Biophysical constraints on the evolution of tissue structure and function.

Phylogenetic analyses based on models of molecular sequence evolution have driven to industrial scale the generation, cataloguing and modelling of nucleic acid and polypeptide structure. The recent application of these techniques to study the evolution of protein interaction networks extends this analytical rigour to the study of nucleic acid and protein function. Can we further extend phylogenetic analysis of protein networks to the study of tissue structure and function? If the study of tissue phylogeny is to join up with mainstream efforts in the molecular evolution domain, the continuum field description of tissue biophysics must be linked to discrete descriptions of molecular biochemistry. In support of this goal we discuss tissue units, and biophysical constraints to molecular function associated with these units, to present a rationale with which to model tissue evolution. Our rationale combines a multiscale hierarchy of functional tissue units (FTUs) with the corresponding application of physical laws to describe molecular interaction networks and flow processes over continuum fields within these units. Non-dimensional numbers, derived from the equations governing biophysical processes in FTUs, are proposed as metrics for comparative studies across individuals, species or evolutionary time. We also outline the challenges inherent to the systematic cataloguing and phylogenetic analysis of tissue features relevant to the maintenance and regulation of molecular interaction networks. These features are key to understanding the core biophysical constraints on tissue evolution.

Myocardial material parameter estimation: a comparison of invariant based orthotropic constitutive equations.

This study investigated a number of invariant based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. A number of orthotropic laws based on Green strain components and one microstructurally based law have previously been investigated to fit experimental measurements of stress-strain behaviour. Here we extend this investigation to include several recently proposed functional forms, i.e. invariant based orthotropic and transversely isotropic constitutive relations. These laws were compared on the basis of (i) 'goodness of fit': how well they fit a set of six shear deformation tests, (ii) 'variability': how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive laws. It was found that a specific form of the polyconvex type as well as the exponential Fung-type law from the previous study were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

Myocardial material parameter estimation: a non-homogeneous finite element study from simple shear tests.

The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) "goodness of fit": how well they fit a set of six shear deformation tests, (ii) "determinability": how well determined the objective function is at the optimal parameter fit, and (iii) "variability": how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study.It was found that the same material law as in the previous study, the orthotropic Fung-type "Costa-Law", was the most suitable for inverse material parameter estimation for myocardium in simple shear.

The Noble cardiac ventricular electrophysiology models in CellML.

We present a review of the cardiac ventricular cell electrophysiology models developed by Prof. Denis Noble and colleagues as an example of how models may be published using a web-based CellML publication framework. The models reviewed have been marked-up in CellML and then used to compute all results presented here. The models are freely available from a website as are the specific numerical experiments discussed in this review and the tools used to perform the simulations.

The IUPS Physiome Project: a framework for computational physiology.

The IUPS Physiome Project is an internationally collaborative open-source project to provide a public domain framework for computational physiology, including the development of modelling standards, computational tools and web-accessible databases of models of structure and function at all spatial scales. A number of papers in this volume deal with the development of specific mathematical models of physiological processes. This paper stands back from the detail of individual models and reviews the current state of the IUPS Physiome Project including organ and organ system continuum models, the interpretation of constitutive law parameters in terms of micro-structural models, and markup languages for standardizing cellular processes. Some current practical applications of the physiome models are given and some of the challenges for the next 5 years of the Physiome Project at the level of organs, cells and proteins are proposed.

Modelling the mechanical properties of cardiac muscle.

A model of passive and active cardiac muscle mechanics is presented, suitable for use in continuum mechanics models of the whole heart. The model is based on an extensive review of experimental data from a variety of preparations (intact trabeculae, skinned fibres and myofibrils) and species (mainly rat and ferret) at temperatures from 20 to 27 degrees C. Experimental tests include isometric tension development, isotonic loading, quick-release/restretch, length step and sinusoidal perturbations. We show that all of these experiments can be interpreted with a four state variable model which includes (i) the passive elasticity of myocardial tissue, (ii) the rapid binding of Ca2+ to troponin C and its slower tension-dependent release, (iii) the kinetics of tropomyosin movement and availability of crossbridge binding sites and the length dependence of this process and (iv) the kinetics of crossbridge tension development under perturbations of myofilament length.

An anatomically based patient-specific finite element model of patella articulation: towards a diagnostic tool.

