A finite element study of invariant-based orthotropic constitutive equations in the context of myocardial material parameter estimation

A previous 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. The study was based on the assumption of a homogeneous deformation. Here, we extend the previous study by performing an inverse finite element material parameter estimation. This ensures a more realistic deformation state and material parameter estimates. The constitutive relations were compared on the basis of (i) ‘goodness of fit’: how well they fit a set of six shear deformation tests and (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 relations. It was found that a specific form of the polyconvex type as well as the exponential Fung-type equations were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.     

Muscle force estimation in clinical gait analysis using AnyBody and OpenSim

A variety of musculoskeletal models are applied in different modelling environments for estimating muscle forces during gait. Influence of different modelling assumptions and approaches on model outputs are still not fully understood, while direct comparisons of standard approaches have been rarely undertaken. This study seeks to compare joint kinematics, joint kinetics and estimated muscle forces of two standard approaches offered in two different modelling environments (AnyBody, OpenSim). It is hypothesised that distinctive differences exist for individual muscles, while summing up synergists show general agreement. Experimental data of 10 healthy participants (28 ± 5 years, 1.72 ± 0.08 m, 69 ± 12 kg) was used for a standard static optimisation muscle force estimation routine in AnyBody and OpenSim while using two gait-specific musculoskeletal models. Statistical parameter mapping paired t-test was used to compare joint angle, moment and muscle force waveforms in Matlab. Results showed differences especially in sagittal ankle and hip angles as well as sagittal knee moments. Differences were also found for some of the muscles, especially of the triceps surae group and the biceps femoris short head, which occur as a result of different anthropometric and anatomical definitions (mass and inertia of segments, muscle properties) and scaling procedures (static vs. dynamic). Understanding these differences and their cause is crucial to operate such modelling environments in a clinical setting. Future research should focus on alternatives to classical generic musculoskeletal models (e.g. implementation of functional calibration tasks), while using experimental data reflecting normal and pathological gait to gain a better understanding of variations and divergent behaviour between approaches.     

A structural mixed model for variances in differential gene expression studies

The importance of variance modelling is now widely known for the analysis of microarray data. In particular the power and accuracy of statistical tests for differential gene expressions are highly dependent on variance modelling. The aim of this paper is to use a structural model on the variances, which includes a condition effect and a random gene effect, and to propose a simple estimation procedure for these parameters by working on the empirical variances. The proposed variance model was compared with various methods on both real and simulated data. It proved to be more powerful than the gene-by-gene analysis and more robust to the number of false positives than the homogeneous variance model. It performed well compared with recently proposed approaches such as SAM and VarMixt even for a small number of replicates, and performed similarly to Limma. The main advantage of the structural model is that, thanks to the use of a linear mixed model on the logarithm of the variances, various factors of variation can easily be incorporated in the model, which is not the case for previously proposed empirical Bayes methods. It is also very fast to compute and is adapted to the comparison of more than two conditions.     

Mathematical modelling in physiology

The article illustrates the method of mathematical modelling in physiology as a unique tool to study physiological processes. A number of demonstrated examples appear as a result of long-term experience in mathematical modelling of electrical and mechanical phenomena in the heart muscle. These examples are presented here to show that the modelling provides insight into mechanisms underlying these phenomena and is capable to predict new ones that were previously unknown. While potentialities of the mathematical modelling are analyzed with regard to the myocardium, they are quite universal to deal with any physiological processes.     

Modelling the maximum voluntary joint torque/angular velocity relationship in human movement

The force exerted by a muscle is a function of the activation level and the maximum (tetanic) muscle force. In "maximum" voluntary knee extensions muscle activation is lower for eccentric muscle velocities than for concentric velocities. The aim of this study was to model this "differential activation" in order to calculate the maximum voluntary knee extensor torque as a function of knee angular velocity. Torque data were collected on two subjects during maximal eccentric-concentric knee extensions using an isovelocity dynamometer with crank angular velocities ranging from 50 to 450 degrees s(-1). The theoretical tetanic torque/angular velocity relationship was modelled using a four parameter function comprising two rectangular hyperbolas while the activation/angular velocity relationship was modelled using a three parameter function that rose from submaximal activation for eccentric velocities to full activation for high concentric velocities. The product of these two functions gave a seven parameter function which was fitted to the joint torque/angular velocity data, giving unbiased root mean square differences of 1.9% and 3.3% of the maximum torques achieved. Differential activation accounts for the non-hyperbolic behaviour of the torque/angular velocity data for low concentric velocities. The maximum voluntary knee extensor torque that can be exerted may be modelled accurately as the product of functions defining the maximum torque and the maximum voluntary activation level. Failure to include differential activation considerations when modelling maximal movements will lead to errors in the estimation of joint torque in the eccentric phase and low velocity concentric phase.     

