On the kinematic modelling and the parameter estimation of the human shoulder.

This paper presents some results on the modelling and the corresponding parameter estimation of the human shoulder. This system consists of the clavicle, the scapula, the humerus and the various joints between these bodies and the trunk through the sternum; it will be represented as a succession of a rotational joint between the sternum and the clavicle and a constant distance joint, representing the scapula between, the clavicle and the humerus head. The parameters of this system are the components of the position vectors of the joint characteristic points (the corresponding centres of the rotations). Experimental results are presented as well as a validation of the proposed model.     

Development and evaluation of the measurement system for the human shoulder joint based on the 6 DOF kinematic modelling

Although numerical models on the shoulder complex joint are currently available, many are impractical because of the procedural complexity coupled with limited and mere simple simulations. The present study defined the clavicle-scapula system as the "base of the humerus" in determining the position of proximal head of humerus, rendering conclusive innovation of a six degree of freedom (DOF) shoulder complex joint model. Furthermore, a complete measurement system where evaluation by calibrating the actual values via the use of an electromagnetic tracking device (ETD) was developed based on the innovated model. The special calibration method using optimizing calculation to work out the rotational center of humerus was employed and actually tested if the theoretical consideration was practically available. As a result of accuracy check experiments, the measurement error was defined within 2-3 mm, indicating sufficient accuracy in studies for human movement. Our findings strongly advocate that the benefit of this novel measurement system would contribute to studies related to shoulder movements in physiological anthropology.     

Mathematical modelling of the light response curve of photoinhibition of Photosystem II

The light response curves of the acceptor and donor side mechanisms of photoinhibition of Photosystem II were calculated, using Arabidopsis as a model organism. Acceptor-side photoinhibition was modelled as double reduction of Q_A, noting that non-photochemical quenching has the same effect on the quantum yield of Q_A double reduction in closed PSII centres as it has on the quantum yield of electron transport in open centres. The light response curve of acceptor-side photoinhibition in Arabidopsis shows very low efficiency under low intensity light and a relatively constant quantum yield above light saturation of photosynthesis. To calculate the light response curve of donor-side photoinhibition, we built a model describing the concentration of the oxidized primary donor P₆₈₀⁺ during steady-state photosynthesis. The model is based on literature values of rate constants of electron transfer reactions of PSII, and it was fitted with fluorescence parameters measured in the steady state. The modelling analysis showed that the quantum yield of donor-side photoinhibition peaks under moderate light. The deviation of the acceptor and donor side mechanisms from the direct proportionality between photoinhibition and photon flux density suggests that these mechanisms cannot solely account for photoinhibition in vivo, but contribution of a reaction whose quantum yield is independent of light intensity is needed. Furthermore, a simple kinetic calculation suggests that the acceptor-side mechanism may not explain singlet oxygen production by photoinhibited leaves. The theoretical framework described here can be used to estimate the yields of different photoinhibition mechanisms under different wavelengths or light intensities.     

Mathematical modelling of carbohydrate degradation by human colonic microbiota

The human colon is an anaerobic ecosystem that remains largely unexplored as a result of its limited accessibility and its complexity. Mathematical models can play a central role for a better insight into its dynamics. In this context, this paper presents the development of a mathematical model of carbohydrate degradation. Our aim was to provide an in silico approach to contribute to a better understanding of the fermentation patterns in such an ecosystem. Our mathematical model is knowledge-based, derived by writing down mass-balance equations. It incorporates physiology of the intestine, metabolic reactions and transport phenomena. The model was used to study various nutritional scenarios and to assess the role of the mucus on the system behavior. Model simulations provided an adequate qualitative representation of the human colon. Our model is complementary to experimental studies on human colonic fermentation, which, of course, is not meant to replace. It may be helpful to gain insight on questions that are still difficult to elucidate by experimentation and suggest future experiments.     