A 3D anatomically based patient-specific finite element (FE) model of patello-femoral (PF) articulation is presented to analyse the main features of patella biomechanics, namely, patella tracking (kinematics), quadriceps extensor forces, surface contact and internal patella stresses. The generic geometries are a subset from the model database of the International Union of Physiological Sciences (IUPS) (http://www.physiome.org.nz) Physiome Project with soft tissue derived from the widely used visible human dataset, and the bones digitised from an anatomically accurate physical model with muscle attachment information. The models are customised to patient magnetic resonance images using a variant of free-form deformation, called 'host-mesh' fitting. The continuum was solved using the governing equation of finite elasticity, with the multibody problem coupled through contact mechanics. Additional constraints such as tissue incompressibility are also imposed. Passive material properties are taken from the literature and implemented for deformable tissue with a non-linear micro-structurally based constitutive law. Bone and cartilage are implemented using a 'St-Venant Kirchoff' model suitable for rigid body rotations. The surface fibre directions have been estimated from anatomy images of cadaver muscle dissections and active muscle contraction was based on a steady-state calcium-tension relation. The 3D continuum model of muscle, tendon and bone is compared with experimental results from the literature, and surgical simulations performed to illustrate its clinical assessment capabilities (a Maquet procedure for reducing patella stresses and a vastus lateralis release for a bipartite patella). Finally, the model limitations, issues and future improvements are discussed.

A cerebral palsy assessment tool using anatomically based geometries and free-form deformation.

A geometrical analysis tool for investigating muscle length change in cerebral palsy (CP) patients is presented. A subset of anatomically based geometries from the International Union of Physiological Sciences (IUPS) Physiome Project is used, which is derived from the visible human (VH) data set with muscle attachment information, and customised using volume-preserving free-form deformation (FFD), the 'host-mesh' technique. The model's intended use is to provide pre- and post-surgery assessment for muscle lengthening, a surgery performed to help slacken tight muscles and improve gait. The model is illustrated using healthy patient data from motion capture as a validation followed by three CP case studies to highlight its use. The methodology is presented in three stages, (1) a FFD of the complete lower limb, (2) a focused geometric study on the semimembranosus (SM) and gastrocnemius (GT) muscles, and (3) an improved hybrid mechanics-FFD approach as an improvement for future analysis, with differentiation between muscle and tendon lengthening, and contact detection between sliding muscles. Finally, the issues, limitations, in particular with the marker system, and model improvements are discussed.

Modelling the passive and nerve activated response of the rectus femoris muscle to a flexion loading: a finite element framework.

A muscle modelling framework is presented which relates the mechanical response of the rectus femoris muscle (at the organ level) to tissue level properties, with the capability of linking to the cellular level as part of the IUPS Physiome Project. This paper will outline our current approach to muscle modelling incorporating micro-structural passive and active properties including fibre orientations and nerve innervation. The technique is based on finite deformation (using FE analysis) coupled to electrical nerve initiated muscle activation, and we present the influence of active tension through an eccentric contraction at specific flexion angles. Finally we discuss the future goals of incorporating cell mechanics and validating at the organ level to provide a complete diagnostic tool with the ability to relate mechanisms of failure across spatial scales.

The IUPS Physiome Project. International Union of Physiological Sciences.

Modern medicine is currently benefiting from the development of new genomic and proteomic techniques, and also from the development of ever more sophisticated clinical imaging devices. This will mean that the clinical assessment of a patient's medical condition could, in the near future, include information from both diagnostic imaging and DNA profile or protein expression data. The Physiome Project of the International Union of Physiological Sciences (IUPS) is attempting to provide a comprehensive framework for modelling the human body using computational methods which can incorporate the biochemistry, biophysics and anatomy of cells, tissues and organs. A major goal of the project is to use computational modelling to analyse integrative biological function in terms of underlying structure and molecular mechanisms. To support that goal the project is establishing web-accessible physiological databases dealing with model-related data, including bibliographic information, at the cell, tissue, organ and organ system levels. This paper discusses the development of comprehensive integrative mathematical models of human physiology based on patient-specific quantitative descriptions of anatomical structures and models of biophysical processes which reach down to the genetic level.

An assessment of the mechanical properties of leaflets from four second-generation porcine bioprostheses with biaxial testing techniques.

The aim of this study was to determine whether second-generation porcine bioprostheses, glutaraldehyde fixed at pressures said to be less than 4 mm Hg, exhibit more natural leaflet material properties than earlier valves fixed at 80 to 100 mm Hg. Biaxial mechanical testing techniques were used to compare Carpentier-Edwards SAV, St. Jude Medical BioImplant, Hancock II, and Medtronic Intact bioprostheses (12 leaflets from four valves in each case) with fresh porcine aortic valves and high pressure-fixed Carpentier-Edwards 6625 bioprostheses (14 leaflets from five valves in each case). The circumferential extensibility of leaflets from Medtronic Intact bioprostheses and from fresh porcine aortic valves were not significantly different (p greater than 0.05), whereas leaflets from the other second-generation valves tested and from Carpentier-Edwards 6625 valves were highly inextensible in the circumferential direction. The radial material properties of leaflets from all bioprostheses differed from those of fresh porcine aortic valves, which were very extensible with a high pretransitional compliance. The radial extensibility and compliance of Hancock II, St. Jude Medical BioImplant, and Carpentier-Edwards 6625 leaflets were not significantly different (p greater than 0.05). In the radial direction, Carpentier-Edwards SAV and Medtronic Intact valve leaflets were substantially more extensible than Carpentier-Edwards 6625 leaflets (p less than 0.01), whereas Medtronic Intact leaflets were more compliant than all other bioprostheses. These data demonstrate (1) that second-generation porcine bioprosthetic valves do not necessarily exhibit more natural leaflet material properties than earlier high pressure-fixed xenografts and (2) that Medtronic Intact valve leaflets have material properties most closely approximating the fresh porcine aortic valve.