Using EMG data to constrain optimization procedure improves finger tendon tension estimations during static fingertip force production

Determining tendon tensions of the finger muscles is crucial for the understanding and the rehabilitation of hand pathologies. Since no direct measurement is possible for a large number of finger muscle tendons, biomechanical modelling presents an alternative solution to indirectly evaluate these forces. However, the main problem is that the number of muscles spanning a joint exceeds the number of degrees of freedom of the joint resulting in mathematical under-determinate problems. In the current study, a method using both numerical optimization and the intra-muscular electromyography (EMG) data was developed to estimate the middle finger tendon tensions during static fingertip force production. The method used a numerical optimization procedure with the muscle stress squared criterion to determine a solution while the EMG data of three extrinsic hand muscles serve to enforce additional inequality constraints. The results were compared with those obtained with a classical numerical optimization and a method based on EMG only. The proposed method provides satisfactory results since the tendon tension estimations respected the mechanical equilibrium of the musculoskeletal system and were concordant with the EMG distribution pattern of the subjects. These results were not observed neither with the classical numerical optimization nor with the EMG-based method. This study demonstrates that including the EMG data of the three extrinsic muscles of the middle finger as inequality constraints in an optimization process can yield relevant tendon tensions with regard to individual muscle activation patterns, particularly concerning the antagonist muscles.     

Robust estimation of physiological cross-sectional area and geometric reconstruction for human skeletal muscle

Understanding muscle architecture is crucial to determining the mechanical function of muscle during body movements, because architectural parameters directly correspond to muscle performance. Accurate parameters are thus essential for reliable simulation. Human cadaveric muscle specimen data provides the anatomical detail needed for in-depth understanding of muscle and accurate parameter estimation. However, as muscle generally has non-uniform architecture, parameter estimation, specifically, physiological cross-sectional area (PCSA), is rarely straightforward. To deal effectively with this non-uniformity, we propose a geometric approach in which a polygon is sought to best approximate the cross-sectional area of each fascicle by accounting for its three-dimensional trajectory and arrangement in the muscle. Those polygons are then aggregated to determine PCSA and volume of muscle. Experiments are run using both synthetic data and muscle specimen data. From comparison of PCSA using synthetic data, we conclude that the proposed method enhances the robustness of PCSA estimation against variation in muscle architecture. Furthermore, we suggest reconstruction methods to extract 3D muscle geometry directly from fascicle data and estimated parameters using the level set method.     

Fluctuation Analysis: Can Estimates Be Trusted?

The estimation of mutation rates and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbrück distribution outside its modelling hypotheses induces an important bias on the estimation of the relative fitness. The model is extended here to any division time distribution. Mutant counts follow a generalization of the Luria-Delbrück distribution, which depends on the mean number of mutations, the relative fitness of normal cells compared to mutants, and the division time distribution of mutant cells. Empirical probability generating function techniques yield precise estimates both of the mean number of mutations and the relative fitness of normal cells compared to mutants. In the case where no information is available on the division time distribution, it is shown that the estimation procedure using constant division times yields more reliable results. Numerical results both on observed and simulated data are reported.     