Mathematical modelling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells II

The Drosophila posterior midgut epithelium mainly consists of intestinal stem cells (ISCs); semi-differentiated cells, i.e. enteroblasts (EBs); and two types of fully differentiated cells, i.e. enteroendocrine cells (EEs) and enterocytes (ECs), which are controlled by signalling pathways. In [M. Kuwamura, K. Maeda, and T. Adachi-Yamada, Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells I, J. Biol. Dyn. 4 (2009), pp. 248-257], on the basis of the functions of the Wnt and Notch signalling pathways, we studied the regulatory mechanism for the proliferation and differentiation of ISCs under the assumption that the Wnt proteins are supplied from outside the cellular system of ISCs. In this paper, we experimentally show that the Wnt proteins are specifically expressed in ISCs, EBs, and EEs, and theoretically show that the cellular system of ISCs can be self-maintained under the assumption that the Wnt proteins are produced in the cellular system of ISCs. These results provide a useful basis for determining whether an environmental niche is required for maintaining the cellular system of tissue stem cells.     

Mathematical modelling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells II

The Drosophila posterior midgut epithelium mainly consists of intestinal stem cells (ISCs); semi-differentiated cells, i.e. enteroblasts (EBs); and two types of fully differentiated cells, i.e. enteroendocrine cells (EEs) and enterocytes (ECs), which are controlled by signalling pathways. In [M. Kuwamura, K. Maeda, and T. Adachi-Yamada, Mathematical modeling and experiments for the proliferation and differentiation of Drosophila intestinal stem cells I, J. Biol. Dyn. 4 (2009), pp. 248–257], on the basis of the functions of the Wnt and Notch signalling pathways, we studied the regulatory mechanism for the proliferation and differentiation of ISCs under the assumption that the Wnt proteins are supplied from outside the cellular system of ISCs. In this paper, we experimentally show that the Wnt proteins are specifically expressed in ISCs, EBs, and EEs, and theoretically show that the cellular system of ISCs can be self-maintained under the assumption that the Wnt proteins are produced in the cellular system of ISCs. These results provide a useful basis for determining whether an environmental niche is required for maintaining the cellular system of tissue stem cells.     

Mathematical modelling of lipid transbilayer movement in the human erythrocyte plasma membrane

A model is presented to simulate transverse lipid movement in the human erythrocyte membrane. The model is based on a system of differential equations describing the time-dependence of phospholipid redistribution and the steady state distribution between the inner and outer membrane monolayer. It takes into account several mechanisms of translocation: (i) ATP-dependent transport via the aminophospholipid translocase; (ii) protein-mediated facilitated and (iii) carrier independent transbilayer diffusion. A reasonable modelling of the known lipid asymmetry could only be achieved by introducing mechanism (iii). We have called this pathway the compensatory flux, which is proportional to the gradient of phospholipids between both membrane leaflets. Using realistic model parameters, the model allows the calculation of the transbilayer motion and distribution of endogenous phospholipids of the human erythrocyte membrane for several biologically relevant conditions. Moreover, the model can also be applied to experiments usually performed to assess phospholipid redistribution in biological membranes. Thus, it is possible to simulate transbilayer motion of exogenously added phospholipid analogues in erythrocyte membranes. Those experiments have been carried out here in parallel using spin labeled lipid analogues. The general application of this model to other membrane systems is outlined.Abbreviations PBS phosphate buffered saline - DFP diisopropyl fluorophosphate - ESR electron spin resonance - RBC red blood cells - PC phosphatidylcholine - PE phosphatidylethanolamine - PS phosphatidylserine - SM sphingomyelin - (0,2)PC 1-palmitoyl-2(4doxylpentanoyl)-PC - (0,2)PE 1-palmitoyl-2(4-doxylpentanoyl)-PE - (0,2) PS 1-palmitoyl-2(4-doxylpentanoyl)-PS     

Mathematical modelling of the action potential of human embryonic stem cell derived cardiomyocytes

ABSTRACT: BACKGROUND: Human embryonic stem cell derived cardiomyocytes (hESC-CMs) hold high potential for basic and applied cardiovascular research. The development of a reliable simulation platform able to mimic the functional properties of hESC-CMs would be of considerable value to perform preliminary test complementing in vitro experimentations. METHODS: We developed the first computational model of hESC-CM action potential by integrating our original electrophysiological recordings of transient-outward, funny, and sodium-calcium exchanger currents and data derived from literature on sodium, calcium and potassium currents in hESC-CMs. RESULTS: The model is able to reproduce basal electrophysiological properties of hESC-CMs at 15--40 days of differentiation (Early stage). Moreover, the model reproduces the modifications occurring through the transition from Early to Late developmental stage (50--110, days of differentiation). After simulated blockade of ionic channels and pumps of the sarcoplasmic reticulum, Ca2+ transient amplitude was decreased by 12% and 33% in Early and Late stage, respectively, suggesting a growing contribution of a functional reticulum during maturation. Finally, as a proof of concept, we tested the effects induced by prototypical channel blockers, namely E4031 and nickel, and their qualitative reproduction by the model. CONCLUSIONS: This study provides a novel modelling tool that may serve useful to investigate physiological properties of hESC-CMs.     