The effect of synthetic patch repair of coarctation on regional deformation of the aortic wall.

BACKGROUND: A long-term complication of synthetic patch repair of coarctation is true aneurysm formation. AIM: An in vitro study was undertaken to determine the effects of patch angioplasty on aortic geometry and strain adjacent to the patch. METHODS: Segments of human descending thoracic aorta were subject to 10 pressure loading cycles (10-120 mm Hg; 1.36-16.32 kPa) before and after simulated coarctation repair with a synthetic patch. Local curvature and strain were estimated by fitting a geometric model to reconstructed three-dimensional surface marker points. RESULTS: In the control aortas, when pressure increased from 11 +/- 1.0 to 124 +/- 4.0 mm Hg (1.5 +/- 0.14 to 16.86 +/- 0.54 kPa), average circumferential curvature decreased from 0.1543 +/- 0.03 to 0.1065 +/- 0.03 mm(-1). The average major extension reached a maximum of 1.43 +/- 0.08. After patch implantation, the average circumferential curvature was reduced relative to control at all pressures. Average major extensions were significantly greater than paired control values and reached a maximum of 1.55 +/- 0.08 at 122 +/- 4.0 mm Hg (16.59 +/- 0. 54 kPa). Substantial strain inhomogeneity was observed and major extensions were greatest immediately adjacent to the patch. INFERENCE: Synthetic patch repair of coarctation of the aorta increases wall strain and produces significant regional gradients in strain. With control aortic material properties there may be a substantial increase in wall stress immediately adjacent to the aorta, which could lead to true aneurysm formation.

An anatomical heart model with applications to myocardial activation and ventricular mechanics.

A three-dimensional finite element model of the mechanical and electrical behavior of the heart is being developed in a collaboration among Auckland University, New Zealand; the University of California at San Diego, U.S.; and McGill University, Canada. The equations of continuum mechanics from the theory of finite deformation elasticity are formulated in a prolate spheroidal coordinate system and solved using a combination of Galerkin and collocation techniques. The finite element basis functions used for the dependent and independent variables range from linear Lagrange to cubic Hermite, depending on the degree of spatial variation and continuity required for each variable. Orthotropic constitutive equations derived from biaxial testing of myocardial sheets are defined with respect to the microstructural axes of the tissue at the Gaussian quadrature points of the model. In particular, we define the muscle fiber orientation and the newly identified myocardial sheet axis orientation throughout the myocardium using finite element fields with nodal parameters fitted by least-squares to comprehensive measurements of these variables. Electrical activation of the model is achieved by solving the FitzHugh-Nagumo equations with collocation at fixed material points of the anatomical finite element model. Electrical propagation relies on an orthotropic conductivity tensor defined with respect to the local material axes. The mechanical constitutive laws for the Galerkin continuum mechanics model are (1) an orthotropic "pole-zero" law for the passive mechanical properties of myocardium and (2) a Wiener cascade model of the active mechanical properties of the muscle fibers. This chapter concentrates on two aspects of the model: first, grid generation, including both the generation of nodal coordinates for the finite element mesh and the generation of orthotropic material axes at each computational point, and, second, the formulation of constitutive laws suitable for numerically intensive finite element computations. Extensions to this model and applications to the mechanical and electrical function of the heart are described in Chapter 16 by McCulloch and co-workers.

Estimation of epicardial strain using the motions of coronary bifurcations in biplane cinéangiography.

A quantitative method is described for estimating epicardial deformation from the motion of the superficial arteries. A structural model of the time-varying surface is constructed using tensor product basis functions which are bicubic Hermite in the spatial domain and sinusoidal in the temporal domain. The loci of the superficial coronary arteries are reconstructed interactively at diastasis and the bifurcations are tracked semiautomatically throughout a cardiac cycle. An initial surface is fitted to the vessels at diastasis and is subsequently deformed under the influence of the bifurcations. The Lagrange-Green strain tensor is used to obtain a complete description of surface strain over the entire region spanned by the model. The calculated deformation field varies smoothly over space and time and is not constrained by assumptions of isotropy or piecewise homogeneity. Results are presented for a single cycle of a human heart.

Involvement of Beet western yellows virus, Cauliflower mosaic virus, and Turnip mosaic virus in Internal Disorders of Stored White Cabbage.

