A volumetric model for growth of arterial walls with arbitrary geometry and loads

Stress and deformation in arterial wall tissue are factors which may influence significantly its response and evolution. In this work we develop models based on nonlinear elasticity and finite element numerical solutions for the mechanical behaviour and the remodelling of the soft tissue of arteries, including anisotropy induced by the presence of collagen fibres. Remodelling and growth in particular constitute important features in order to interpret stenosis and atherosclerosis. The main object of this work is to model accurately volumetric growth, induced by fluid shear stress in the intima and local wall stress in arteries with patient-specific geometry and loads. The model is implemented in a nonlinear finite element setting which may be applied to realistic 3D geometries obtained from in vivo measurements. The capabilities of this method are demonstrated in several examples. Firstly a stenotic process on an idealised geometry induced by a non-uniform shear stress distribution is considered. Following the growth of a right coronary artery from an in vivo reconstructed geometry is presented. Finally, experimental measurements for growth under hypertension for rat carotid arteries are modelled.     

An interface model for the periodontal ligament

A nonlinear interface constitutive law is formulated for modeling the mechanical behavior of the periodontal ligament. This gives an accurate interpolation of the few available experimental results and provides a reasonably simple model for mechanical applications. The model is analyzed from the viewpoints of both mathematical consistency and effectiveness in numerical calculations. In order to demonstrate the latter, suitable two- and three-dimensional nonlinear interface finite elements have been implemented.     

Data reconciliation and parameter estimation in flux-balance analysis

Flux blance analysis (FBA) has been shown to be a very effective tool to interpret and predict the metabolism of various microorganisms when the set of available measurements is not sufficient to determine the fluxes within the cell. In this methodology, an underdetermined stoichiometric model is solved using a linear programming (LP) approach. The predictions of FBA models can be improved if noisy measurements are checked for consistency, and these in turn are used to estimate model parameters. In this work, a formal methodology for data reconciliation and parameter estimation with underdetermined stoichiometric models is developed and assessed. The procedure is formulated as a nonlinear optimization problem, where the LP is transformed into a set of nonlinear constraints. However, some of these constraints violate standard regularity conditions, making the direct numerical solution very difficult. Hence, a barrier formulation is used to represent these constraints, and an iterative procedure is defined that allows solving the problem to the desired degree of convergence. This methodology is assessed using a stoichiometric yeast model. The procedure is used for data reconciliation where more reliable estimations of noisy measurements are computed. On the other hand, assuming unknown biomass composition, the procedure is applied for simultaneous data reconciliation and biomass composition estimation. In both cases it is verified that the f measurements required to get unbiased and reliable estimations is reduced if the LP approach is included as additional constraints in the optimization.     

A method for the identification of in-vivo segmental stiffness properties of the spine

A numerical algorithm is used to estimate in-vivo segmental stiffness properties of individual spine segments based upon existing load-displacement data. A static nonlinear finite element model stimulates a pathological spine and corrective instrumentation system. A systematic procedure for establishing the model's stiffness parameters is described, in the form of a nonlinear constrained optimal design problem. The numerical method is demonstrated using as an example a case of adolescent idiopathic scoliosis requiring corrective surgery.     