A kinematic model of the shoulder complex to evaluate the arm-reachable workspace

Upper-arm evaluation including shoulder motion in physiotherapy has no three-dimensional tool for an arm-functioning evaluation, which hampers an uniform, objective comparison. Human shoulder complex models suffer from lack of shoulder girdle kinematic data. A kinematic shoulder-complex model with six degrees of freedom is proposed as the composition of the inner joint representing the shoulder-girdle joints and outer joint representing the glenohumeral joint. The outer shoulder joint has three perpendicular rotations: adduction/abduction, retroflexion/flexion and internal/external rotation of the humerus. The inner shoulder joint has two rotations, depression/elevation and retraction/protraction, and one translation, which are all dependent on the elevation angle of the humerus. The human arm-reachable workspace that represents the area within reach of the wrist is calculated on the basis of the shoulder-complex model and the additional elbow-joint direct kinematics. It was demonstrated that cross-sections of the calculated workspace are in agreement with the measured arm-reachable workspace in all three anatomical planes. The arm-reachable workspace volume and graphics were calculated and a comparison of the arm's workspaces during a patient's shoulder treatment was made. The obtained numerical and graphical arm-reachable workspaces can be used for arm-functioning evaluations in rehabilitation and ergonomics.     

Mathematical modelling of stimulus-secretion coupling in the pancreatic B-cell. II. Calcium-stimulated calcium release

An attempt was made to simulate in a mathematical model one of the two major effects of glucose upon 45Ca fractional outflow rate from prelabelled pancreatic islets, namely the increase in effluent radioactivity which is currently ascribed to the displacement of 45Ca from intracellular sites, as resulting from a facilitated influx of unlabelled 40Ca into the islet cells. The occurrence of such a rise in effluent radioactivity and its suppression in the absence of extracellular Ca2+ could only be simulated if the release of Ca by the vacuolar system was assumed to be stimulated by a rise in the cytosolic Ca concentration. It is proposed therefore that, in islets like in muscle, a process of Ca-stimulated Ca release may participate in the regulation of intracellular Ca distribution.     

Mathematical modelling of the mitochondrial apoptosis pathway

Mitochondria are pivotal for cellular bioenergetics, but are also a core component of the cell death machinery. Hypothesis-driven research approaches have greatly advanced our understanding of the role of mitochondria in cell death and cell survival, but traditionally focus on a single gene or specific signalling pathway at a time. Predictions originating from these approaches become limited when signalling pathways show increased complexity and invariably include redundancies, feedback loops, anisotropies or compartmentalisation. By introducing methods from theoretical chemistry, control theory, and biophysics, computational models have provided new quantitative insights into cell decision processes and have led to an increased understanding of the key regulatory principles of apoptosis. In this review, we describe the currently applied modelling approaches, discuss the suitability of different modelling techniques, and evaluate their contribution to the understanding of the mitochondrial apoptosis pathway. This article is part of a Special Issue entitled Mitochondria: the deadly organelle.     

Three-dimensional micro-level computational study of Wolff's law via trabecular bone remodeling in the human proximal femur using design space topology optimization

