlinear elasticity, governing the mechanical response of the biological material. In addition, by changing from a Eulerian to a Lagrangian configuration, the bidomain or monodomain equations modeling the evolution of the electrical propagation exhibit a nonlinear diffusion term. Piecewise quadratic finite elements are employed to approximate the displacements field, whereas for pressure, electrical potentials and ionic variables are approximated by piecewise linear elements. Various numerical tests performed with a parallel finite element code illustrate that the proposed model can capture some important features of the electromechanical coupling and show that our numerical scheme is efficient and accurate. Copyright © 2011 John Wiley & Sons, Ltd.

We propose a finite element approximation to solve the coupling between the propagation of electrical potential and large deformations of the cardiac tissue, based on the active strain assumption. A new phenomenological model for the mechanical activation is introduced and various numerical tests performed with a parallel finite element code illustrate that the proposed method can capture some important features of the excitation-contraction mechanism.

In this paper, a highly parallel coupled electromechanical model of the heart is presented and assessed. The parallel-coupled model is thoroughly discussed, with scalability proven up to hundreds of cores. This work focuses on the mechanical part, including the constitutive model (proposing some modifications to pre-existent models), the numerical scheme and the coupling strategy. The model is next assessed through two examples. First, the simulation of a small piece of cardiac tissue is used to introduce the main features of the coupled model and calibrate its parameters against experimental evidence. Then, a more realistic problem is solved using those parameters, with a mesh of the Oxford ventricular rabbit model. The results of both examples demonstrate the capability of the model to run efficiently in hundreds of processors and to reproduce some basic characteristic of cardiac deformation. Copyright © 2012 John Wiley & Sons, Ltd.

In this paper, a parallel-coupled electromechanical model of the heart is presented and assessed. The parallel-coupled model is thoroughly discussed, with scalability proven up to hundreds of cores. This work focuses on the mechanical part including the constitutive model, the numerical scheme and the coupling strategy.

In the present work, we develop a three-dimensional isotropic finite-strain damage model for abdominal aortic aneurysm (AAA) wall that considers both the characteristic softening of the material caused by damage and the spatial variation of the material properties. A strain energy function is formulated that accounts for a hyperelastic, slightly compressible, isotropic material behavior during the elastic phase, whereas the damage process only contributes to the material response when the elastic limit of the AAA wall is exceeded. Material and damage parameters are obtained by fitting the strain energy function to the experimental data obtained by uniaxial tensile tests of freshly harvested AAA wall samples. The damage model extends the validity of the material law to a strain range of up to 50%. Purely elastic material laws for AAA wall are only valid for a strain range of up to 17%. In a series of finite element simulations of patient-specific AAAs, serving as numerical examples, we investigate the applicability of the damage model. The use of the damage model does not yield a more distinct identification of rupture-prone AAAs than other computational-based risk indices. However, the benefit of the finite-strain damage model is the potential capability to trigger growth and remodeling processes in mechanobiological models. Copyright © 2011 John Wiley & Sons, Ltd.

In the present work, we develop a three-dimensional isotropic finite-strain damage model for abdominal aortic aneurysm (AAA) wall that considers both the characteristic softening of the material caused by damage and the spatial variation of the material properties. A strain energy function is formulated that accounts for a hyperelastic, slightly compressible, isotropic material behavior during the elastic phase, whereas the damage process only contributes to the material response when the elastic limit of the AAA wall is exceeded. Material and damage parameters are obtained by fitting the strain energy function to the experimental data obtained by uniaxial tensile tests of freshly harvested AAA wall samples.

This work aims to present some fluid-structure models for analyzing the dynamics of the aorta during a brusque loading. Indeed, various lesions may appear at the aortic arch during car crash or other accident such as brusque falling. Aortic stresses evolution are simulated during the shock at the cross section and along the aorta. One hot question was that if a brusque deceleration can generate tissue tearing, or a shock is necessary to provoke such a damage. Different constitutive laws of blood are then tested whereas the aorta is assumed linear and elastic. The overall shock model is inspired from an experimental jig. We show that the viscosity has strong influence on the stress and parietal moments and forces. The nonlinear viscosity has no significant additional effects for healthy aorta, but modifies the stress and parietal loadings for the stenotic aorta. Copyright © 2011 John Wiley & Sons, Ltd.

We analyse the influence of blood viscosity and stenosis on the aorta loadings during shock.