ABSTRACT Experiments over two growing seasons clearly showed that Turnip mosaic virus (TuMV) infection was associated with internal necrosis (sunken necrotic spots 5 to 10 mm in diameter) and Beet western yellows virus (BWYV) infection was associated with collapse of leaf tissue at the margins (tipburn) in heads of stored white cabbage (Brassica oleracea var. capitata). Virtually no tipburn was seen in cv. Polinius, whereas cv. Impala was affected severely. Internal necrotic spots were seen in both cultivars. BWYV appeared to interact with TuMV. Plants infected with both viruses showed a lower incidence of external symptoms and had less internal necrosis than plants infected with TuMV alone. Cauliflower mosaic virus (CaMV) did not induce significant amounts of internal necrosis or tipburn, but did, in most cases, exacerbate symptoms caused by TuMV and BWYV. BWYV-induced tipburn worsened significantly during storage. Post-transplanting inoculation with TuMV induced more internal necrosis than pre-transplant inoculation. There was a significant association between detection of TuMV just prior to harvest and subsequent development of internal necrotic spots. Individually, all three viruses significantly reduced the yield of cv. Polinius, whereas only BWYV and CaMV treatments reduced the yield of cv. Impala.

Myocardial constitutive laws for continuum mechanics models of the heart.

Myocardial constitutive laws, for use in anatomically accurate finite element models of the heart, are presented for the passive and active mechanical properties of cardiac muscle. Biaxial testing of tissue sheets together with observations of tissue microstructure are used to define a "pole-zero" strain energy function for passive myocardium. A "fading memory" model of actively developed tension is based here on published work on the active properties of cardiac trabeculae.

Strain measurement in biaxially loaded inhomogeneous, anisotropic elastic membranes.

This paper considers the problem of measuring the strain field in biaxially loaded elastic membranes, such as soft biological tissue. Cross-correlation of intrinsic or applied speckle patterns were used to calculate the 2D displacements of small regions on the surface of a deforming membrane. This method was able to resolve 2D displacements to within a twentieth of a pixel. A finite-element model with bicubic-Hermite interpolation was used to represent the geometry of the membrane in the undeformed state. This model was fitted to the measured displacements to obtain the geometry of the membrane in the deformed state, and the strain field was calculated from the change in geometry. The strain fields were measured in both an inhomogeneous isotropic rubber membrane and a section of sheep diaphragm.

Instrumentation and procedures for estimating the constitutive parameters of inhomogeneous elastic membranes.

This study presents a method for estimating the spatial variations in material properties of elastic membranes, such as biological tissue, which contain both inhomogeneous strain fields and inhomogeneous material properties. In order to validate the method, an inhomogeneous, isotropic rubber membrane was biaxially loaded to obtain a set of states. A neo-Hookean finite element model, together with the measured strains, was used to estimate the material parameters by minimizing the residuals between the measured and modelled residual on surface tractions.

Anatomically based geometric modelling of the musculo-skeletal system and other organs.

Anatomically based finite element geometries are becoming increasingly popular in physiological modelling, owing to the demand for modelling that links organ function to spatially distributed properties at the protein, cell and tissue level. We present a collection of anatomically based finite element geometries of the musculo-skeletal system and other organs suitable for use in continuum analysis. These meshes are derived from the widely used Visible Human (VH) dataset and constitute a contribution to the world wide International Union of Physiological Sciences (IUPS) Physiome Project (www.physiome.org.nz). The method of mesh generation and fitting of tricubic Hermite volume meshes to a given dataset is illustrated using a least-squares algorithm that is modified with smoothing (Sobolev) constraints via the penalty method to account for sparse and scattered data. A technique ("host mesh" fitting) based on "free-form" deformation (FFD) is used to customise the fitted (generic) geometry. Lung lobes, the rectus femoris muscle and the lower limb bones are used as examples to illustrate these methods. Geometries of the lower limb, knee joint, forearm and neck are also presented. Finally, the issues and limitations of the methods are discussed.

Ophthalmic microsurgical robot and associated virtual environment.

An ophthalmic virtual environment has been developed as part of a teleoperated microsurgical robot built to perform surgery on the eye. The virtual environment is unique in that it incorporates a detailed continuum model of the anatomical structures of the eye, its mechanics and optical properties, together with a less detailed geometric-mechanical model of the face. In addition to providing a realistic visual display of the eye being operated on, the virtual environment simulates tissue properties during manipulation and cutting and the forces involved are determined by solving a mechanical finite element model of the tissue. These forces are then fed back to the operator via a force reflecting master and so the surgeon can experience both the visual and mechanical sensations associated with performing surgery. The virtual environment can be used to enhance the images produced by the camera on the microsurgical slave robot during surgery and as a surgical simulator in which it replaces these images with computer graphics generated from the eye model.