Assessment of spatial discordance of primary and effective seed dispersal of European beech (Fagus sylvatica L.) by ecological and genetic methods

Spatial discordance between primary and effective dispersal in plant populations indicates that postdispersal processes erase the seed rain signal in recruitment patterns. Five different models were used to test the spatial concordance of the primary and effective dispersal patterns in a European beech (Fagus sylvatica) population from central Spain. An ecological method was based on classical inverse modelling (SSS), using the number of seed/seedlings as input data. Genetic models were based on direct kernel fitting of mother‐to‐offspring distances estimated by a parentage analysis or were spatially explicit models based on the genotype frequencies of offspring (competing sources model and Moran‐Clark's Model). A fully integrated mixed model was based on inverse modelling, but used the number of genotypes as input data (gene shadow model). The potential sources of error and limitations of each seed dispersal estimation method are discussed. The mean dispersal distances for seeds and saplings estimated with these five methods were higher than those obtained by previous estimations for European beech forests. All the methods show strong discordance between primary and effective dispersal kernel parameters, and for dispersal directionality. While seed rain was released mostly under the canopy, saplings were established far from mother trees. This discordant pattern may be the result of the action of secondary dispersal by animals or density‐dependent effects; that is, the Janzen‐Connell effect.     

Inertia and muscle contraction parameters for musculoskeletal modelling of the shoulder mechanism

To develop a musculoskeletal model of the shoulder mechanism, both shoulders of seven cadavers were measured to obtain a complete set of parameters. Using antropometric measurements, the mass and rotational inertia of segments were estimated, followed by three-dimensional measurements of all morphological structures relevant for modelling, i.e. muscle origins and insertions, muscle bundle directions, ligament attachments and articular surfaces; all in relation to selected bony landmarks. Subsequently, muscle contraction parameters as muscle mass and physiological cross-sectional area were measured. The method of data collection and the results for inertia and muscle contraction parameters as prerequisities for modelling are described.     

Measuring morphological parameters of the pelvic floor for finite element modelling purposes

The goal of this study was to obtain a complete data set needed for studying the complex biomechanical behaviour of the pelvic floor muscles using a computer model based on the finite element (FE) theory. The model should be able to predict the effect of surgical interventions and give insight into the function of pelvic floor muscles. Because there was a lack of any information concerning morphological parameters of the pelvic floor muscle structures, we performed an experimental measurement to uncover those morphological parameters. Geometric parameters as well as muscle parameters of the pelvic floor muscles were measured on an embalmed female cadaver. A three-dimensional (3D) geometric data set of the pelvic floor including muscle fibre directions was obtained using a palpator device. A 3D surface model based on the experimental data, needed for mathematical modelling of the pelvic floor, was created. For all parts of the diaphragma pelvis, the optimal muscle fibre length was determined by laser diffraction measurements of the sarcomere length. In addition, other muscle parameters such as physiological cross-sectional area and total muscle fibre length were determined. Apart from these measurements we obtained a data set of the pelvic floor structures based on nuclear magnetic resonance imaging (MRI) on the same cadaver specimen. The purpose of this experiment was to discover the relationship between the MRI morphology and geometrical parameters obtained from the previous measurements. The produced data set is not only important for biomechanical modelling of the pelvic floor muscles, but it also describes the geometry of muscle fibres and is useful for functional analysis of the pelvic floor in general. By the use of many reference landmarks all these morphologic data concerning fibre directions and optimal fibre length can be morphed to the geometrical data based on segmentation from MRI scans.These data can be directly used as an input for building a mathematical model based on FE theory.     

Adjoint multi-start-based estimation of cardiac hyperelastic material parameters using shear data

Cardiac muscle tissue during relaxation is commonly modeled as a hyperelastic material with strongly nonlinear and anisotropic stress response. Adapting the behavior of such a model to experimental or patient data gives rise to a parameter estimation problem which involves a significant number of parameters. Gradient-based optimization algorithms provide a way to solve such nonlinear parameter estimation problems with relatively few iterations, but require the gradient of the objective functional with respect to the model parameters. This gradient has traditionally been obtained using finite differences, the calculation of which scales linearly with the number of model parameters, and introduces a differencing error. By using an automatically derived adjoint equation, we are able to calculate this gradient more efficiently, and with minimal implementation effort. We test this adjoint framework on a least squares fitting problem involving data from simple shear tests on cardiac tissue samples. A second challenge which arises in gradient-based optimization is the dependency of the algorithm on a suitable initial guess. We show how a multi-start procedure can alleviate this dependency. Finally, we provide estimates for the material parameters of the Holzapfel and Ogden strain energy law using finite element models together with experimental shear data.     