This paper presents a three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea and of linguistics and speech therapy. The anatomical data was obtained from the Visible Human Project, and the underlying histological data was also extracted and incorporated into the model. Hyperelastic constitutive models were used to describe the material behaviour, and material incompressibility was accounted for. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue. The neural stimulus for each muscle group was determined through the use of a genetic algorithm-based neural control model. The fundamental behaviour of the tongue under gravitational and breathing-induced loading is investigated. It is demonstrated that, when a time-dependent loading is applied to the tongue, the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus. Copyright © 2012 John Wiley & Sons, Ltd.

This paper presents an anatomically realistic three-dimensional finite element model of the tongue and surrounding soft tissues with potential application to the study of sleep apnoea. An active Hill three-element muscle model was used to represent the muscular tissue of the tongue, and a genetic algorithm-based neural control model is developed to control movement. It is demonstrated that the neural model is able to control the position of the tongue and produce a physiologically realistic response for the genioglossus under breathing-induced loading conditions.

An overview of surface and volume mesh generation techniques for creating valid meshes to carry out biomedical flows is provided. The methods presented are designed for robust numerical modelling of biofluid flow through subject-specific geometries. The applications of interest are haemodynamics in blood vessels and air flow in upper human respiratory tract. The methods described are designed to minimize distortion to a given domain boundary. They are also designed to generate a triangular surface mesh first and then volume mesh (tetrahedrons) with high quality surface and volume elements. For blood flow applications, a simple procedure to generate a boundary layer mesh is also described. The methods described here are semi-automatic in nature because of the fact that the geometries are complex, and automation of the procedures may be possible if high quality scans are used. Copyright © 2011 John Wiley & Sons, Ltd.

An overview of surface and volume mesh generation techniques for creating valid meshes to carry out biomedical flows is provided. The methods presented are designed for robust numerical modelling of biofluid flow through subject-specific geometries. The applications of interest are haemodynamics in blood vessels and air flow in upper human respiratory tract. The methods described are designed to minimize distortion to a given domain boundary. They are also designed to generate a triangular surface mesh first and then volume mesh (tetrahedrons) with high quality surface and volume elements.

The automated extraction of anatomical reference parameters may improve speed, precision and accuracy of surgical procedures. In this study, an automated method for extracting the femoral anatomical axis (FAA) from a 3D surface mesh, based on geometrical entity fitting, is presented. This was applied to conventional total knee arthroplasty, which uses an intramedullary rod (FIR) to orient the femoral prosthesis with respect to the FAA. The orientation and entry point of a FIR with a length of 200 mm are automatically determined from the FAA, as it has been shown that errors in these parameters may lead to malalignment of the mechanical axis. Moreover, the effect of partially scanning the leg was investigated by creating reduced femur models and comparing the results with the full models. Precise measurements are obtained for 50 models by using a central and two outer parts, with lengths of 20 and 120 mm, which correspond to 58% of the mean femoral length. The deviations were less than 2 mm for the FAA, 2.8 mm for the FAA endpoints and 0.7°and 1.3 mm for the FIR orientation and entry point. The computer-based techniques might eventually be used for preoperative planning of total knee arthroplasty. Copyright © 2011 John Wiley & Sons, Ltd.

The anatomical axis of the femur (FAA) can be automatically extracted from a 3D image by fitting hyperboloids to the diaphysis. The orientation and entry point of a 200-mm long intramedullary rod (FIR), which is used for prosthesis positioning during total knee arthroplasty, can then be computed by fitting a line to the FAA. Precise results are obtained from images that are reduced to 60% of the length, meaning that partial scans can be used for preoperative planning.

Variation in masticatory induced stress, caused by shape changes in the human skull, is quantified in this article. A comparison on masticatory induced stress is presented subject to a variation in human skull shape. Non-rigid registration is employed to obtain appropriate computational domain representations. This procedure allows the isolation of shape from other variations that could affect the results. An added benefit, revealed through the use of non-rigid registration to acquire appropriate domain representation, is the possibility of direct and objective comparison and manipulation. The effect of mapping uncertainty on the direct comparison is also quantified. As shown in this study, exact difference values are not necessarily obtained, but a non-rigid map between subject shapes and numerical results gives an objective indication on the location of differences. Copyright © 2012 John Wiley & Sons, Ltd.

Non-rigid registration is used to represent variations in human skull shape. Subsequent finite element analyses quantify stresses caused by mastication, and differences in stresses caused by skull shape variation. The effect of mapping uncertainty on these stress differences is also quantified.