The law of bone remodeling, commonly referred to as Wolff's Law, asserts that the internal trabecular bone adapts to external loadings, reorienting with the principal stress trajectories to maximize mechanical efficiency creating a naturally optimum structure. The goal of the current study was to utilize an advanced structural optimization algorithm, called design space optimization (DSO), to perform a micro-level three-dimensional finite element bone remodeling simulation on the human proximal femur and analyse the results to determine the validity of Wolff's hypothesis. DSO optimizes the layout of material by iteratively distributing it into the areas of highest loading, while simultaneously changing the design domain to increase computational efficiency. The result is a "fully stressed" structure with minimized compliance and increased stiffness. The large-scale computational simulation utilized a 175 μm mesh resolution and the routine daily loading activities of walking and stair climbing. The resulting anisotropic trabecular architecture was compared to both Wolff's trajectory hypothesis and natural femur samples from literature using a variety of visualization techniques, including radiography and computed tomography (CT). The results qualitatively revealed several anisotropic trabecular regions, that were comparable to the natural human femurs. Quantitatively, the various regional bone volume fractions from the computational results were consistent with quantitative CT analyses. The global strain energy proceeded to become more uniform during optimization; implying increased mechanical efficiency was achieved. The realistic simulated trabecular geometry suggests that the DSO method can accurately predict bone adaptation due to mechanical loading and that the proximal femur is an optimum structure as the Wolff hypothesized.     

Scapulothoracic kinematic pattern in the shoulder pain and scapular dyskinesis: A principal component analysis approach

The relationship between shoulder pain and scapular dyskinesis (SDK) is unclear. Differences between groups with and without SDK have been demonstrated, focusing on the amount of scapular motion at specific degrees of humeral elevation. However, this approach does not consider the temporal information and shape of the scapular motion temporal series. Principal Component Analysis (PCA) may clarify this variability and advance current understanding of ‘abnormal’ movement patterns. This study aimed to evaluate the scapular kinematics in patients with shoulder pain and in asymptomatic participants with and without SDK using PCA. Data were collected in 98 participants separated in four groups: Pain + SDK (n = 24), Pain (n = 25), No Pain + SDK (n = 24), and No Pain (n = 25). Scapulothoracic kinematic data were measured with an electromagnetic tracking device during arm elevation and lowering phases. PCA and analysis of variance were used to compare the groups. The No Pain + SDK group had a progressive increasing in anterior tilt over the elevation phase compared to the Pain (effect size = 0.79) and No Pain (effect size = 0.80) groups. During the arm-lowering, the Pain + SDK group had a progressive increasing in anterior tilt over this phase in comparison to the No Pain + SDK group (effect size = 0.68). Therefore, PCA demonstrated differences in the scapular anterior tilt related to SDK and shoulder pain. The presence of SDK revealed a scapular pattern with progressive increasing in anterior tilt over the elevation phase. However, during the arm-lowering phase, asymptomatic participants with SDK changed their motion pattern, unlike the symptomatic group, reinforcing the suggested association between scapular modifications and shoulder symptoms.     

Mathematical modelling of dynamics and control in metabolic networks. II. Simple dimeric enzymes

The dynamics of enzyme cooperativity are examined by studying a homotropic dimeric enzyme with identical reaction sites, both of which follow irreversible Michaelis-Menten kinetics. The problem is approached via scaling and linearization of the governing mass action kinetic equations. Homotropic interaction between the two sites are found to depend on three dimensionless groups, two for the substrate binding step and one for the chemical transformation. The interaction between the two reaction sites is shown capable of producing dynamic behavior qualitatively different from that of a simple Michaelis-Menten system; when the two sites interact to increase enzymatic activity over that of two independent monomeric enzymes (positive cooperativity) damped oscillatory behavior is possible, and for negative cooperativity in the chemical transformation step a multiplicity of steady states can occur, with one state unstable and leading to runaway behavior. Linear analysis gives significant insight into system dynamics, and their parametric sensitivity, and a way to identify regions of the parameter space where the approximate quasi-stationary and quasi-equilibrium analyses are appropriate.     

Mathematical modelling of mycelia: a question of scale

Recent advances in systems biology have driven many aspects of biological research in a direction heavily weighted towards computational, quantitative and predictive analysis, based on, or assisted by mathematical modelling. In particular, mathematical modelling has played a significant role in the development of our understanding of the growth and function of the fungal mycelium. One of the main problems that faces modellers in this context is the choice of scale. In the study of fungal mycelia, the question of scale is expressed in an extreme manner: Their indeterminate growth habit ensures that the investigation of the growth and function of mycelial fungi has to consider scales ranging from the (sub) micron to the kilometer. An excellent and extensive review of the applications of mathematical modelling to fungal growth, conducted up to the mid-1990s, can be found in Prosser (1995). In this article, we will concentrate on work since that date, with the emphasis being on recent developments in understanding fungal mycelia at all scales.