Composite Hazard Functions Reflecting Competing Latent Processes

A method for fitting parametric models to apparently complex hazard rates in survival data is suggested. Hazard complexity may indicate competing causes of failure. A competing risks model is constructed on the assumption that a failure time can be considered as the first passage time of possibly several latent, stochastic processes competing in reaching a barrier. An additional assumption of independence between the hidden processes leads directly to a composite hazard function as the sum of the cause specific hazards. We show how this composite hazard model based on Wiener processes can serve as a flexible tool for modelling complex hazards by varying the number of processes and their starting conditions. An example with real data is presented. Parameter estimation and model assessment are based on Markov Chain Monte Carlo methods. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Is more data always better? A simulation study of benefits and limitations of integrated distribution models

Species distribution models are popular and widely applied ecological tools. Recent increases in data availability have led to opportunities and challenges for species distribution modelling. Each data source has different qualities, determined by how it was collected. As several data sources can inform on a single species, ecologists have often analysed just one of the data sources, but this loses information, as some data sources are discarded. Integrated distribution models (IDMs) were developed to enable inclusion of multiple datasets in a single model, whilst accounting for different data collection protocols. This is advantageous because it allows efficient use of all data available, can improve estimation and account for biases in data collection. What is not yet known is when integrating different data sources does not bring advantages. Here, for the first time, we explore the potential limits of IDMs using a simulation study integrating a spatially biased, opportunistic, presence-only dataset with a structured, presence–absence dataset. We explore four scenarios based on real ecological problems; small sample sizes, low levels of detection probability, correlations between covariates and a lack of knowledge of the drivers of bias in data collection. For each scenario we ask; do we see improvements in parameter estimation or the accuracy of spatial pattern prediction in the IDM versus modelling either data source alone? We found integration alone was unable to correct for spatial bias in presence-only data. Including a covariate to explain bias or adding a flexible spatial term improved IDM performance beyond single dataset models, with the models including a flexible spatial term producing the most accurate and robust estimates. Increasing the sample size of presence–absence data and having no correlated covariates also improved estimation. These results demonstrate under which conditions integrated models provide benefits over modelling single data sources.     

Volumic patient-specific reconstruction of muscular system based on a reduced dataset of medical images

Three-dimensional mechanical modelling of muscles is essential for various biomechanical applications and clinical evaluation, but it requires a tedious manual processing of numerous images. A muscle reconstruction method is presented based on a reduced set of images to generate an approximate parametric object from basic dimensions of muscle contours. A regular volumic mesh is constructed based on this parametric object. The approximate object and the corresponding mesh are deformed to fit the exact muscles contours yielding patient-specific geometry. Evaluation was performed by comparison of geometry to that obtained by contouring all computed tomography (CT) slices, and by quantification of the mesh quality criteria. Muscle fatty infiltration was estimated using a threshold between fat and muscle. Volumic fat index (VFI) of a muscle was computed using first all the complete CT scan slices containing the muscle (VFI(ref)) and a second time only the slices used for reconstruction (VFI(recons)). Mean volume error estimation was 2.6% and hexahedron meshes fulfilled quality criteria. VFI(recons) respect the individual variation of fat content.     

TRITON: in silico construction of protein mutants and prediction of their activities

MOTIVATION: One of the objectives of protein engineering is to propose and construct modified proteins with improved activity for the substrate of interest. Systematic computational investigation of many protein variants requires the preparation and handling of a large number of data files. The type of the data generated during the modelling of protein variants and the estimation of their activities offers the possibility of process automatization. RESULTS: The graphical program TRITON has been developed for modelling protein mutants and assessment of their activities. Protein mutants are modelled from the wild type structure by homology modelling using the external program MODELLER. Chemical reactions taking place in the mutants active site are modelled using the semi-empirical quantum mechanic program MOPAC. Semi-quantitative predictions of mutants activities can be achieved by evaluating the changes in energies of the system and partial atomic charges of active site residues during the reaction. The program TRITON offers graphical tools for the preparation of the input data files, for calculation and for the analysis of the generated output data. AVAILABILITY: The program TRITON can run under operating systems IRIX, Linux and NetBSD. The software is available at http://www.chemi.muni.cz/lbsd/triton.ht ml.     