Method for characterizing viscoelasticity of human gluteal tissue

Characterizing compressive transient large deformation properties of biological tissue is becoming increasingly important in impact biomechanics and rehabilitation engineering, which includes devices interfacing with the human body and virtual surgical guidance simulation. Individual mechanical in vivo behaviour, specifically of human gluteal adipose and passive skeletal muscle tissue compressed with finite strain, has, however, been sparsely characterised. Employing a combined experimental and numerical approach, a method is presented to investigate the time-dependent properties of in vivo gluteal adipose and passive skeletal muscle tissue. Specifically, displacement-controlled ramp-and-hold indentation relaxation tests were performed and documented with magnetic resonance imaging. A time domain quasi-linear viscoelasticity (QLV) formulation with Prony series valid for finite strains was used in conjunction with a hyperelastic model formulation for soft tissue constitutive model parameter identification and calibration of the relaxation test data. A finite element model of the indentation region was employed. Strong non-linear elastic but linear viscoelastic tissue material behaviour at finite strains was apparent for both adipose and passive skeletal muscle mechanical properties with orthogonal skin and transversal muscle fibre loading. Using a force-equilibrium assumption, the employed material model was well suited to fit the experimental data and derive viscoelastic model parameters by inverse finite element parameter estimation. An individual characterisation of in vivo gluteal adipose and muscle tissue could thus be established. Initial shear moduli were calculated from the long-term parameters for human gluteal skin/fat: G(∞,S/F)=1850 Pa and for cross-fibre gluteal muscle tissue: G(∞,M)=881 Pa. Instantaneous shear moduli were found at the employed ramp speed: G(0,S/F)=1920 Pa and G(0,M)=1032 Pa.     

Measurement and Prediction of Insertion Force for the Mosquito Fascicle Penetrating into Human Skin

Mosquitoes are exceptional in their ability to pierce into human skin with a natural ultimate painless microneedle, namedfascicle. Here the structure of the Aedes albopictus mosquito fascicle is obtained using a Scanning Electron Microscope (SEM),and the whole process of the fascicle inserting into human skin is observed using a high-speed video imaging technique. Directmeasurements of the insertion force for mosquito fascicle to penetrate into human skin are reported. Results show that themosquito uses a very low force (average 18 μN) to penetrate into the skin. This force is at least three orders of magnitude smallerthan the reported lowest insertion force for an artificial microneedle with an ultra sharp tip to insert into the human skin. In orderto understand the piercing mechanism of mosquito fascicle tip into human multilayer skin tissue, a numerical simulation isconducted to analyze the insertion process using a nonlinear finite element method. A good agreement occurs between thenumerical results and the experimental measurements.     

Numerical Analysis of An Anastomotic Device

The explicit dynamic finite element method was utilized to investigate the deformation behaviour of a woven wire mesh tubular device that is used in a side-to-side anastomotic procedure for achieving gastrointestinal anastomosis. The numerical model was initially verified by comparison to experimental results that were obtained using a specialized testing mechanism. Once validated, the finite element model (FEM) was parameterized to ascertain the influence of several device parameters on its deformation behaviour. The importance of these parameters, as related to its optimal design for use in minimally invasive surgery (MIS), was subsequently ascertained and discussed.     

Numerical and experimental models of post-operative realistic flows in stenosed coronary bypasses.

By means of both experimental and finite element methods, we simulated three-dimensional unsteady flows through coronary bypass anastomosis. The host artery includes a stenosis shape located at two different distances of grafting. The inflow rates are issued from in vivo measurements in patients who had undergone coronary bypass surgery a few days before. We provide a comparison between experimental and numerical velocity profiles coupled with the numerical analysis of spatial and temporal wall shear stress evolution. The interaction between the graft and coronary flows has been demonstrated. The phase inflow difference can partly be responsible for specific flow phenomena: jet deflection towards a preferential wall or feedback phenomenon that causes the flapping of the post-stenotic jet during the cardiac cycle. In conclusion, we showed the sensitivity of these typical flows to distance of grafting, inflows waveforms but also to their phase difference.     

Which factors influence the ability of a computational model to predict the in vivo deformation behaviour of skeletal muscle?

Deep tissue injury (DTI) is a severe form of pressure ulcer where tissue damage starts in deep tissues underneath intact skin. Tissue deformation may play an important role in the aetiology, which can be investigated using an experimental–numerical approach. Recently, an animal-specific finite element model has been developed to simulate experiments in which muscle tissue was compressed with an indenter. In this study, the material behaviour and boundary conditions were adapted to improve the agreement between model and experiment and to investigate the influence of these adaptations on the predicted strain distribution. The use of a highly nonlinear material law and including friction between the indenter and the muscle both improved the quality of the model and considerably influenced the estimated strain distribution. With the improved model, the required sample size to detect significant differences between loading conditions can be diminished, which is clearly relevant in experiments involving animals.     