Recombination hotspots as a point process

The variation of the recombination rate along chromosomal DNA is one of the important determinants of the patterns of linkage disequilibrium. A number of inferential methods have been developed which estimate the recombination rate and its variation from population genetic data. The majority of these methods are based on modelling the genealogical process underlying a sample of DNA sequences and thus explicitly include a model of the demographic process. Here we propose a different inferential procedure based on a previously introduced framework where recombination is modelled as a point process along a DNA sequence. The approach infers regions containing putative hotspots based on the inferred minimum number of recombination events; it thus depends only indirectly on the underlying population demography. A Poisson point process model with local rates is then used to infer patterns of recombination rate estimation in a fully Bayesian framework. We illustrate this new approach by applying it to several population genetic datasets, including a region with an experimentally confirmed recombination hotspot.     

Integrin organization: linking adhesion ligand nanopatterns with altered cell responses

This paper presents a modelling framework in which the mechanochemical properties of smooth muscle cells may be studied. The activation of smooth muscles is considered in a three-dimensional continuum model which is key to realistically capture the function of hollow organs such as blood vessels. On the basis of a general thermodynamical framework the mechanical and chemical phases are specialized in order to quantify the coupled mechanochemical process. A free-energy function is proposed as the sum of a mechanical energy stored in the passive tissue, a coupling between the mechanical and chemical kinetics and an energy related purely to the chemical kinetics and the calcium ion concentration. For the chemical phase it is shown that the cross-bridge model of Hai and Murphy [1988. Am. J. Physiol. Cell Physiol. 254, C99-C106] is included in the developed evolution law as a special case. In order to show the specific features and the potential of the proposed continuum model a uniaxial extension test of a tissue strip is analysed in detail and the related kinematics and stress-stretch relations are derived. Parameter studies point to coupling phenomena; in particular the tissue response is analysed in terms of the calcium ion level. The model for smooth muscle contraction may significantly contribute to current modelling efforts of smooth muscle tissue responses.     

Using nest captures and video cameras to estimate survival and abundance of breeding Piping Plovers Charadrius melodus

The estimation of abundance is fundamental to ecology and conservation but often is difficult or impossible to accomplish reliably. Recent improvements in wildlife cameras and ecological modelling have allowed for improved accuracy in estimates of abundance. In this study, we paired nest captures and high-definition nest video camera monitoring with modelling for a novel approach to estimate survival and abundance of threatened Piping Plovers Charadrius melodus breeding on Missouri River sandbars. From 2005 to 2014, we captured individuals on nests and uniquely marked them and recaptured previously marked individuals. In 2015–2017, we resighted marked individuals using small, high-definition video cameras deployed at nests, and counted the number of marked and unmarked breeding individuals associated with nests. We estimated apparent survival and derived estimates of the abundance of breeding individuals and population growth each year using a state-space Jolly–Seber superpopulation model with the addition of a binomial band ratio model for data collected using nest video cameras. Apparent survival averaged 0.73 ± 0.03 (mean ± sd) throughout the study. The number of breeding individuals varied, with the population increasing from 2012 to 2017 following a major habitat creation event. This study provides one of the few examples of camera data being used to produce demographic parameter and abundance estimates for an avian species. The camera and modelling methods described in this study may be applicable to other avian species in which some portion of the breeding population is uniquely marked.     

Estimating the effect of inbreeding on survival

Conservation biologists need to be able to estimate reliably the effects of inbreeding on survival, and need to be able to do so with a range of different data types. Kalinowski and Hedrick described a non-linear maximum likelihood estimation procedure for modelling relationships between survivorship and inbreeding. Although their method is useful for illustrating the concepts involved in modelling such relationships, it is only applicable to simple datasets. We illustrate that the parameter estimates generated by Kalinowski and Hedrick's method are easily obtained using generalized linear modelling procedures available in standard statistical packages, and that these offer several advantages even with simple datasets. We suggest procedures that can be used for modelling relationships between survival and inbreeding with more complex data types, including datasets with multiple and ragged encounters, uncertain detection and random effects.