Mechanical characterisation of in vivo human skin using a 3D force-sensitive micro-robot and finite element analysis

The complex mechanical properties of skin have been the subject of much study in recent years. Several experimental methods developed to measure the mechanical properties of skin in vivo, such as suction or torsion, are unable to measure skin’s anisotropic characteristics. An experiment characterising the mechanical properties of in vivo human skin using a novel force-sensitive micro-robot is presented. The micro-robot applied in-plane deformations to the anterior forearm and the posterior upper arm. The behaviour of the skin in each area is highly nonlinear, anisotropic, and viscoelastic. The response of the upper arm skin is very dependent on the orientation of the arm. A finite element model consisting of an Ogden strain energy function and quasi-linear viscoelasticity was developed to simulate the experiments. An orthogonal initial stress field, representing the in vivo skin tension, was used as an additional model parameter. The model simulated the experiments accurately with an error-of-fit of 17.5% for the anterior lower forearm area, 6.5% for the anterior upper forearm and 9.3% for the posterior upper arm. The maximum in vivo tension in each area determined by the model was 6.2 Nm⁻¹ in the anterior lower forearm, 11.4 Nm⁻¹ in anterior upper forearm and 5.6 Nm⁻¹ in the posterior upper arm. The results also show that a finite element model with a neo-Hookean strain energy function cannot simulate the experiments with the same accuracy.     

Numerical analysis of an anastomotic device

The explicit dynamic finite element method was utilized to investigate the deformation behaviour of a woven wire mesh tubular device that is used in a side-to-side anastomotic procedure for achieving gastrointestinal anastomosis. The numerical model was initially verified by comparison to experimental results that were obtained using a specialized testing mechanism. Once validated, the finite element model (FEM) was parameterized to ascertain the influence of several device parameters on its deformation behaviour. The importance of these parameters, as related to its optimal design for use in minimally invasive surgery (MIS), was subsequently ascertained and discussed.     

Nonlinear model of human descending thoracic aortic segments with residual stresses

The nonlinear static deformation of human descending thoracic aortic segments is investigated. The aorta segments are modeled as straight axisymmetric circular cylindrical shells with three hyperelastic anisotropic layers and residual stresses by using an advanced nonlinear shell theory with higher-order thickness deformation not available in commercial finite element codes. The residual stresses are evaluated in the closed configuration in an original way making use of the multiplicative decomposition. The model was initially validated through comparison with published numerical and experimental data for artery and aorta segments. Then, two different cases of healthy thoracic descending aorta segments were numerically simulated. Material data and residual stresses used in the models came from published layer-specific experiments for human aortas. The material model adopted in the study is the mechanically based Gasser–Ogden–Holzapfel, which takes into account collagen fiber dispersion. Numerical results present a difference between systolic and diastolic inner radii close to the data available in literature from in vivo measurements for the corresponding age groups. Constant length of the aortic segment between systolic and diastolic pressures was obtained for the material model that takes the dispersion of the fiber orientations into account.     

New extensometer to measure in vivo uniaxial mechanical properties of human skin

Biomechanical properties of skin are important for clinical decision making as well as clinical intervention. Measuring these properties in vivo is critical for estimating dimensional behaviour of skin flap or graft after harvest. However, existing methodologies and devices often suffer from lack of standardisation and unwanted peripheral force contribution due to the deformation of surrounding tissues during measurement. This naturally leads to measurement inaccuracies and lack of reproducibility. In order to improve the measurement accuracy, a new portable extensometer, which measures the non-invasive in vivo biomechanical properties of skin, has been designed and constructed. This design incorporates three pads that attach to the skin, including a C-shaped pad to shield the force sensor from peripheral forces. Such design produces data that are significantly closer to in vitro measurements. The results have been verified by finite element analysis, and experiments on rubber sheets and pig skins. This device can be used to obtain biomechanical properties of skin that will aid doctors in measuring skin elasticity and surgical planning, especially in skin flap surgery.     

Thermoelastic modelling of the skin at finite deformations

The modelling and computation of the coupled thermal and mechanical response of human skin at finite deformations is considered. The model extends current thermal models to account for thermally- and mechanically-induced deformations. Details of the solution of the highly nonlinear system of governing equations using the finite element method are presented. A representative numerical example illustrates the importance of considering the coupled response for the problem of a rigid, hot indenter in contact with the skin.     

Finite element implementation of a generalized Fung-elastic constitutive model for planar soft tissues

Numerical simulations of the anisotropic mechanical properties of soft tissues and tissue-derived biomaterials using accurate constitutive models remain an important and challenging research area in biomechanics. While most constitutive modeling efforts have focused on the characterization of experimental data, only limited studies are available on the feasibility of utilizing those models in complex computational applications. An example is the widely utilized exponential constitutive model proposed by Fung. Although present in the biomechanics literature for several decades, implementation of this model into finite element (FE) simulations has been limited. A major reason for limited numerical implementations are problems associated with inherent numerical instability and convergence. To address this issue, we developed and applied two restrictions for a generalized Fung-elastic constitutive model necessary to achieve numerical stability. These are (1) convexity of the strain energy function, and (2) the condition number of material stiffness matrix set lower than a prescribed value. These constraints were implemented in the nonlinear regression used for constitutive model parameter estimation to the experimental biaxial mechanical data. We then implemented the generalized Fung-elastic model into a commercial FE code (ABAQUS, Pawtucket, RI, USA). Single element and multi-element planar biaxial test simulations were conducted to verify the accuracy and robustness of the implementation. Results indicated that numerical convergence and accurate FE implementation were consistently obtained. The present study thus presents an integrated framework for accurate and robust implementation of pseudo-elastic constitutive models for planar soft tissues. Moreover, since our approach is formulated within a general FE code, it can be straightforwardly adopted across multiple software platforms.     

Quantifying the mechanical properties of human skin to optimise future microneedle device design

Microneedle devices are a promising minimally invasive means of delivering drugs/vaccines across or into the skin. However, there is currently a diversity of microneedle designs and application methods that have, primarily, been intuitively developed by the research community. To enable the rational design of optimised microneedle devices, a greater understanding of human skin biomechanics under small deformations is required. This study aims to develop a representative stratified model of human skin, informed by in vivo data. A multilayer finite element model incorporating the epidermis, dermis and hypodermis was established. This was correlated with a series of in-vivo indentation measurements, and the Ogden material coefficients were optimised using a material parameter extraction algorithm. The finite element simulation was subsequently used to model microneedle application to human skin before penetration and was validated by comparing these predictions with the in-vivo measurements. Our model has provided an excellent tool to predict micron-scale human skin deformation in vivo and is currently being used to inform optimised microneedle designs.     

A study of absorption of energy of the extremely high frequency electromagnetic radiation in the rat skin by various dosimetric methods and approaches

Using experimental and theoretical methods of dosimetry, the energy absorption of extremely high-frequency electromagnetic radiation (EHF EMR) in the skin of laboratory rats was analyzed. Specific absorption rate (SAR) in the skin was determined on the basis of both microthermometric measurements of initial rates of temperature rise in rat skin induced by the exposure and microcalorimetric measurements of specific heat of the skin. Theoretical calculations of SAR in the skin were performed with consideration for dielectric parameters of rat skin obtained from the measurements of the standing wave ratio upon reflection of electromagnetic waves from the skin surface and for the effective area of stationary overheating measured by infrared thermography. A numerical method was developed to determine electromagnetic wave energy reflected, absorbed, and transmitted in the model of flat layers. The algorithm of the method was realized in a computer program and used to calculate SAR in the skin on the basis of the complex dielectric constant of rat skin. The SAR values obtained from experimental measurements, theoretical calculations and numerical analysis are in good mutual correspondence and make about 220-280 W/kg at a frequency of 42.25 GHz and a power of 20 mW at the radiator output. The results obtained can be used for dosimetric supply of biomedical experiments on studying the physicochemical mechanisms of the biological effects of EHF EMR.